ASVAB - Arithmetic Reasoning/Mathematics Knowledge

1 Acre = _ ft^2 _ mi^2

43,560 ft^2 0.00156 mi^2

Solve 2/3 a - 5 = 9

A = 21 2/3 a - 5 = 9 (add 5 to both sides) 2/3 a = 14 (multiply the inverse of 2/3 to both sides) 2/3 (3/2) a = 14/1 (3/2) (divide out common factors of 14 and 2) a = 7/1 (3/1) (cross multiply) a = 21

The _ _ is the number that when multiplied by itself equals the original number. For example; the _ _ of 36 is 6, if you square 6 or mulitply it by itself, you produce 36.

Square Root

Changing Decimals to Fractions: Every decimal is really a fraction whose Denominator is a power of ten. Ex: 0.01228 = 1228/100000 Ex: .50 = 50/100 = 1/2 Ex: 6.1 = 61/10

Changing Decimals to Fractions

Changing Improper Fractions into Mixed Numbers: Ex: Change 37/5 to a mixed number. If 37 is divided by 5, the quotient is 7, and the remainder is 2- or, expressed another way, 37/5 = 7 and 2/5.

Changing Fractions

Changing a % to a Decimal: 1) Drop the percent sign and move the decimal point two places to the left. 2) Add extra zeros, if needed, to fill out the correct number of places. If the percent is given as a fraction, first change the fraction to a decimal. Ex: 4% = .04, 55% = .55, 17% = .17, 1.7% = .017, 1/5% = .20% = .002

Changing a % to a Decimal

Changing a % to a Fraction: Drop the percent sign and multiply by 1/100. Ex: 7% is the same as 7 * 1/100 or 7/100 Ex: 25% is the same as 25 * 1/100 or 25/100

Changing a % to a fraction

Changing a Decimal to a %: Move the decimal point two places to the right and add the percent sign. Ex: 0.47 = 47%, 0.008 = .8%, 0.03 = 3%, 3.27 = 327%

Changing a Decimal to a %

Changing Mixed Numbers into Improper Fractions: Ex: Change 8 and 3/5 to an improper fraction. Multiply the whole part of the mixed number by the fraction's denominator, and then add the result to the original numerator. Therefore, 8 and 3/5 = (8*5+3)/5 = 43/5.

Changing fractions

Changing Fractions to Decimals: Divide the Numerator by the Denominator. Place a decimal place to the right of the Numerator, and add a zero for each decimal place you want to show in your answer.

Changing fractions to decimals

What is this? 3.14(r^2)h

Cylinder Volume

The cost of a protein bar increased from $2.50 to $2.80. The percent increase to the $2.80 rate was how much? (a) 16% (b) 10% (c) 15% (d) 12%

D) 12% Find the difference then use that number to divide the original cost $2.50 ÷ $0.30 = 0.12 or 12%

How many square feet of carpeting are needed to carpet a 12-foot × 12-foot room? (a) 24 (b) 120 (c) 48 (d) 144

D) 144 To determine sq. footage, multiply length by width. 12 x 12 = 144

If you roll two six-sided dice, what's the probability of not rolling a five on either die? (a) ¹/₃₆ (b) ¹/₆ (c) ⁴/₃₆ (d) ²⁵/₃₆

D) 25/36 The probability of rolling a 5 is a 1 out of 6 chance, so the probability of NOT rolling a 5 is 5 out of 6. With two die the probability is ⁵/₆ × ⁵/₆ = ²⁵/₃₆

What would an unknown number plus 7 look like?

x + 7

Write: when y is subtracted from x, the result is less than 33

x - y < 33

Write: when x is divided by 5, the result is greater than or equal to the value of z

x / 5 > or = z

Solve x/5 - 4 = 2

x = 30 x/5 - 4 = 2 (add 4 to both sides) x/5 = 6 (multiply 5 to both sides) x = 30

Solve x/3 = 12

x = 36 x/3 = 12 (multiply 3 to both sides) x = 36

Solve 3x = 18

x = 6 3x = 18 (divide both sides by 3 to isolate the variable x) 3x/3 = 18/3 x = 6

Solve 3x + 5 > 8

x > 1 3x + 5 > 8 (subtract 5 from both sides) 3x > 3 (divide 3 from both sides) x > 1

Write: the value of x is greater than 13

x > 13

Solve 5 - 2x > 9

x > 2 5 - 2x > 9 (subtract 5 from both sides) -2x > 4 (divide -2 a negative number to both sides, change sign) x > 2

Write: the value of y is less than 45

y < 45

Solve 7y = 3y - 12

y = -3 7y = 3y - 12 (subtract 3y from both sides to isolate the variable) 7y - 3y = 3y - 3y - 12 4y = - 12 (divide 4 from both sides to isolate the variable) y = -12/4 (odd number of negative sign = negative answer) y = -3

Solve y - 4 = 20

y = 24 y - 4 = 20 (add 20 to both sides of the equation) y -4+4 = 20+4 y = 24

Solve 16 + z = 24

z = 8 16 + z = 24 (subtract 16 from both sides) z = 8

Metric equivalent of 2 pints (pt.)

1 quart (qt.)

7 days = _ week

1 week

12 months = _ year

1 year

365 days = _ year

1 year

52 weeks = _ year

1 year

1 century = _ years _ decades

100 years 10 decades

212'F = _'C and the _ point of water

100'C Boiling

1 dozen =

12

12 less the sum of 3 and some number

12 - (3+x)

1 ft = _ in.

12 in

1 year = _ months _ weeks _ days

12 months 52 weeks 365 days

The product of some number and 12?

12x

A straight line is _ degrees

180

Supplementary angles are two angles that equal _ degrees when added together

180

Evaluate the fraction a + b over 4 + a over b + c, if a = 2 b=6 and c=10

2 1/8 a + b/4 + a/b + c 2 + 6/4 + 2/6 + 10 8/4 + 2/16 (simplify the first fraction) 2 + 2/16 (simplify the second fraction) 2 + 1/8 = 2 1/8

1 ton = _ lbs

2,000

1 Hectacre = _ acres

2.47 acres

1 in. = _ cm. ( metric equiv.)

2.54 cm

What is the reciprocal of 1/2?

2/1 Because 1/2 times 2/1 = 1

100'C = _'F and the _ point of water

212'F Boiling

The fourth root of 16 is:

2x2x2x2

1 yard = _ ft _ in.

3 ft 36 in.

Pi = _

3.14

1 gal = _ L

3.8 L

0' C = _' Fahrenheit and the _ point of water

32' F Freezing

1 leap year = _ days

366 days

1 m. = _ in.

39.37 in

Metric Equivalent of 1 Teaspoon (tsp. or t.)

4.93 milliliters (mL)

Is, was, are, were, amounts to... are all _ clue words.

Division

Share, distribute, ratio, quotient, average, per, out of, percent... are all _ clue words.

Division

If you know the lengths of two sides of a right triangle, you can determine the length of the third side by using the formula a2 + b2 = c2.. aka the _ _

Pythagorean Theorem

A _ equation is one that includes the square of a variable

Quadric

The _ is the difference between the highest number and lowest number in a series when put into order.

Range

A _ is a fixed quantity. A 5% interest rate, for example.

Rate

What formula is this? distance / time

Rate

A _ is a quadrilateral that has exactly two sides that are parallel.

Trapezoid

What is this? A = 1/2(b1+b2)h

Trapezoid Area

4! = __. (a) 4 (b) 16 (c) 24 (d) 256

(c) 24 The exclamation mark indicates a factorial. A factorial is an integer multiplied by every smaller integer, down to the number 1, like this: 4! = 4 x 3 x 2 x 1 = 24

The Circumference of a Circle: _ x (_.__) x R

(2x3.14xR)

The Area of a Circle (_.__) x Radius^2 (_.__ x R^2)

(3.14) x Radius^2 (3.14 x R^2)

Micheal bought 2 1/4 pounds of lumber at $4.00 per pound. If a 7% sales tax was added, how much did Micheal pay? (a) $9.63 (b) $9.98 (c) $10.70 (d) $11.77

(a) $9.63 Since 1 pound of lumber costs $4.00, 2 1/4 pounds of lumber cost 2.25 x $4.00 = $9.00. Then add 7% sales tax to $9.00. Find 7% of $9.00 by multiplying 0.07 x $9.00 = $0.63. Add $0.63 to $9.00 to get $9.63, choice (a).

20 - (-5) = __. (a) -25 (b) 25 (c) 15 (d) -15

(b) 25 Subtracting a negative number is the same as addition, so 20 - (-5) is really 20 + 5 = 25.

Metric equivalent of 2 cups (c.)

1 pint (pt)

An acute angle is more than _ degrees but less than _.

0 90

32'F = _'C and the _ point of water

0'C Freezing

1 Acre = _ Hectacres

0.4 hectacres

1,760 yards = _ mile

1

12 inches = _ ft

1

3 feet = _ yard

1

5,280 ft = _ mile

1

smallest whole unit of digital storage contraction of the words BInary digiT one character of information either a 1 or 0 representing yes/no or true/false

1 Bit

10 Deciliters (dL) = _ Liter

1 L

Metric equivalent of 3 Teaspoons (tsp. or t)

1 Tablespoon (Tbsp or T)

10 milliliters = _ centiliter

1 cL

10 decades = _ century

1 century

10 mmm = _ cm

1 cm

Metric equivalent of 8 fluid ounces. (fl. oz.)

1 cup (c.)

10 centiliters (cL) = _ Deciliter (dL)

1 dL

24 hours = _ day

1 day

10 years = _ decade

1 decade

10 cm = _ decimeters (dm)

1 dm

Metric equivalent of 2 Tablespoons (Tbsp. or T)

1 fluid ounce (fl. oz.)

Metric equivalent of 4 quarts (qt.)

1 gallon (gal.)

60 min. = _ hour

1 hour

10 Hectoliters (hL) = _ Kiloliter (kL)

1 kL

10 dm. = _ meter

1 m

10 centuries = _ millennium

1 millennium

60 sec. = _ minute

1 min

1 Liter ( in smaller metric equivalents ) = ? mL = ? cL = ? dL

1,000 mL 100 cL 10 dL

1 meter = _ mm _ cm _ dm

1,000 mm 100 cm 10 dm

1 kilobyte = _ bytes

1,024 Bytes

What is short for these? 1. K_ = 1,000 2. H_ = 100 3. D_ = 10 4. U_ = 1 5. D_ = .1 (one tenth) 6. C_ = .01 (one one-hundredth) 7. M_ = .001 (one one-thousandth)

1. Kilo 2. Hecto 3. Deca 4. Unit 5. Deci 6. Centi 7. Milli

The cube root of 27 is:

3x3x3

Metric equivalent of 1 gallon ( in smaller english equivalents too ) = ? qt = ? pt = ? c = ? fl. oz. = ? Tbsp = ? tsp

4 quarts 8 pints 16 cups 128 fl. oz. 256. Tbsp 768 tsp.

1 Liter = _ quarts

1.06 qt.

1 knot = _ mph

1.15 mph

1 mi. = _ km _ meters

1.609 km 1,609 meters

The Area of a Triangle is: (_/_B x H)

1/2 Base x Height (1/2B x H)

10 Liters = _ Decaliters (daL)

10 daL

10 Decaliters = _ Hectoliter (hL)

10 hL

1 Hectare = _ meters^2 _ km^2

10,000 meters^2 0.01 km^2

The product of 5 and the sum of x and y?

5 ( x + y )

1 mi. = _ ft _ yards

5,280 ft 1,760 yards

The ratio of 6 and some number?

6 / x

Arcs of a circle and angles are measured in degrees and in minutes or even seconds. 1 degree = ?

60 seconds 60 mins .. 1 min = 60 sec.

What would an unknown number times 6 look like?

6x

What would an unknown number subtracted from 8 look like?

8 - x

1 Byte = _ bits

8 bits

1 Qt = _ L

9.5 L

A Right Angle is _'.

90

A right angle is exactly _ degrees

90

A 2-ton truck is taxed at a rate of $0.12 per pound. How much is the total tax bill? (a) $480 (b) $240 (c) $120 (d) $600

A) $480 2,000 pounds to a ton. 4,000 × .12 = 480

An _ Angle is an angle more than 0' but less than 90'

Acute

Adding Mixed Numbers 1) Add the whole numbers. 2) Add the fractions (find a common denominator if need be). 3) Add the sum of the whole numbers to the sum of the fractions. Ex: 3 and 2/3 + 12 and 2/3 = 15 and 4/3 = 16 and 1/3.

Adding Mixed Numbers

Adding/Subtracting Simple Fractions: 1) Add or subtract fractions with the SAME denominator only. 2) Add or subtract only those fractions Numerators, keeping the same denominator. 3) If the denominators are different, find a common one. Ex: 1/4 + 1/5 + 1/6 = (15+12+10)/60 = 37/60

Adding/Subtracting Simple Fractions

Adding/Subtracting Decimals: Line up the numbers so that the decimal points are directly under one another, then add or subtract in the same way that you would with whole numbers. Write zeros at the end of the decimals to make placeholders and keep them lined up.

Adding/SubtractingDecimals

Sum, total, in all, perimeter, increased by, combined, added.. are all _ clue words

Addition

0, and, when added to any number will result in that number is known as _ identity. Example; 7+0=0.

Additive

_ inverse is the negative of that number. When a number is added to its _ inverse, the answer is 0. For example; 4 + -4 = 0

Additive

When two lines meet at a point they form an _

Angle

_ property is that regrouping numbers being added or multiplied will NOT affect the sum.

Associative

(a+b) + c = a + (b+c) is known as the _ _ for _

Associative Law for Addition

(a x b) x c = a x (b x c) is known as the _ _ for _

Associative Law for Multiplication

Your car uses gasoline at a rate of 21 miles per gallon. If gasoline costs $2.82 per gallon and you drive for 7 hours at a speed of 48 miles per hour, how much will you pay for gasoline for the trip? (a) $38.18 (b) $45.12 (c) $47.73 (d) $59.27

B) $45.12 First determine the miles traveled d = st (7hr × 48mph = 336 miles), then divide by the rate per gallon, 21. So now you know you need 16 gallons at $2.82 per gallon to pay for the trip. 16 × $2.82 = $45.12

Karl is driving in Austria, where the speed limit is posted in kilometers per hour. The car's speedometer shows that he's traveling at a rate of 75 kilometers per hour. Karl knows that a kilometer is about ⁵/₈ of mile. Approximately how many miles per hour is Karl traveling? (a) 47 (b) 120 (c) 50 (d) 53

B) 120 Multiply 75 by 5/8, 375 / 46.8 = 47 mph

A _ is a number that's used as a factor at least two times-it's a number raised to an exponent. For example, the _ of 4^3 is 4.

Base

What is this? l x w x h

Box volume

side x side x side or s^3 is the formula to find the Volume of a _ ?

Cube

What is this? A = 3.14(r)^2

Circle Area

What is this? A = 3.14(d)

Circumference

_ property is that reversing the order of addition or multiplication will NOT affect the sum.

Communative

a + b = b + a is also known as the _ _ for _

Communicative Law for Addition

a x b = b x a is also known as the _ _ for _

Communicative Law for Multiplication

A _ Angle has two angles that have measurements that add up to 90'

Complementary

A _ number is a number that can be divided evenly by itself, 1, and by at least one other whole number. Ex: 4, 6, 10, 15, 27, 82...

Composite

A _ number is a whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers

Composite

A train headed south for Wichita left the station at the same time a train headed north for Des Moines left the same station. The train headed to Wichita traveled 55 miles per hour. The train headed for Des Moines traveled at 70 miles per hour. How many miles apart are the trains at the end of three hours? (a) 210 miles (b) 165 miles (c) 125 miles (d) 375 miles

D) 375 miles D. Distance = speed × time, take the distance traveled by the Wichita train (55mph × 3hr = 165 miles) then add that to the distance traveled by the Des Moines train (70mph × 3hr = 210 miles). The trains are 375 miles apart in 3 hours. Another option: add the two trains mph then multiply by 3 hours (55 + 70) = 125 × 3 = 375 miles

Decimal Fractions: Special fractions whose denominators are powers (multiples) of ten. The Exponent tells you how many zeroes there are in the power of ten. Ex: 10^1 = 10, 10^2= 100, 10^3 = 1,000...

Decimal Fractions

To change a % to a decimal, you must _ the percent sign and move the _ _ two places to the _. Adding zeros as needed.

Decimal Point Left

To change a decimal into a %, you must move the _ _ two spaces to the _ and _ a % sign. For example; 0.6 becomes 60%

Decimal point Right Add

_ is measured as a line passing through the center of a circle, from a point on one side of the circle all the way to a point on the other side of the circle.

Diameter

D = rt is the _ formula

Distance

What formula is this? rate (speed) x time

Distance

a (b+c) = ab + bc is also known as the _ law

Distributive

To figure out your gas mileage, you _ the number of _ by the amount of _.

Divide Miles Gas

To change a fraction to a decimal, you must _ the _ by the _.

Divide the Numerator by the Denominator

Dividing Fractions: To divide with fractions, you have to multiply by the reciprocal. EX: (1/2)/(3) = 1/2 x 1/3 = 1/6

Dividing Fractions

Dividing Decimals by the Powers of 10: Count the number of zeros in the power of 10, then move that many places to the left of the decimal. Ex: 182.7/10^1 = 182.7/10 = 18.27 Ex: .47/10^2 = .47/100 = .0047

Dividing decimals by the powers of 10

An _ is a mathematical statement that contains an equal ( = ) sign.

Equation

An _ triangle has all equal sides

Equilateral

Example : Percent Increase Or Decrease $60 to $39 First, you have to see if its increasing or decreasing. In this case, it is decreasing. Then, you put (Amount of change over original number) 60 - 39 over 60 this = 21/60 than you divide and get .35 which is 35%

Example

Example: Percent Increase Or Decrease 110 to 440 First, you have to see if its increasing or decreasing. In this case, it is increasing.. So you put (Amount of change over the original number) 110+440 over 110 = 330/110= 300%

Example

An _ is a shorthand method of indicating repeated multiplication, for example; 15x15 can also be expressed at 15^2

Exponent

A _ is represented by an (!), you calculate a _ by finding the product of (multiplying) a whole number and all the whole numbers less than it down to 1, so 6 _ is 6x5x4x3x2x1

Factorial

_ are whole numbers

Factors

Greatest Common Factor (GCF): Break down both integers into their prime factorizations and multiply all prime factors they have in common

GCF

How to solve an equation for the unknown. keeping the equation balanced by doing the same operation of numbers on both sides to isolate variables on one side when adding or subtracting from one side cancel it out on that side then move the number to the other side of the equation and change its sign. multiplying or dividing by the same number on both sides works the same way

How to solve an equation for the unknown.

A _ triangle is the side opposite the right angle which is the longest side of a right triangle.

Hypotenuse

a x 1 = a is also known as the _ law for multiplication

Identity Law For Multiplication

a + 0 = a is also known as the _ law for _

Identity Law for Addition

_ are statements that show certain relationships between selected variables and numbers are not equal ( ≠ ), greater than ( > ), less than ( < ), greater than or equal to ( ≥ ), and less than or equal to ( ≤ )

Inequalities

_ are whole numbers, including 0 and negative whole numbers.

Integers

_ numbers are whole numbers that have square roots that are decimals that go on forever and have no pattern that repeats.

Irrational

The _ is the middle number is a series of numbers when placed in order.

Median

The _ is when you add all the numbers in a series of numbers than divide by the amount of numbers in that series.

Mean

The _ is the number that appears the most in a series of numbers.

Mode

A _ is a number that a given number will divide into with no remainder

Multiple

Product also means:

Multiplication

Product, total, area, cubic, times, multiplied by, of... are all _ clue words.

Multiplication

1, and when multiplied by any number, will result in that number is also known as the _ identity.

Multiplicative

_ inverse is the reciprocal of that number (one divided by that number). When a number is multiplied by is _ inverse, the answer is 1

Multiplicative

Dividing a fraction is the same thing as _ it by the _ of that number.

Multiplying Inverse

Multiplying Mixed Numbers: When multiplying or dividing a Mixed Number, change the mixed number to an Improper Fraction before working the problem. Ex: 2 and 2/3 5/7 = 8/3 5/7 = 40/21 = 1 and 19/21

Multiplying Mixed Numbers

How to Multiply Fractions: For two or more fractions, multiply the numerators by each other, and multiply the denominators by each other.

Multiplying fractions

The ≠ symbol means _ _ _

Not equal to

An _ Angle is an angle that is more than 90' but less than 180'

Obtuse

A _ is a quadrilateral that has opposite sides that are parallel, and their opposite sides and angles are equal. The sides don't have to be right angles.

Parallelogram

PEMDAS is an order of operations that stands for:

Parenthesis Exponents Division Addition Subtraction

_ lines are lines that are equidistant from each other at every point along both lines so that even if they were infinitely long, they would never touch.

Parrallel

_ lines are lines that meet to form a right angle (90')

Perpendicular

A _ is made up of 3 or more lines that are connected so that an area is enclosed.

Polygon

A _ number is a number that can be divided evenly by itself and 1, but not by any other whole number.. Ex: 1, 2, 3, 5, 7, 11, 13...

Prime

A _ number is a whole number that can be divided evenly by itself and by 1 but not by any other number

Prime

When you divide, you are left with a _

Quotient

A _ is a quadrilateral that has four sides of equal length, but the angles don't have to be right angles.

Rhombus

_ is limiting a number to fewer decimal places

Rounding

A _ triangle is one in which all 3 sides and all 3 angles are UNEQUAL

Scalene

I = Prt Where I = the amount of interest, P = the initial amount invested, r = interest rate, and t = the length of time the money is invested. This is called the _ _ formula.

Simple interest

Difference also means:

Subtraction

Difference, how much more, exceed, less than, fewer than, decreased... are all _ clue words.

Subtraction

A _ Angle is an angle whose measurements add up to 180' ( a straight line )

Supplementary

The _ is the point where the lines meet of the angle

Vertex

_ is the space a solid shape takes up, measured in cubic units.

Volume

The Area of a Square is:

the length of one side squared (L^2)

The Area of a Rectangle is _ x _ ( _ x _ )

length x width ( l x w )

Prime Factorization: Keep breaking it down until you are left with only prime numbers. Ex: 168=2x2x2x3x7

prime factorization

A circle always is _ degrees

360

Quadrilaterals are shapes with four sides whose angles total _ degrees.

360

Express 403,000,000,000,000 in scientific notation.

4.03 x 10^14

Quotient also means:

Division

What would an unknown number less than 12 look like?

x - 12

Some number divided by 4?

x / 4

Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his backpack. If he pulls out one pen at random from his backpack, what is the probability that the pen is either red or black? (a) 2/3 (b) 3/5 (c) 2/5 (d) 1/3

(a) 2/3 To find probability, determine the number of desired outcomes and divide that by the number of possible outcomes. The probability formula looks like this: Probability = # of desired outcomes/# of possible outcomes In this case, Marty is pulling one pen at random from his knapsack, and you want to determine the probability that the pen is either red or black. There are 5 blue pens, 6 black pens, and 4 red pens in the knapsack. Let's return to the probability formula: Probability = # of desired outcomes/ # of possible outcomes = number of red + black pens/number of red+ black + blue pens = 4 + 6/ 4+6+5 = 10/15=2/3

If 50% of (x) is 150, what is 75% of (x)? (a) 225 (b) 250 (c) 275 (d) 300

(a) 225 The calculations aren't too bad on this one. The most important thing to keep in mind is that you're solving for 75% of (x) and not for (x) itself. First, you are told that 50% of (x) is 150. That means that half of (x) is 150, and that (x) is 300. So 75% of (x) = 0.75 x 300 = 225.

If a car travels 1/100 of a kilometer each second, how many kilometers does it travel in an hour? (a) 36 (b) 60 (c) 72 (d) 100

(a) 36 Find the number of seconds in an hour and then multiply this by the distance the car is traveling each second. There are 60 seconds in a minute and 60 minute in one hour; therefore, there are 60 x 60, or 3,600, seconds in an hour. In one second the car travels 1/100 kilometers; in one hour the car will travel 3,600 x 1/100 or 36 kilometers.

A painter charges $12 an hour while his son charges $6 an hour. If the father and son worked the same amount of time together on a job, how many hours did each of them work if their combined charge for their labor was $108? (a) 6 (b) 9 (c) 12 (d) 18

(a) 6 When the painter and his son work together, they charge the sum of their hourly rates, $12 + $6, or $18 per hour. Their bill equals the product of this combined rate and the number of hours they worked, Therefore $108 must equal $18 per hour times the number of hours they worked. Divide $108 by $18 per hour to find the number of hours. $108 / $18 = 6.

A 25 ounce solution is 20% alcohol. If 50 ounces of water are added to it, what percent of the new solution is alcohol? (a) 6 2/3 % (b) 7 1/2 % (c) 10% (d) 13 1/3%

(a) 6 2/3% You're asked what percent of the new solution is alcohol. The (part) is the number of ounces of alcohol; the (whole) is the total number of ounces of the new solution. There were 25 ounces originally. Then 50 ounces were added, so there are 75 ounces of new solution. How many ounces are alcohol? 20% of the original 25-ounces solution was alcohol. 20% is 1/5, so 1/5 of 25, or 5 ounces are alcohol. Now you can find the percent of alcohol in the new solution: % alcohol = alcohol/total solution x 100% = 5/75 x 100% = 20/3% = 6 2/3%

At garage (A), it cost $8.75 to park a car for the first hour and $1.25 for each additional hour. At garage (B), it costs $5.50 to park a car for the first hour and $2.50 for each additional hour. What is the difference between the cost of parking a car for 5 hours at garage (A) and parking it for the same length of time at garage (B)? (a) $2.25 (b) $1.75 (c) $1.50 (d) $1.25

(b) $1.75 Compute the cost of parking a car for 5 hours at each garage. Since the two garages have a split-rate system of charging, the cost for the first hour is different from the cost of each remaining hour. The first hour at garage (A) costs $8.75 The next 4 hours cost 4 x $1.25 = $5.00 The total cost for parking at garage (A) = $8.75 + 5.00 = $13.75 The first hour at garage (B) costs $5.50 The next 4 hours cost 4 x $2.50 = $10.00 The total cost for parking at garage (B) = $5.50 + $10.00 = $15.50 So the difference in cost = $15.50 - $13.75 = $1.75, (B).

Six pizzas are pepperoni, seven are hamburger, four are cheese, and three are "with everything". What's the probability that a randomly selected pizza is pepperoni?

1/4. There are 6 + 7 + 4 + 3 = 20 pizzas total. So the probability is 6/20, which is 1/4.

Stan bought a monster truck for a $2,000 down payment and $450 a month for five years. What's the total cost of the monster truck? (a) $4,250 (b) $29,000 (c) $27,000 (d) $34,000

B) $29,000 Five years contains 60 months, $450 payments at 60 months = $27,000. Now add the down payment, $27,000 + $2,000 = $29,000

Sum also means:

Addition

June's weekly salary is $70 less than Kelly's, which is $50 more than Eileen's. If Eileen earns $280 per week, how much does June earn per week? (a) $160 (b) $260 (c) $280 (d) $300

(b) $260 You're told that Eileen earns $2800 per week. Kelly earns $50 more Than Eileen, so Kelly earns $280 + $50 = $330 per week. June's salary is $70 less than Kelly's, so June earns $330 - $70 = $260 per week, and (b) is correct.

A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in one hour? (a) 15 (b) 18 (c) 20 (d) 30

(b) 18 First, set up the rate as a proportion, where (x) is the number of stations. 3 stations/10 minutes = (x) stations/1 hour Then, convert the units. 3 stations/10 minutes = (x) stations/60 minutes Cross multiply and solve for (x). 180 = 10(x) 18 = (x)

On a certain map, 3/4 inch represents one mile. What distance, in miles, is presented by 1 3/4 inches? (a) 1 1/2 (b) 2 1/3 (c) 2 1/2 (d) 5 1/4

(b) 2 1/3 In this question, the ratio is implied: for every 3/4 inch of map there is 1 real mile, so the ratio of inches to the miles they represent is always 3/4 to 1. Therefore, you can set up the proportion: number of inches/ number of miles = 3/4 / 1 = 3/4 Now 1 3/4 inches = 7/4 inches. Set up a proportion: 7/4 inches 7/4 inches / number of miles = 3/4 Cross-multiply: 7/4(4) = 3 (number of miles) 7= 3(number of miles) 7/3 = number of miles or 2 1/3 = number of miles

A student finishes the first half of an exam in 2/3 the time it takes him to finish the second half. If the entire exam takes him an hour, how many minutes does he spend on the first half of the exam? (a) 20 (b) s4 (c) 27 (d) 36

(b) 24 The time it takes to complete the entire exam is the sum of the time spent on the first half of the exam and the time spent on the second half. The time spent on the first half is 2/3 of the time spent on he second half. If (S) represents the time spent on the second half, then the total time spent is 2/3(S) + (S) or 5/3 (S). You know this total time is one hour, or 60 minutes. Set up a simple equation and solve for (S). 5/3(S) = 60 3/5 x 5/3(S) = 3/5 x 60 (S) = 36 So the second half takes 36 minutes. The first half takes 2/3 of this, or 24 minutes. You could also find the first half by subtracting 36 minutes from the total time, 60 minutes.

If a man earns $200 for his first 40 hours of work in a week and then is paid one-and-one-half times his regular rate for any additional hours, how many hours must be work to make $230 in a week? (a) 43 (b) 44 (c) 45 (d)46

(b) 44 To learn the man's overtime rate of pay, first figure out his regular rate of pay. Divide the amount of money made, $200, by the time it took to make it, 40 hours. $200 / 40 hours = $5 per hour. That is the normal rate. The man is paid 1 1/2 times his regular rate during overtime, so when working more than 40 hours he makes 3/2 x $5 per hour = $7.50 per hour. Now figure out how long it takes the man to make $230. It takes him 40 hours to make the first $200. The last $30 are made at the overtime rate. Since it takes the man one hour to make $7.50 at this rate, you can figure out the number of extra hours by dividing $30 by $7.50 per hour. $30 / $7.50 per hour = 4 hours. The total time needed is 40 hours plus 4 hours, or 44 hours.

John bought a camera on sale that normally costs $160. If the price was reduced 20% during the sale, what was the sale price of the camera? (a) $120 (b) $124 (c) $128 (d) $140

(c) $128 This question asks you to determine the sale price of a camera that normally sells at $160 and is discounted 20%. To solve, determine what 20% of $160 equals. Rewrite 20% as a decimal. 20% = 0.20. So 20% of $160 = 0.20 x $160 = $32. The sale price of the camera would be $160 - $32 = $128, choice (c)

Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon of gasoline and gasoline cost $1.25 per gallon, what was the cost in dollars of the gasoline for the trip? (a) $20.00 (b) $ 24.00 (c) $ 25.00 (d) $40.00

(c) $25.00 If Ms. Smith's car average 35 miles per gallon, she can go 35 miles on 1 gallon. To go 700 miles she will need 700/35, or 20 gallons of gasoline. The price of gasoline was $1.25 per gallon, so she spent 20 x $1.25, or $25, for her trip.

After spending 5/12 of his salary, a man has $420 left. What is his salary? (a) $175 (b) $245 (c) $720 (d) $1,008

(c) $720 You can save valuable time by estimating on this one. Pay special attention to how much you have left and how much you've already spent. If a man spent 5/12 of his salary and was left with $420, that means that he had 7/12 left, and if the man's salary is (x) dollars, then 7/12(x) = $420 That means that $420 is a little more than half of his salary. So his salary would be little less than 2($420) = $840. Choice (c), $720 is a little less than $840. So (c) works perfectly, and it's the correct answer here.

Joan can shovel a certain driveway in 50 minutes. If Mary can shovel the same driveway in 20 minutes, how long will it take them, to the nearest minute, to shovel the driveway if they work together? (a) 12 (b) 13 (c) 14 (d) 15

(c) 14 This is a combined work problem. Joan can shovel the whole driveway in 50 minutes, so each minute she does 1/50 of the driveway. Mary can shovel the whole driveway in 20 minutes: each minute she does 1/20 of the driveway. In one minute they do: 1/50 + 1/20 + = 2/100 + 5/100 = 7/100 If they do 7/100 of the driveway in one minute, they do the entire driveway in 100/7 minutes. (If you do 1/2 of a job in 1 minute, you do the whole job in the reciprocal of 1/2, or 2 minutes.) So all that remains is to round 100/7 off to the nearest integer. Since 100/7= 14 2/7, 100/7 is approximately 14. It takes about 14 minutes for both of them to shovel the driveway.

What is the prime factorization of 140? (a) 2 x 70 (b) 2 x 3 x 5 x 7 (c) 2 x 2 x 5 x 7 (d) 2 x 2 x 2 x 5 x 7

(c) 2 x 2 x 5 x 7 To find the prime factorization of a number, find one prime that will go into the number (here 2 is a good place to start). Express the number as that prime multiplied by some other number. 140 = 2 x 70 Then keep breaking down the larger factor until you are left with only prime numbers. 140 = 2 x 2 x 35 140 = 2 x 2 x 5 x 7

A stock decreases in value by 20%. By what percent must the stock price increase to reach its former value? (a) 15% (b) 20% (c) 25% (d) 40%

(c) 25% They key to this question is that while the value of the stock decreases and increases by the same amount, it doesn't decrease and increase by the same percent. When the stock first decreases, the amount of changes is part of a larger whole. If the stock were to increase to its former value, that same amount of change would be a larger percent of a smaller whole. Pick a number for the original value of the stock, such as $100. (Since it's easy to take percents of 100, it's usually best to choose 100.) The 20% decrease represents $20, so the stock decreases to a value of $80. Now in order for the stock to reach the value of $100 again, there must be a $20 increase. What percent of $80 is $20? It's $20/$80 x 100%, or 1/4 x 100%, or 25%.

Jan types at an average rate of 12 pages per hour. At that rate, how long will it take Jan to type 100 pages? (a) 8 hours and 10 minutes (b) 8 hours and 15 minutes (c) 8 hours and 20 minutes (d) 8 hours and 30 minutes

(c) 8 hours and 20 minutes Set up a proportion: 12 pages/1 hour = 100 pages/ (x) hours 12(x) = 100 (x) = 100/12 = 8 1/3 An hour is 60 minutes; one third of that is 20 minutes. So 8 1/3 hours is 8 hours and 20 minutes.

Four people shared a taxi to the airport. The fare was $36.00, and they gave the driver a tip equal to 25% of the fare. If they equally shared the cost of the fare and tip, how much did each person pay? (a) $9.75 (b) $10.25 (c) $10.75 (d) $11.25

(d) $11.25 The total cost of the taxi ride equals $36 + (25% of $36), or $36 + (.25 x $36) = $36 + $9 = $45. If four people split the cost equally, then each person paid $45/4, or $11.25 each.

The total fare for two adults and three children on an excursion boat is $14. If each child's fare is one half of each adult's fare, what is the adult fare? (a) $2.00 (b) $3.00 (c) $3.50 (d) $4.00

(d) $4.00 This question where Backsolving (plugging in an answer choice to see if it's correct) can save you a lot of time. Let's start with choice (b) and see if it works. If (b) is correct, an adult's ticket would cost $3.00, and a child's ticket would cost $1.50. The total fare you're asked for is for two adults and three children. If an adult's fare was $3.00, that total fare would be 2($3.00) + 3($1.50) = $6.00 + $4.50 = $10.50. That's too low since the question states that the total fare is $14.00. Now see what happens if an adult fare was more expensive. If (d) was correct, an adult's ticket would cost $4.00 and a child's ticket would cost $2.00. The total fare would equal 2($4.00) + 3($2.00) = $8.00 + $6.00 = $14.00. That's the total fare you're looking for, so (d) is correct.

The ratio of 3 1/4 t0 5 1/4 is equivalent to the ratio of __. (a) 3 to 5 (b) 4 to 7 (c) 8 to 13 (d) 13 to 21

(d) 13 to 21 The question asks which of five ratios is equivalent to the ratio of 3 1/4 to 5 1/4. Since the ratios in the answer choices are expressed in whole numbers, turn this ratio into whole numbers. Start by turning the ratio into improper fractions: 3 1/4 : 2 1/4 = 13/4: 21/4 Multiply both sides of the ratio by 4. = 13:21

Two large sodas contain the same amount as three medium sodas. Two medium sodas contain the same amount as three small sodas. How many small sodas contain the same amount as eight large sodas? (a) 24 (b) 18 (c) 16 (d) 12

(d) 18 This problem sets up relationships among large, medium, and small sodas - 2 large sodas are equal to 3 medium sodas, and 2 medium sodas are equal to 3 small sodas. How many small sodas equal 8 large sodas? Well, 2 larges equal 3 mediums, so 12 mediums must equal 4 x 2 or 8 large sodas. You now can find how many small sodas represent 12 mediums. Since 2 mediums are the same as 3 small sodas, 12 mediums must equal 6 x 3 or 18 small sodas.

A cat is fed 3/8 of a pound of cat food every day. For how many days will 72 pounds of this cat food feed the cat? (a) 160 (b) 172 (c) 180 (d) 192

(d) 192 Set up the proportion. 3/8 lb / 1 day = 72 lbs / (x) days Cross multiply. 3/8 (x) = 72 (x) = 72 x 8/3 (x) = 192

If each digit 5 in the number 258,546 is replaced with the digit 7, by how much will the number be increased? (a) 2,020 (b) 2,200 (c) 20,020 (d) 20,200

(d) 20,200 If you change each digit 5 into a 7 in the number 258,546, the new number would be 278,746. The difference between these two numbers would be 278,746 - 258,546 = 20,200.

From 1980 through 1990, the population of Country X increased by 100%. From 1990 to 2000, he population increased by 50%. What was the continued increase for the period 1980-2000? (a) 150% (b) 166 2/3% (c) 175% (d) 200%

(d) 200% Be careful with combined percent increase. You cannot just add the two percents, because they're percents of different bases. In this instance, the 100% increase is based on the 1980 population, but the 50% increase is based on the larger 1990 population. If you just added 100% and 50% to get 150%, you would have chosen the wrong answer. The best way to do a problem like this one is to pick a number for the original whole and just see what happens. The best number to pick here is 100. (That may be a small number for the population of a country, but reality is not important - all that matters is the math.) If the 1990 population was 100, then a 100% increase would put the 1990 population at 200. And a 50% increase over 200 would be 200 + 100 = 300. Since the population went from 100 to 300, that's a percent increase of 200%. 300 - 100/100 x 100% = 200/100 X 100% = 200%

A certain box contains baseballs and golf balls. If the ratio of baseballs to golf balls is 2:3 and there are 30 baseballs in the box, how many golf balls are in the box? (a) 18 (b) 20 (c) 36 (d) 45

(d) 45 You can express the ratio of baseballs to golf balls as 2/3. Since you know the number of baseballs, you can set up a proportion: 2/3 = 30/ (x) where (x) is the number of golf balls. To solve, cross-multiply to get 2(x) = 90, or x = 45.

After eating 25% of the jelly beans, Brett had 72 left. How many jelly beans did Brett have originally? (a) 90 (b) 94 (c) 95 (d) 96

(d) 96 Be careful with a question like this one. You're given the percent decrease (25%) and the new number (72), and you're asked to reconstruct the original number. Don't just take 25% of 72 and add it on. That 25% is based not on the new number, 72, but on the original number - the number you're looking for. The best way to do a problem like this is to set up an equation: (original number) - (25% of original number) = new number (x) - 0.25(x) = 72 0.75x = 72 x = 96 Alternatively, you can use the answer choices to determine the correct answer. The original number of jelly beans has to be reducible by 25%, or 1/4. That means the original number of jelly beans has to be a multiple of 4 (or else you'd be reducing by pieces of jelly beans). Only the correct answer, 96, is a multiple of 4.

Evaluate 2x^2 + 4y + 5, if x = 2 and y = 3

25 2 (2)^2 + 4 (3) + 5 2 (4) + 12 + 5 8 + 12 + 5 = 25

Which of the following fractions is the largest? 2/3 , 5/8, 11/16 or 3/4?

3/4 Find a common denominator for the fractions - which is 48 2/3 > 32/48, 5/8 > 30/48, 11/16 > 33/48, 3/4 > 36/48 The largest numerator is the largest fractions, which is 3/4.

What is the square root of 54?

7.3 (to the nearest tenth) You know 7x7 = 49, 8x8= 64 Closer to 49, so try 7.3 x 7.3 = 53.29 ... 7.4 x 7.4 = 54.76 53.29 is closer

Evaluate a + b + c, if a = 2, b = 4, and c = 3.

9 a + b + c 2 + 4 + 3 = 9

Complementary angles are two angles that equal _ degrees when added together.

90

9 times some number plus the sum of 5 and y

9x + (5+y)

Kiya had only one coupon for 10% off one frozen turkey breast. The turkey breast costs $8.50 each, and Kiya wanted to buy two. How much did she pay? (a) $16.15 (b) $17.00 (c) $15.30 (d) $7.65

A) $16.15 First find the discounted turkey's price ($8.50 × .10 = $0.85, $8.50 - $0.85 = $7.35) then add another $8.50 because she needs two turkey breast. $7.35 + $8.50 = $16.15

A carpenter earns $12.30 an hour for a 40-hour week. His overtime pay is 1¹/₂ times his base pay. If he puts in a 46-hour week, how much is his weekly pay? (a) $602.70 (b) $492.00 (c) $565.80 (d) $110.70

A) $602.70 You need to add the carpenters base pay and overtime to find his total pay for the week. First find his base pay per week: $12.30 × 40hrs = $492. Then find his overtime rate per hour, which is 1¹/₂ time the base pay: $12.30 × 1.5 = $18.45. Multiply this rate by the number of hours of overtime to find his overtime pay: $18.45 × 6 hr. = $110.70. Finally add the base pay and overtime to find the total for the week, $492 + $110.7 = $602.70

Miriam bought five cases of motor oil on sale. A case of motor oil normally costs $24.00, but she was able to purchase the oil for $22.50 a case. How much money did Miriam save on her entire purchase? (a) $7.50 (b) $1.50 (c) $8.00 (d) $22.50

A) $7.50 Subtract the sale price from the original price, $24.00 - $22.50 = $1.50. Now, multiply that number by the amunt of cases to get the final answer. $1.50 x 5 = $7.50.

A carpenter needs to cut four sections, each 3 feet, 8 inches long, from a piece of molding. If the board is only sold by the foot, what's the shortest length of board she can buy? (a) 15 feet (b) 14 feet (c) 16 feet (d) 12 feet

A) 15 feet Each section is 3²/₃ feet, times that by four and you get 14²/₃ so 15 is the shortest board possible.

The sum of two numbers is 70. One number is 8 more than the other. What's the smaller number? (a) 31 (b) 33 (c) 35 (d) 36

A) 31 x + x + 8 = 70, solve for x. x = 31

An office building has 30 employees and provides 42 square feet of work space per employee. If five more employees are hired, how much less work space will each employee have? (a) 6 square feet (b) 7 square feet (c) 7.5 square feet (d) 36 square feet

A) 6 square feet First find the area of the office, 42 ft. × 30 = 1260 sq ft. Then divide the space by 35 employees, each employee now has 36 sq ft of workspace, which is 6 feet less than originally.

As a member of FEMA, you're required to set up a contingency plan to supply meals to residents of a town devastated by a tornado. A breakfast ration weights 12 ounces and the lunch and dinner rations weight 18 ounces each. Assuming a food truck can carry 3 tons and that each resident will receive 3 meals per day, how many residents can you feed from one truck during a 10-day period? (a) 150 residents (b) 200 residents (c) 250 residents (d) 300 residents

B) 200 Residents First find how many ounces each truck can hold. 2,000lb. are in a ton, so each truck can carry three times that 6,000lb. There are 16 ounces to a pound so one truck can carry 96,000 ounces ( 16oz. × 6,000lb.). Now find the daily total for each persons three meals 12oz + 18oz + 18oz = 48oz. Now 96,000 × 48 = 2,000 daily rations. This rations need to last 10 days (2,000 ÷ 10 = 200) So 200 residents can be fed by one truck for 10 days.

The population of Grand Island, Nebraska, grew by 600,000 people between 1995 and 2005, one-fifth more than the town council predicted. The town originally predicted the city;s population to grow by (a) 400,000 (b) 500,000 (c) 300,000 (d) 100,000

B) 500,000 Let x = the original number predicted. An ¹/₅ would make the population growth ⁶/₅ or 120%, of x. Express the equation as 1.2x = 600,000, solve for x. x = 500,000.

Jenny's test grades are 93,89, 96, and 98. If she wishes to raise her average to 95, what does she need to score on her next test? (a) 100 (b) 99 (c) 97 (d) 95

B) 99 x = the unknown score. (93 + 89 + 96 + 98 + x) / 5 or (376 + x) / 5. Now solve for x. x= 99

MIchael needs 55 gallons if paint to paint an apartment building. He would like to purchase the paint for the least amount money possible. Which of the following should he buy? (a) two 25-gallon buckets at $550 each (b) eleven 5-gallon buckets at $108 each (c) six at 10-gallon buckets at $215 each (d) fifty-five 1-gallon bucket at $23 each

B) Eleven 5-gallon buckets at $108 each Choice (a) doesn't have enough paint (2 ×25 gal = 50 gal) so it's wrong. Choice (b): 11 × $108 = $1,188 Choice (c): 6 × $215 = $1,290 Choice (d): 55 × $23 = $1265

Jack loaned Bob $1,500 at an annual interest rate of 7%. After one year, how much will Bob owe Jack? (a) $105 (b) $1,500 (c) $1,605 (d) $1,507

C) $1,605 First find interest then add to the loan. $1,500 × 0.07 = 106, $106 + $1,500 = 1,605

If a car is towed 12 miles to the repair shop and the tow charge is $3.50 per mile, how much does the tow cost? (a) $12.00 (b) $3.50 (c) $42.00 (d) $100.00

C) $42.00 Multiply 12 miles by $3.50 per mile. 12 x $3.50 = $42.00

Joe received an hourly wage of $8.15. His boss gave him a 7% raise. How much does Joe make per hour now? (a) $0.57 (b) $8.90 (c) $8.72 (d) $13.85

C) $8.72 To calculate the new wage first multiply $8.15 x 0.07 = $0.57. Then add that to the original wage, $8.15 + $0.57 = $8.72

A half-pint of cream is what part of a gallon? (a) ¹/₈ (b) ¹/₄ (c) ¹/₁₆ (d) ¹/₆

C) 1/16 2 pints in a quart, 4 quarts to a gallon. Therefore 8 pints are to a gallon or 16 half-pints, ¹/₁₆.

A security guard walks the equivalent of six city blocks when he makes a circuit around the building. If he walks at a pace of eight city blocks every 30 minutes, how long will it take him to complete a circuit around the building, assuming he doesn't run into any thieves? (a) 20.00 minutes (b) 3.75 minutes (c) 22.50 minutes (d) 7.5 minutes

C) 22.50 minutes Divide 30 by 8 to determine how long it takes to walk one city block = 3.75 minutes. Then, multiply by 6, the number it takes to complete the circuit.

If ab = 10 and a² + b² = 30, solve for y in the equation y = (a+b)². (a) 40 (b) 45 (c) 50 (d) 55

C) 50 First expand the equation (a+b)² or (a+b)(a=b) into y = a² + b² +2ab. You already know ab = 10 and a² + b² = 30, so substitute the known values and solve for y. 30 + 2(10) = 50

Alice leaves her house, driving east at 45 miles per hour (mph). Thirty minutes later her husband Dave notices she forgot her cell phone and sets off after her. How fast must Dave travel in order to catch up with Alice 3 hours after he leaves? (a) 49 mph (b) 50.5 mph (c) 52.5 mph (d) 54 mph

C) 52.5 mph Distance = speed x time. First, find how far Alice had traveled 31/2 hours at 45 mph, or 157.5 mph. Dave has three hours to cover this distance. Now find his speed. 157.5 mi / 3 hr = 52.5 mph.

An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m., the plane passes over Sea Side Naval Air Station, 120 miles away. How fast is the aircraft traveling? (a) 400 mph (b) 500 mph (c) 600 mph (d) 700 mph

C) 600 mph The plane traveled 120 miles in 12 minutes or ¹/₅ of an hour. d=st, 120 = ¹/₅x or 120 × 5 = 600 mph

Solve: A baker has S lbs of sugar to use in baking. After she uses 50 lbs to make donuts, how much sugar does she have left? A) s + 50 B) 50 - 2 C) s - 50 D) s / 50

C) S - 50

A sales manager buys antacid in bottles the gross. If he goes through 3 bottles antacid everyday, how long will the gross last? (a) 144 days (b) 3 days (c) 20 days (d) 48 days

D) 144 days 144 bottles in a gross, and 144 / 3 (bottles per day) = 48 days

an _ is a positive, negative, or zero whole number.

Integer

An _ triangle has two equal sides

Isosceles

A _ is a letter that represents a number and can change in value.

Variable

What would an unknown number divided by 5 or the ratio of the unknown number and 5 look like?

x / 5

Solve for x: If the scale on a road map is 1 inch = 250 miles, how many inches would represent 1,250 miles?

x = 5, 5 inches = 1,250 miles. 1 inch = 250 miles, x = 1250 miles. The problem can be expressed as two ratios set equal to each other, known as proportion: 1/250 = x/1250