Hesi A2 Math Practice (test)
How many grams for 1 mg?
0.001 grams
How many grams in 1 mg? use decimal
0.001 grams
How many kg in 1 gram? use decimal
0.001 kg
0.0068
0.002 x 3.4 = _______.
How many lbs for 1 oz?
0.0625 lbs
1 lb is how many kilograms?
0.45 kilogram
1 milliliter = ____ cubic centimeter
1
Roman Numeral I = ____
1
l
1
4 1/20
1 1/4 + 2 8/10 = _______.
How many cubic centimeter in 1 ml?
1 cubic centimeter
How many cups for 8 oz?
1 cup
1 foot is how many centimeters?
1 foot = 12 inch 1 inch = 2.54 centimeters Therefore, 1 foot = 12 x 2.54 = 30.48 centimeters
How many gallons in 128 oz?
1 g
How many gallons for 4 quarts?
1 gallon
How many grams in 0.001 kg?
1 gram
How many grams in 1,000 mg?
1 gram
How many kg for 1,000 grams?
1 kg
1,000
1 kilometer = _______ meters.
How many lbs for 16 oz?
1 lb
How many liters in 1,000 ml?
1 liter
1,000
1 liter = _______ milliliters.
How many mg for 0.001 grams?
1 mg
How many mg for 1/1000 grams?
1 mg
1,760
1 mile = _______ yards.
How many ml in 1 cubic centimeter?
1 ml
How many ounce in 28 grams?
1 ounce
30
1 ounce = _______ milliliters.
How many ounce for 30 milliliters?
1 oz
How many oz for 0.0625 lbs?
1 oz
How many pints for 2 cups?
1 pint
16
1 pound = _______ ounces.
How many quarts in 32 oz?
1 qt
How many quarts for 2 pints?
1 quart
Instructions require you to dilute a powder in 3 quarts of water. You only have a container that is marked in liters. How many liters would you use to dilute the powder?
1 quart = 32 oz 3 quarts = 96 oz There are 30 milliliters per oz, so 96 oz = 2,880 milliliters There are 1000 milliliters per liter, so 2,880 mL = 2.88 liters
2
1 quart = _______ pints.
2,000
1 ton = _______ pounds.
3
1 yard = _______ feet.
How many grams for 1 kg?
1,000 grams
How many mg in 1 gram?
1,000 mg
How many ml for 1 liter?
1,000 milliliters
How many milliliters in 1 liter?
1,000 ml
How many centimeters are in millimeter?
1/10 centimeters
How many grams in 1 mg? use fraction
1/1000 grams
8/6
1/2 / 3/8 = _______.
9/10
1/5 + 7/10 = _______.
Roman Numeral X = ____
10
X
10
How many millimeters are in a centimeter?
10 millimeters
1 meter = ____ centimeters
100
C
100
Roman Numeral C = ____
100
How many centimeters are in a meter?
100 centimeters
1 gram = ____ milligrams
1000
1 kilogram = ____ grams
1000
1 kilometer = ____ meters
1000
1 liter = ____ milliliters
1000
M
1000
Roman Numeral M = ____
1000
1 kilogram is how many grams?
1000 grams
How many grams are in a kilogram?
1000 grams
How many meters in a kilometer?
1000 meters
How many milliliters are in 1 liter?
1000 ml
Xl
11
1 foot = ____ inches
12
1 gallon = ____ ounces
128
How many ounces in 1 gallon?
128 oz
115
13 x 5 _______.
A survey company must contact 136 people via phone calls. How many buttons must be pushed to make the 136 long distance calls?
136 x 10= 1360 buttons
1 pint = ____ ounces
16
1 pound = ____ ounces
16
How many oz for 1 lb?
16 oz
1 mile = ____ yards
1760
1 pint = ____ cups
2
1 quart = ____ pints
2
ll
2
How many cups for 1 pint?
2 cups
A car dealer offers 10 different brands of cars for sale. The average daily sales for the dealer are: Honda - 2 models, sells 20 of each model per day Toyota - 3 models, sells 15 of each model per day Kia - 1 model, sells 7 each day Ford - 4 models, sells 6 of each model per day How many total cars are sold per day?
2 hondas x 20 cars = 40 3 toyotas x 15 cars = 45 1 kia x 7 cars = 7 4 fords x 6 cars=24 40+45+7+24=116 cars
How many pints for 1 quart?
2 pints
A patient on a clear diet consumes the following for the day: 2 pints of water 1 8 oz. serving of clear soup 1 8 oz. cup of coffee A nurse reviewing his intake and output notes that his drainage bag shows 1,000 mL for the past day. What is his deficit in milliliters?
2 pints of water x 16 oz per pint = 32 oz. 32 oz h2o + 8 oz coffee + 8 oz soup = 48 oz. To convert oz to (mL) multiply by 30 oz/ml 48 oz. x 30 oz/mL = 1440 mL. Therefore the deficit in ml is 1440-1000 = 440 mL
1 pound = ____ kilograms
2.2
1 kilogram is How many lbs?
2.2 lbs
12.34
2.468 / 0.2 = _______.
3 12/25
2.48 = _______.
1 inch = ____ centimeters
2.54
5.7
2.6 + 3.1 = _______.
XX
20
1 ton = ____ pounds
2000
MMIII
2003 in roman numerals is _______.
100 Degrees Celsius = ____ Degrees Fahrenheit
212
How many grams in 1 oz?
28 grams
1 yard = ____ feet
3
lll
3
5/7
3/7 + 3/7 = _______.
1 ounce = ____ milliliters
30
XXX
30
How many milliliters for 1 ounce?
30 ml
0 Degrees Celsius = ____ Degrees Fahrenheit
32
1 quart = ____ ounces
32
How many oz in 1 quart?
32 oz
13.6
34 / 2.5 = _______.
1 gallon = ____ quarts
4
lV
4
How many quarts for 1 gallon?
4 quarts
2/5
4/5 x 1/2 = _______.
XL
40
5
40 / 8 _______.
428
457 - 20 = _______.
595
462 + 133 = _______.
Roman Numeral V = ____
5
V
5
17.34
5 / 12.34 = _______.
1 13/15
5 2/3 - 4 4/5 = _______.
1 7/13
5 x 4/13 = _______.
1,122
5,234 - 4,112 = _______.
7/24
5/12 - 1/8 = _______.
2 4/9
5/6 / 3/4 = _______.
L
50
Roman Numeral L = ____
50
D
500
Roman Numeral D = ____
500
1 mile = ____ feet
5280
Vl
6
LX
60
28, 035
623 x 45 _______.
There are 453.59 grams per pound. An infant weighs 6,577 grams. What is the weight of the infant in pounds and ounces?
6577 grams -:- 453.59=14.5 lbs ie: there are 16 oz per lb, •so 16x .5=8oz ---→ 14lbs 8oz
112
672 / 6 _______.
Vll
7
1/3
7/9 - 4/9 = _______.
LXX
70
158.97
75.7 x 2.1 = _______.
X = 20
7:10 :: 14:x
1 cup = ____ ounces
8
Vlll
8
How many ounces for 1 cup?
8 oz
How many oz for 1 cup?
8 oz
LXXX
80
LXXX
80 in roman numerals is _______.
1,394
835 + 559 = _______.
lX
9
XC
90
Terminating Decimal
A decimal that is not continuous.
Factor
A number that divides evenly into another number.
Digit
A numeral.
Ratio
A relationship between two numbers.
1 3/8 feet
Alan is making a table. The table will be 6 ½ feet long and 4 feet wide. The board for the table is 7 7/8 feet long and 4 feet wide. How much of the board will Alan need to cut off?
16 ½
Alec has six friends who each give him 2 ¾ pieces of gum. How many pieces of gum does Alec have now?
(5 + x) (5 - x)
Answer: (25-x2) Explanation: First - OUtside- Inside - Last First: 5x5 =25 Outside : -5x Inside: 5x Last: -x2 Combine 25 + -5x + 5x - x2 = 25- x2 (answer)
23/12 - 45/3 =
Answer: - 13 1/12 Explanation: This is another complex fraction that will take too much of your time to find a common denominator. Instead long divide each fraction so that you have two decimal numbers that you can use. Notice that 3 goes into 45 more times than 12 goes into 23, so the answer will be negative.
34x - 2xy ( 34x + 2xy) - 32x ( 3x) - 44x
Answer: -2x [ 48x + 34xy +2xy2 + 5] Explanation: None of the items in parentheses can be combined. When multiplying by the number outside of the parentheses, remember that "x times y"= xy and that "x times x" = x2
4 3/7 - 7 34/9 =
Answer: -6.34 Explanation: These are two mixed numerals. Change each of the mixed numerals into an improper fraction, then divide the denominator into each numerator so that you have two decimals which you can then subtract. But always be sure that you know if the answer will be negative or positive. Once you can see which decimal is bigger, just do the subtraction as a normal subtraction problem and then apply the negative sign.
10-3
Answer: 0.001 Explanation: The negative 3 indicates that the decimal is going to make the number smaller, so we move three places to the left.
0.245/ 234
Answer: 0.00104 Explanation: To make this division easier, 0.245 can be written as 245 x 10 ^-3 (10 to the power negative 3), then perform the division.
Write 4% as a decimal.
Answer: 0.04 Explanation: 4% = 4/100 =0.04
0.000567/0.00589
Answer: 0.096 Explanation: The best way to tackle this problem is to first turn each number into a factor of ten, then divide the numbers. (567 x 10-6 )/(589 x10-5 ) Long divide 589 into 567 and then use the rules of exponents for the factors of 10, 10-6-(-5) = 10-1
Write 33 1/3% as a decimal.
Answer: 0.3333 Explanation: 33 is our whole number, so we won't be doing anything with it, however the fraction 1/3 needs to become a decimal. We can find the decimal by dividing 3 into 1 which goes 0.33 times. So our percentage is 33.33% which when divided by 100, or when we move the decimal place to the left two places we have.... 0.3333
70%
Answer: 0.70 Explanation: Percentages always indicate a part out of 100. Therefore 70% is the same thing as saying 70/100 = 0.70
389 is what percent of 27,689?
Answer: 1.4% Explanation: Use the key words. 389 is(=) x (what) ( 27,689) is (implies equals) what( implies the variable x) of ( implies the operation of multiplication) Setting this problem up requires that we divide both sides by 27,689. That leaves "x" by itself and then divide 27,689 into 389. Don't take it out to more than the thousandths place. You will be able to discern the answer from the choices given.
3/6 + 2/7 =
Answer: 11/14 Explanation: When adding, subtracting, multiplying or dividing fractions, always look for the fractions that can be reduced before performing any operations. For instance, in this problem we can see that 3/6 reduces to 1/2. Now all we have to do is find a common denominator that both 2 and 7 can divide into evenly. That would be 14. Now we construct two equivalent fractions. To do this we must simply divide both the 2 and the 7 into the number 14 and multiply the resulting number with the numerator. So our new equivalent fractions become, 7/14 + 4/14 = 11/14
Sarah traveled 2/7 of her total trip of 400 miles. How far did Sarah travel?
Answer: 114.3miles Explanation: The operating word is the word "of", so turn 2/7 into a decimal which is 0.285 and multiply this times the number of miles she traveled. 0.285 (400)=114.2, the answer on the test will probably be rounded to the nearest mile which would make it 114 miles
13% of $900.00 is what?
Answer: 117 Explanation: 0.13 (900)= x = 117
Convert to a percent; 1.25
Answer: 125% Explanation: Move the decimal point two places to the right, which is the same as multiplying by 100. 125%
3 runners out of 10 runners is the same as _____________ runners out of 50.
Answer: 15 Explanation: This is a ratio and proportion problem. Set it up as follows: 3/10= x/50 and solve for x by multiplying both sides by 50
What is 30% of 657?
Answer: 197.10 Explanation: Multiply 0.30 time 657
24,000,000/0.000012
Answer: 2 x 1012 Explanation: Powers of 10 for both numerator and denominator 24 x 106/12 x 10-6 24/12 = 2 10(6-(-6))=1012 2x1012
16 marbles out of 27 marbles is similar to 12 marbles out of _____________.
Answer: 20.25 Explanation: Set it up: 16/27 = 12/x Solve for x, since x is in the denominator, we must first get x in the numerator. So begin by rewriting the ratio, 27/16 =x/12, now multiply each side by 12.
What is 30% of 70?
Answer: 21 Explanation: When you are given this type of problem be sure to read the operating words,.. x =0.30 (70), this equation is the translation of the above statement. answer 21
(0.000068)3
Answer: 3.14x10-13 Explanation: Simplify the expression in parentheses first; (68 x 10-6)3 When raising an exponent to any power, multiply that power to each of the items powers in parenthesis. 683x10-18 Any time that there is a negative exponent, it indicates that the item is in the denominator, and the exponent then becomes positive 683/1018
Bill makes three times what Dave makes in two days. Dave makes 50% less than Peter in two days. If Peter makes $100 per day, how much does Bill Make?
Answer: 300 Explanation: (Dx2)/3 =B 2xD=(Px2) These equations were set up as equalities. Now substitue 100 for P, solve for D, then substitute D and solve for B.
The measurements of a shape are as follows: 12 feet, 13 feet, 2 feet and 6 feet. What is the perimeter?
Answer: 33 ft Explanation: Perimeter implies to add up all of the sides.
(24/0.45) x 65 + 3/4
Answer: 3467 Explanation: Perfom the division within the parenthesis, then the multiply, then the add.
12/13 of 40 is what percent?
Answer: 36.9% Explanation: The word, "of" indicates the operation of multiplication., therefore change 12/13 into a decimal and multiply,,, 0.92 (40) = 36.9 , now if we divide this by 40 and multiply by 100 we get 92.3%
27 is what percent of 67?
Answer: 40.3% Explanation: 27 = x(67), solve for x by dividing both sides by 67.
What percent of 78 is 34?
Answer: 43.6% Explanation: x(78) = 34, solve for x by dividing both sides by 78. Then multiply by 100.
15% of all basketball players at a college practice 3 hours per day, 25% practice 4 hours per day and the rest only practice for 1 hour daily. What is the number of players that practice for 1 hour per day, given that there are 75 basketball players on the team.
Answer: 45 Explanation: Add up the percentages, 15 + 25 = 40, and 100-40=60 Therefore take 0.60x75
0.5% of $1000 is what?
Answer: 5 Explanation: You must first turn the percentage into a decimal then multiply. so 0.5% implies to divide this by 100 or 0.5/100 = 0.005 (1000) =5
Jake rode his bicycle at 10 miles per hour, to a store one mile down the road. How long did it take Jake to arrive at the store?
Answer: 6 minutes Explanation: Distance = rate x time 1 mile = 10mi/hr (x) 0.10 hr x 60min/1hr = 6 min
25 is what percent of 40?
Answer: 62.5% Explanation: This is a word problem; look at the main operating words. 25 is(=) what (x)40 so we have as our problem 25 = x40, now solve for x by dividing both sides of the equation by 40, 25/40 = x, now reduce your fraction... 5/8 , turn this into a decimal and multiply by 100. =62.5%
Write 5/8 as a percent
Answer: 62.5% Explanation: First turn this into a decimal by dividing 8 into 5.= 0.2, then multiply this by 100 = 20
324 out of 1000 is similar to 21 out of _____________.
Answer: 65 Explanation: 324/1000 = 21/x re-write so that x is in the numerator 1000/324 =x/21, multiiply both sides by 21.
Write 65 5/8 as a decimal.
Answer: 65.625 Explanation: A decimal is always a number smaller than one, so we can leave 65 as it is and just turn the fraction into a decimal., so our decimal becomes 65.625
Round your answer to the nearest whole number. 22.67 x 3.3 =
Answer: 75
78 is what percent of 900?
Answer: 8.67% Explanation: 78 = x(900), solve for x by dividing both sides by 900
Write 9/11 as a percent.
Answer: 82% Explanation: Divide 11 into 9 to get 0.818 and multiply this by 100 to get about 81% or 81.8%
There are 400 students in the school, 34% of them are all A students, 44% are all B students, and the rest are all C students. How many C students are there?
Answer: 88 Explanation: Add up all the percentages, 34 + 44 = 78, this leaves a percentage of 22 to make 100. Next, take 0.22 x400 to find the C students.
Two angles of a triangle have the following measurements, 30 degrees, and 60 degrees. What is the measure of the third angle?
Answer: 90 degrees Explanation: All angles of a triangle must add up to 180 degrees, therefore given two of the angles you can find the third by subtracting the sum of the two angles from 180.
3.75
Bill has 2.5 vacation days left for the rest of the year and 1.25 sick days left. If bill uses all of his sick days and his vacation days, how many days will he have off work?
What is the decimal equation to convert Fahrenheit to Celsius?
C = F-32/1.8
1:40
Change 0.025 into a ratio.
13%
Change 0.13 into a percent.
9/10
Change 0.9 into a fraction.
16.667%
Change 1/6 into a percent.
11.7333
Change 11 11/15 into a decimal.
3 2/5
Change 17/5 into a mixed number.
0.6666
Change 2/3 into a decimal.
3 11/200
Change 3.055 into a fraction.
0.75
Change 3/4 into a decimal.
17/3
Change 5 2/3 into an improper fraction.
83.3%
Change 5/6 into a percent.
9:11:23pm
Concert 21:11:34 hours into regular time.
Your stock current costs is $34.56 dollars per share. At the closing of the Dow, your stock went up 1/8%. How much is your stock worth now?
Correct answer: $34.60 Explanation: 1/8% is equal to 0.125/100 = 0.00125, now if we multiply this times the stock value, we get 0.00432 and then we add this to our stock amount =0.0423 + 34.56 = 34.60.
-9 1/12 - 6 1/4 =
Correct answer: -15.33 Explanation: This problem requires that you know how to use the negative sign. Here we are adding two negative mixed numerals. First turn each mixed numeral into an improper fraction and then long divide the denominator into each numerator.
Solve for x: 3(3/4)x + 23x + 45/6 = 3
Correct answer: -18/101 Explanation: First 45/6 can be reduced to 15/2. Combine all like terms and solve for x.
4 7/8 - 34 12/5 =
Correct answer: -32 Explanation: These are mixed numerals. The first step is to turn them into improper fractions. This is a fraction that has a larger numerator than the denominator. To do this multiply the denominator to the whole number and add that answer to the numerator. This will give us 39/8 and 171/5. It is easy to see that the answer will be negative since 5 goes into 171 more times than 8 goes into 39. Now just long divde each denominator into the numerator and perform the operation.
3 - 7 1/8 - 3/9 =
Correct answer: -4.458 Explanation: Here you must combine a whole number, a mixed number, and a fraction. Reduce if possible. First, 3/9 reduces to 1/3, then turn the mixed number into a fraction 57/8, and then find a common denominator for 1,8, and 3, which is 24. Notice that the denominator for the 3 or for any whole number is always a 1. Keep track of your negatives and positives. Here, you will add two negative numbers and then add a positive number. The number that is the biggest will determine the sign. For instance -89 + 8= -81, this is because there are more negative numbers that make -89 than make +8.
5.6/78.9 + 35/8 - 67 + 1 1/4
Correct answer: -61.3 Explanation: The best way to tackle this problem is to turn all fractions into decimals and then perform the addition and subtraction.
4(5x -7) = -56
Correct answer: -7/5 Explanation: 4(5x -7) = -56 How to solve? The first thing that we must do is to see if we can solve or combine like terms in the parentheses. Answer is no we cannot. Next we use the distributive property of multiplication to distribute the 4 to each of the items within the brackets. So we have.... 4(5x) -4(7) = -56 Which gives us.. 20x -28 = -56 now we must add 28 (which is the opposite of -28) to both sides of the equation. 20x -28 + 28 = -56 +28 20x = -28 (remember that when you are adding or combining two signed numbers, take the difference just like you would a normal subtraction problem, but keep the sign of the number that is the largest. In our case a negative. Now let's solve for x by dividing both sides by 20 20x/20 = -28/20 (x) = - 7/5 or - 1 2/5
10-7/100
Correct answer: 0.0000001 Explanation: 10(-7-0) = 10-7 = 0.0000001
0.055%
Correct answer: 0.00055 Explanation: This is out of 100, so we can either perform long division of 0.055/100 or use the factor of 10 55x10-3(10-2) 55x10-5 0.00055 10-2=1/100
Susan gained 30 pounds during her last trimester of pregrancy. How many pounds per day did Susan gain? You can assume each month has 30 days.
Correct answer: 0.33 lb Explanation: A trimester is 3 months. So Susan gained 30 lbs in 3 months. There are 30 days in a month, or 90 days in three months, or 10 pounds in one month or 10 lb/30 day, reduces to 1/3 = 0.33 lbs per day.
Convert to a percent; 0.0087
Correct answer: 0.87% Explanation: Any time you are asked to change a number to a percent, simply multiply that number by 100 or find the decimal and move it two places to the right.
10,000/104
Correct answer: 1 Explanation: Use exponents to solve this rather than long division. 104/104= 10(4-4) = 100 =1
If Brad can walk 10 miles in 5 hours, how far can he walk in 30 minutes?
Correct answer: 1 Mile Explanation: 30min x10mi/5hrx 1hr/60min = units hours and minutes cancel leaving miles.
(57 x 2/3)/24
Correct answer: 1.6 Explanation: Multiply the items in parenthesis first, then divide by 24
5/6 + 7/9 =
Correct answer: 1.6 Explanation: Since we can't reduce any farther, find the common denominator, which is 18 and construct two new equivalent fractions and then add.
104/120 - 44/55 =
Correct answer: 1/15 Explanation: Remember, don't get nervous when you see these large fractions. The first step is to see if you can reduce them into smaller fractions. 44/55 reduces to 4/5, and 104/120 reduces to 13/15. In this form the fractions are easier to use. Now find the common denominator, which is 15, and construct two new equivalent fractions. It is hard to tell by inspection whether or not the answer will be positive or negative, so don't guess, work it out to see.
According to the diet clinic Angie was diagnosed as being 15 pounds overweight for her body size. If Angie weighs 150 pounds, what percentage her weight needs to be lost?
Correct answer: 10% Explanation: The question here is,,,,,, 15 pounds is what % of 150 or.... 15 = x 150,, so we divide both sides of the equation by 150 to get 30 percent. Did you remember to multiply by 100 to get your percent?
The dimensions of a room are 10 feet by 10 feet. What is the area?
Correct answer: 100 ft^2 Explanation: Area implies to multiply lenght time width. Therefore 10feet x 10 feet= 100 ft^2 or 100 squared feet.
0.120
Correct answer: 12% Explanation: To convert any number to a percent, always multiply by 100, or remember to move the decimal point two places to the right. 12%
Fred drove 300 miles in 4 hours. How many miles can Fred drive in 2 days if he drives 8 hours per day?
Correct answer: 1200 Miles Explanation: Given: 300mi/4hr Fred drives 16 hours in two day. Therefore; 16hr x 300mi/4hr= units of hours cancel, 4 goes into 16, 4 times, and 4 times 300= 1200miles
Mary is 4 years older than Jane. If the combined sum of their ages is 32, how old is Jane?
Correct answer: 14 Explanation: (J+4) + J = 32 2J + 4 = 32 2J + 4 -4= 32-4 2J = 28, now divide both sides by 2, J = 14 and M=18 Jane is 14
Fred makes $12.34 per hour. John makes $10.98 per hour. After working for 8 hours, Fred makes time and a half for each additional hour worked. If John worked 10 hours, and Fred worked 10 hours, what would be the difference in pay, considering that Fred made 50% more an hour after working 8 hours?
Correct answer: 14.96 Explanation: John makes $10.98 for 10 hours with no extra for overtime. Multiply $10.98 times 10 hours for a total of $109.80. Fred makes $12.34 per hour for the first 8 hours, or $12.34 multiplied by 8 equalling $98.72. Fred then makes time and a half for the next 2 hours - $12.34 per hour multiplied by 1.5 equals $18.51 per hour times 2 hours for and total of $37.02 for the 2 extra hours. $37.02 plus the $98.72 Fred earned for his first 8 hours give Fred a total pay of $135.74. $135.74 minus $109.80 equals $25.94 more that Fred earned.
85% of all the students have B's. What is the percentage that do not have B's, if the total number of students is 160.
Correct answer: 15% Explanation: This is a trick question. All you have to know is that everything is out of 100%, so if 85% is given, the balance is simply 15%
Solve for x : 32x - 2.4y + 16x = 15 + z
Correct answer: 15/48 + z/48 + y/20 Explanation: The key is to get all of the "x" containing numbers on one side and the other variables on the other side of the equal sign. combine 32x+16x = 48x, Add 2.4y to both sides and then divide the entire equation by 48. 48x/48 = 2.4y/48 + 15 /48+ z/48 x = 2.4y/48 + 15/48 + z/48, now just reduce the fraction 15/48, ALWAYS REDUCE ALL FRACTIONS TO LOWEST TERMS
¼(x) -1/8(x) = 3 - 1/16(x)
Correct answer: 16 Explanation: ¼(x) -1/8(x) = 3 - 1/16(x) 16{1/4(x) -1/8(x) = 3 - 1/16(x)} Now distribute the 16 to each of the items within the parentheses So now we have.... 16(1/4)x - 16(1/8)x = 16(3) - 16(1/16)x O.K., do you see what is going on? We are simply multiplying a whole number times a fraction right? So how do we multiply a whole number times a fraction? Answer: Numerator times the numerator and the denominator times the denominator. But what if our number doesn't have a denominator? No problem, we just put a 1 under the number. It doesn't change the number does it? No, of course not. So..... 4x - 2x = 48 - x do you see how we came up with these numbers? Well if you get your calculator and multiply 16 and ¼ or 0.25 you should get 4 and 4 times x is 4x. Just like the rest of the items in the equation, the denominator goes into the numerator., so 8 divides into 16 and 16 divides into 16 to get 1. Now we can easily solve for x. First combine like terms on both side of the equation. 4x -2x = 2x = 48 -x 2x = 48 -x ( now we must eliminate the x next to the 48, so that numbers are on one side of the equal sign and letters or variables are on the other. Let us add a positive x to both sides of the equation. 2x +x = 48 -x + x 3x = 48 (now divide (opposite of multiplication) 3 by both sides of the equation. 3/3 (x) = 48/3 (x) = 16 now put this back into the equation to verify that it works.
50 is what percent of 300?
Correct answer: 17% Explanation: Again, here is our operating words, 50 is, or equals, what or x, percent of 300. so we have 50 = x (300),,, now divide both sides by 300 and reduce the fraction 50/300 and then multiply by 100 for a percent. 1/6 (100) = 16%
John walked ¾ the distance of Bob. If Bob walked 3 ¼ miles, how far did John walk?
Correct answer: 2 and 7/16 of a mile Explanation: 1. 2 and 7/16 of a mile 2. 3 miles 3. 2.5 miles Solution; Take ¾ of 3 ¼. The word "of" means to multiply. ¾(3 ¼) ¾ (13/4) Numerator multiples numerator and denominator multiples denominator. 39/16 This is an improper fraction which needs to be made into a mixed numeral. John walked 2 and 7/16 of a mile
If 15% of all Americans are millionaires, how many Americans are not millionaires, if there are 245,000,000 Americans?
Correct answer: 208,250,000 Explanation: Remember 15% is the balance of 85%, which are the percentage of Americans that are not millionniares. So just take 0.85 times the population. 280,250,000
When Mike is 18 years old, Mary is half his age. How old is Mary when Mike is 30 years old?
Correct answer: 21 Explanation: If Mary is half of Mike's age when Mike is 18 years old, the Mary is 9. She will always be 9 years younger than Mike, even when Mike is 30.
Write 2 1/5 as a percent.
Correct answer: 220% Explanation: 2 and 1/5 in decimal form is 2.8, multiply this times 100 and we get 280%
Write 2.5 as a percent.
Correct answer: 250% Explanation: 250%, any time you are asked to turn a number into a percent, just multiply that number by 100 and put your percentage sign.
4 24/23 - 1 2/3 =
Correct answer: 3.38
Write 15% as a fraction.
Correct answer: 3/20 Explanation: A fraction is always out of 100, so take the percentage and divide it by 100,,,,, 15% = 15/100 reduces to 3/ 20 = 0.15
12 is what percent of 40?
Correct answer: 30% Explanation: 12 = x40 divide both sides by 40 and you get.. 12/40 which reduces to 3/10, turn this into a decimal..=0.3 and multiply this by 100 to get 30%
0.00078/0.00002
Correct answer: 39 Explanation: Turn the numerator and denominator into a factor of 10. 78 x 10 -5 ÷ 2.0 x10-5 Divide 2 into 78 = 39 Subtract the numerator exponent from the denominator exponent: 10 (-5 -(-5)) = 100 = 1 39x1 =39
Simplify, 23x ( 2x + 4) - 32x + 1.245y + 21x
Correct answer: 46x2 +81x +1.245y Explanation: There can be nothing done within the parentheses, so the next step is to muliply 23x times that which is in the paraenthesis. The next step is to see if any number can be factored out.
Mary made $28,990.87 for the year. She had to pay 20% of her salary to her husband for alimony. How much money did Mary have to pay monthly?
Correct answer: 483.18 Explanation: This question requires that you know how to use percentages. Simply take 20% of Mary's income, by multiplying her income time 0.20, then divide that number by 12 to find out how much she had to pay monthly.
0.00045/9
Correct answer: 5 (10-5) Explanation: Use powers of 10 for the numerator and then divide. (45x10-5)/9 45/9 = 5 (10-5)
Mark made twice as much as Fred. Fred made four times as much as Paul. If Mark made $400,000, how much did Paul make?
Correct answer: 50,000 Explanation: This problem requires that you know how to set up a question with a variable. We have three expressions: Mark made two times Fred or F/2 = M Fred made 4 times Paul or P/4 = F Mark made $400,000 Now substitute 400,000 for M and solve for F. Once you have solved for F, than solve for P.
(24x - 4) ( 2x - 2)8
Correct answer: 64 (6x-1) (x-1) Explanation: Factor out a 4 from one set of parentheses and and 2 from the other, this leaves 64 (6x-1)(x-1), in simpliest form
6/5 of 49 is similar to 7/8 of __________.
Correct answer: 67.2 Explanation: This is saying, 6/5 times 49 = 7/8 x multiply each side by 8/7, so "x" will be by itself, we have: 8/7(6/5)49 =x
Place in order of greatest to least. 3/4, 7/8, 9/11
Correct answer: 7/8, 9/11, 3/4 Explanation: First try to reduce any to lowest terms. Then find a common denominator for all and convert each fraction to an equivalent fraction. The common denominator is 352. 264/352, 308/352, 288/352 these would then be ordered from greatest to least. 7/8>9/11>3/4
(0.000034)-2
Correct answer: 86.5x107 Explanation: What does the operation ask us to perform? (0.000034)-1 x (0.000034)-1 Simplify expression in parenthesis: (34x10-6)-1 x ( 34x10-6)-1 = 34-1x 34-1 x 10-6(-1) x 10-6(-1)= 34-2 x 1012 which is also the same as....... 1/342 = 1/1156 = 8.6505 x 10-4 or 0.00086505 now multiply this times 1012 and we get... moving the decimal point 12 places to the right. 8.6505 x 108
There are 700 employees at the ACME firm. Out of 50% of the employees, only 57 will get bonuses. What is the percentages that won't get bonuses out of the total amount of employees?
Correct answer: 91.8% Explanation: It doesn't matter that only 57 employees out of 50% got bonuses. What does matter is that 700-57= the number of people that didn't get bonuses. Take that number and divide it into 700 to get the percentage.
Jake's salary after a five day work week is $550.00. If 10% of his salary is deducted for taxes weekly how much does he make per day?
Correct answer: 99 Explanation: Multiply 0.10 times 550.00 then divide by 5.
21x ( 3x +7) - 4x( 2.5x - 56x) + 24x/4
Correct answer: x ( 277x + 153) Explanation: Combine if you can all items in parentheses, then multiply, add and subtract.
15
Danny has 11 1/4 cups of chocolate syrup. He is going to make chocolate sundaes for his friends. Each sundae will have 3/4 cup of chocolate. How many sundaes can Danny make?
Place Value
Each digit in a number occupies a position; that position is called its _______.
What is the decimal equation to convert Celsius to Fahrenheit?
F = (C*1.8)+32
36
Find the LCD for 3.4 and 7/9.
24
Find the LCD for 3/12 and 1/8.
On an annual basis, a hospital deliver 1,820 babies. If 55% of the babies born are boys, how many girls were born in a year?
If 55% are boys, then 45% must be girls. 1820 x 45% = 819 girl babies
870
Jan is preparing an examination for 29 students. Each student will have 30 questions, with no student having duplicate questions. How many questions will Jan need to prepare?
13 Miles
Jeff walks 5 miles west and then turns north and walks 8 miles. How far has Jeff walked?
19.2
Jenny lost 3.2 lb each month for 6 months. How much weight has Jenny lost?
x = $7.50
John buys 3 bags of chips for $4.50. how much will it cost John to buy five bags of chips?
The Roman numeral MCMLXVII is equivalent to which Arabic number?
M stands for 1000 C for 100 L for 50 X for 10 V for 5 I for 1 The MCM stands for 1900 (putting the C before the M means subtract 100 from 1000). The LXVII stands for 67 (50+10+5+2)
2003
MMlll
4 1/6
Mary is going to make a birthday cake. She will need 1 2/3 cups of sugar for the cake and 2 ½ cups of sugar for the frosting. How many cups of sugar will Mary need for the frosted birthday cake?
A nurse's shift in a military hospital is from 1400 to 2100. What time of day does the nurse work?
Military time is based on a 24 hour clock. To convert from military time to standard time, simply subtract 1200 from the time. 1400 - 1200 is 2 pm.
Reciprocals
Pairs of numbers that when multiplied together equal 1.
The patient currently drink 4 12 oz. cans of diet soda per day. How many ounces of diet soda can the patient drink if he reduces his intake by 25%?
Patient currently consumes 48 ounces (4x12 oz) Patient has to give up 25% of 48 ounces = 48 x .25 = 12 oz the patient can drink 48 - 12 = 36 ounces
Percent
Per hundred.
3/5
Reduce 12/20.
3
Reduce 21/7.
1/3
Reduce 7/21.
A woman has 8 black shoes, 5 brown shoes, 2 red shoes, and 5 boots. What percentage of her collection is boots?
Since she has 20 overall items in her collection, boots make up 25% of her collection (5/20=25%)
224
Stewart has 56 acres of land. He wants to divide the land into plots of 0.25 acres. How many plots of land will Stewart have after he divides the 56 acres?
Quotient
The answer to a division problem.
Product
The answer to a multiplication problem.
Denominator
The bottom number in a fraction.
0 and 100
The freezing point and boiling point of water in Celsius are _______ and _______.
32 and 212
The freezing point and boiling point of water in Fahrenheit are _______ and _______.
Fraction Bar
The line between the numerator and denominator. That bar is another symbol of division.
45
The number 9 is 20% of what number?
Dividend
The number being divided.
Divisor
The number by which the dividend is divided.
Least Common Denominator
The smallest multiple that two numbers share.
Numerator
The top number in a fraction.
25 chain saws, 14 snow blowers, 18 floor sanders, 12 leaf blowers and 19 power washers. If 25% of the total inventory is available for rental, how many tools can be rented?
The total inventory is 88 (25+14+18+12+19) 25% of 88 = 88 x 0.25 = 22
You have $100 to spend. You pick out two items to purchase. The first item is $64.57. The second item is $26.82. If you buy both of these items, how much money will you have left?
The two items total $91.39 ($64.57+$26.82=$91.39) you have $100-$91.39=$8.61 left.
How many gallons are in 80 fluid ounces?
There are 128 oz per gallon so, 80 fluid oz = 80 / 128 =0.625 gallons
14
There are 350 pieces of candy in a large jar. Ben wants to give the 25 campers in his group an even amount of candy. How many pieces of candy will each camper receive?
98.6 degrees Fahrenheit is what temperature in Celsius?
To convert Fahrenheit to Celsius: 98.6 - 32=66.6 66.6 x 0.56 = 37 degrees Celsius
A man's waist measurement is 88.9 centimeters. What is his waist in inches?
To convert centimeters to inches: 88.9 -:- 2.54 = 35 in
10 kilograms is equivalent to how many pounds?
To convert kilograms to pounds: 10 x 2.2 = 22 lbs
Common Denominator
Two or more fractions having the same denominator.
Proportion
Two ratios that have equal values.
3/4
What is 0.75 as a fraction?
0.50
What is 1/2 as a decimal?
50 %
What is 1/2 as a percent?
0.25
What is 1/4 as a decimal?
25%
What is 1/4 as a percent?
1000
What is 10:00am in military time?
3:00pm
What is 1500 in regular time?
66.6%
What is 2/3 as a percent?
1/5
What is 20% as a fraction?
30.6
What is 68% of 45?
1900
What is 7:00pm in military time?
90
XC is _______.
1
_______ centimeters = 10 millimeters.
1
_______ gram = 1,000 milligrams.
A sample contains 2/3 oz of liquid How many (mL) is this?
multiply by 30 oz/mL. 2/3 x 30 = 60/3 = 20 mL
87.5%
what is 7 out of 8 expressed as a percent?
