Math

28.25°F/hr

A roast was cooked at 325 °F in the oven for 4 hours. The internal temperature rose from 32 °F to 145 °F.What was the average rise in temperature per hour?

175 mg

A vitamin's expiration date has passed. It was supposed to contain 500 mg of Calcium, but it has lost 325 mg of Calcium. How many mg of Calcium is left?

25% (Since she has 20 overall items in her collection, boots make up 25% of her collection (5/20=25%))

A woman has 8 black shoes, 5 brown shoes, 2 red shoes, and 5 boots. What percentage of her collection is boots?

3.4

Divide: 223 ÷ 65 =

61 (Substitute the values of x and y into the given equation and evaluate: = 3^4 − (20) = 81 − 20 = 61 )

Evaluate x^4 − y if x = 3 and y = 20

2 (Tim will make $120 in 4 hours and Joe will need 6 hours to make $120. So 6 − 4 = 2)

Joe makes $20 an hour and Tim makes $30 an hour. How many hours more than Tim must Joe work to earn the same amount Tim makes in 4 hours?

0.060300 (The product of two decimals will always have the same number of decimal places as the sum of the number of decimal places that the multiplicand and the multiplier have. (67)(9) = 603. The multiplicand is .67 and has 2 decimal places. The multiplier is .09 and has 2 decimal places. Our product should have 4 decimal places. Therefore, our answer is .0603. Don't get tripped up by the extra zeros. Zeros before our answer and after the decimal point increase the number of decimal places. Zeros after our answer and after the decimal point do not increase the number of decimal places.)

Multiply: (0.67)(0.09) =

12,497.8

Multiply: (226)(55.3) =

2,468.64

Multiply: (44.44)(55.55) =

millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones (Use these place values to line up addition and subtraction problems.)

What are the place values from largest to smallest for seven places to the left of the decimal? (ones to millions / 7)

(Move the decimal to the right in both the divisor and the dividend, making both whole numbers. The number of places moved for the dividend must be the same number of places for the divisor. Add zeroes where necessary to do this. Divide as usual, putting the decimal point directly above its place in the dividend. 0.0023÷2.32 becomes 23÷23200)

0.0023 ÷ 2.32 (dividing decimals)

0.25795 (Multiply the numbers as usual. Count the number of digits to the right of the decimal point in the numbers being multiplied. The final answer must contain the same number of digits to the right of the decimal place as in the numbers being multiplied. [0.2345 ⋅1.1 ] There are 5 numbers to the right of the decimal point, so the answer will contain 5 numbers to the right of the decimal point. [0.2345⋅1.1=0.25795])

0.2345 ⋅1.1 (multiplying decimals)

758/1000 or 379/500 (Take note of the smallest place value of the number. This will be the denominator. The numbers to the right of the decimal will be the numerator. Reduce if possible.)

0.758 (decimal to fraction)

10 mm

1 cm = ? mm

8 oz

1 cup = ? oz

12 inches

1 foot = ? inches

30.48 cm (1 foot = 12 inch. 1 inch = 2.54 centimeters. Therefore, 1 foot = 12 x 2.54 = 30.48 centimeters.)

1 foot is how many centimeters (Note: There are 2.54 centimeters per inch)

about 3.79 liters (3.78541 liters)

1 gallon = ? liters

4 quarts

1 gallon = ? quarts

1000 milligrams

1 gram = ? milligrams

2.54 cm

1 in = ? cm

1000 grams

1 kilogram = ? grams

about 2.2 pounds (2.20462 pounds)

1 kilogram = ? pounds

about 0.62 miles (0.621371 miles)

1 kilometer = ? miles

1000 meters

1 km = ? meters

1000 mL

1 liter = ? mL

100 cm

1 meter = ? cm

1000 mm

1 meter = ? mm

5280 feet

1 mile = ? feet

1760 yards

1 mile = ? yards

about 1.61 kilometers (1.60934 kilometers)

1 mile/hour = ? kilometers/hour

0.001 meter (1 millimeter = 1/1000 meter=0.001 meter or a thousandth meter) (Milli- = one thousandth Centi- = one hundredth Kilo- = one thousand)

1 millimeter is how many meters?

about 28.35 grams (28.3495 grams)

1 oz = ? grams

about 29.57 ml (29.5735 ml)

1 oz = ? ml

2 cups

1 pint = ? cups

453.592 grams

1 pound = ? grams

16 oz

1 pound = ? oz

about 0.95 liter (0.946353 liter)

1 qt = ? liter

32 oz

1 quart = ? oz

2 pints

1 quart = ? pints

2000 pounds

1 ton = ? pounds

3 feet

1 yard = ? feet

(Vertically align the numbers so that the decimal points are on top of each other, add zeroes as placeholders where necessary, and add or subtract as usual. 1.1 minus 3.02 becomes 1.10−3.02. The added 0 in 1.1 acts as a placeholder and does not change the number's value.)

1.1 - 3.02 (subtracting decimals)

29/21 (or 1 8/21) (For fractions with a common denominator: Add or subtract the numerators as usual while keeping the denominator. For fractions with unlike denominators: Determine the least common denominator (LCD). Convert the first fraction to an equivalent fraction with the LCD as its denominator. Do the same with the second fraction. Add the two fractions as you would with fractions with a common denominator. Subtraction will follow the same procedures except that you use subtraction or "minus.")

2/3 + 5/7 (adding fractions)

8/15 (Multiply the first fraction by the reciprocal of the second fraction.)

2/3 ÷ 5/4 (dividing fractions)

9:40 pm (Standard and military time formats are the same from 1:00 (in the morning) to 12:59 (in the afternoon), except that standard time indicates a.m. for the morning and p.m. starting from 12 noon. Military time uses no other notation. Starting at 1:00 pm (standard time), add 12 to convert from standard to military. To convert military time (applicable for the time from 13:00 to 24:00), simply subtract 12 and you get the equivalent standard time. Standard time uses the 12-hour format, making distinction between a.m. and p.m. Military time uses the 24-hour format, where a day starts at 00:01 and ends at 24:00. Military time from 00:01-12:59 matches up with 12:01 a.m.-12:59 p.m., and from 13:00-24:00 matches up with 1:00 p.m.-12:00 a.m. 21:40 is the same as 9:40 p.m. (21:40 - 12 = 9:40) )

21:40 (convert to standard time)

25000 meters ( 25 kilometers = 25⋅1000 = 25,000 meters or 25 thousand meters ) (Milli- = one thousandth Centi- = one hundredth Kilo- = one thousand)

25 kilometers is how many meters?

100

25% of 400 =

9 2/3 (Improper fraction to mixed number: Divide the numerator by the denominator to find the whole number. If there is a remainder, this becomes the numerator of the fraction which you place above the denominator.)

29/3 (convert improper function to mixed number)

11/3 (Mixed number to improper fraction: Multiply the whole number and the denominator. Add this product to the numerator. The result becomes the new numerator which you put over the denominator.)

3 2/3 (convert the mixed number to improper fraction)

4.67 (sum of the data / number of data = average)

3, 5, 6 (find the average)

1/4

3/4 - 1/2 =

99

33% of 300 =

0.04 gram (4 centigrams=4/100gram=0.04 or 4 hundredth gram) (Milli- = one thousandth Centi- = one hundredth Kilo- = one thousand)

4 centigrams is how many grams?

42% (41.66666%) (is/of = percent/100 or part/whole = percent/100) (5/12 = percent/100) (Cross multiply to solve.)

5 is what percentage of 12 (find percentage of a number) (round to whole number)

0.758 (Fraction to decimal: divide the numerator by the denominator.)

758/1000 (fraction to decimal)

1/2 (1/2 = 2/4 = 16/12 = 8/16) (To reduce fractions: Divide both the numerator and denominator by their greatest common factor. Equivalent fractions are those that have the same value when reduced to their simplest form.)

8/16 (reduce this fraction/equivalent fractions)

37 C (To convert Fahrenheit to Celsius, you subtract 32 degrees and multiply by 5/9. So 98.6-32=66.6. 66.6*5/9 = 37 degrees Celsius )

98.6 degrees Fahrenheit is what temperature in Celsius?

443.50 (First you must calculate how many hours the nurse works each week. Three 8-hour shifts plus one 12-hour shift equals 36 hours per week. Beginning Salary = 36 x $17.81 = $641.16 Deductions = $102.80 + $24.58 + $18.13 + $52.15 = $197.66 Take-Home Pay = $641.16 − $197.66 = $443.50)

A nurse working at a medical clinic earns $17.81 per hour. The nurse works three 8-hour shifts and one 12-hour shift every week, and is paid weekly. Weekly deductions are: federal tax $102.80, state tax $24.58, federal insurance $18.13, and family health insurance $52.15. What is the nurse's take-home pay each week?

A little bit after midnight. ( Converted to regular time, their schedule is 3:00 PM to 1:00 AM. So they will get off at 1:00 AM, which is a little bit after midnight. )

A nurse's schedule is written in military time, and shows their shift is from 1500 to 0100. When will they get off work?

3 minutes (If the rats speed is reduced by 50%, then it will take the rat twice as long, or 6 minutes. This is 3 minutes longer than it took before.)

A rat can finish a maze in about 3 minutes. If a small backpack is put on the rat so it reduces its speed by 50%, how much longer will it take the rat to finish the maze?

1.399

Add: 1.332 + 0.067

20.73 (Vertically align the numbers so that the decimals are on top of each other: 11.30 +9.43 ------ 20.73 )

Add: 9.43 + 11.3 =

12.05 (Three comics at $2.65 would equal a total of $7.95. The change would equal $20 − $7.95 = $12.05.)

At a comic book store, Robert purchased three comics for $2.65 each. If he paid with a $20 bill, how much change did he receive?

1,987,200 seconds (Dimensional analysis is also known as conversion factor method or factor-label method. It involves expressing numbers and dimensions of a thing in one unit of measurement to another without changing the value of that thing. It is useful for performing unit conversions, especially complex unit conversions (such as converting from the English System to the International or metric system). Convert 23 days to seconds: 23 days x 24 hours/1day x 60 minutes/1hour x 60 seconds/1 minute = 1987200 seconds. Notice that a measurement unit occurring on top of a fraction cancels out the same unit at the bottom of the fraction. All other units are cancelled in this manner, leaving the unit we want the original value converted to.)

Convert 23 days to seconds.

78.8 F (To convert from Celsius to Fahrenheit you can use this formula: (°C × 9/5) + 32 = °F Or you can just follow these steps: 1) Multiply by 9 2.) Divide by 5 3.) Add 32 )

Convert 26° Celsius to Fahrenheit.

3:17:52 PM (Question 11 Explanation: For a military time that's 13 hours or higher, simply subtract 12 hours to get the standard time. Also, since the military time in this case starts higher than 12 hours, we know that it is PM.)

Convert the following military time to regular time: 15:17:52 hours

13 (Write a proportion to represent the situation: 3 eggs/1 cake = 40 eggs/x cake Cross multiply and solve for the variable x: 3x = 40 -> x = 13 1/3)

For a recipe, there are 3 eggs needed for every pound of cake needed. How many pounds of cake can be made if there are 40 eggs?

2.4

Fried's rule for computing an infant's dose of medication is: infant's dose = ( Child's age in months x adult dose) / 150 If the adult dose of medication is 15 mg, how much should be given to a 2 year-old child?

1/10

How many centimeters are in millimeter?

30.5 (30.48) ( There are 2.54 cm in one inch, and 12 inches in a foot. (12)(2.54) = 30.48 2.54 cm = 1 inch 0.39 inch = 1 cm )

How many centimeters are there in a foot?

.625 gallons (There are 128 ounces per gallon. Therefore, 80 fluid ounces = 80/128 = 0.625 gallons)

How many gallons are in 80 fluid ounces?

5,000 (The prefix "milli-" means 1,000. There are 1,000 millimeters in 1 meter, so there are 5,000 millimeters in 5 meters. Alternatively, use dimensional analysis to convert: ( 5 meters x 100 cm / 1 meter x 10 mm / 1 cm = 5000 cm) (1 Kilometer = 1,000 Meters 1 Meter = 100 Centimeters 1 Centimeter = 10 Millimeters)

How many millimeters are there in 5 meters?

32,000 (There are 16 ounces in a pound and 2,000 pounds in a ton. (16)(2,000) = 32,000)

How many ounces are in a ton?

128 (Use dimensional analysis to convert from gallons to ounces. 1 Gallon = 4 Quarts 1 Quart = 2 Pints 1 Pint = 2 Cups 1 Cup = 8 Ounces 1 gallon x 4 quarts/1 gallon x 2 pints/1 quart x 2 cups / 1 pint x 9 ounces / 1 cup = 128 ounces)

How many ounces are there in a gallon?

1,760 (Question 25 Explanation: Remember that one mile is equal to 1,760 yards. 1 Mile = 1,760 Yards 1 Mile = 5,280 Feet 1 Yard = 3 Feet 1 Foot = 12 Inches)

How many yards are in a mile?

1/5 (12.8 / 64 = 0.20. 0.20= 20/100, reduce 20/100 to 1/5)

If the average person drinks 8, (8oz) glasses of water per day, a person who drinks 12.8 oz of water after a morning exercise session has consumed what fraction of the daily average?

2 (Moving right of the decimal point one space is the tenths position)

In the number 743.25 which digit represents the tenths space?

33%

In your class there are 48 student; 32 students are female. Approximately what percentage is male?

2.88 liters ( 1 quart = 32 oz. Therefore 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 )

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?

x = 10 (This is a basic algebra problem where you are need to solve for a variable. To solve this, first divide both sides by 3: 3(x − 4) = 18 x − 4 = 18/3 x − 4 = 6 Then solve for x: x − 4 = 6 x = 6 + 4 x = 10)

Solve for x: 3(x − 4) = 18

36 ( Question 13 Explanation: The first step to solving a proportion problem is to rewrite the problem as a fraction. 9 / 14 = x / 56 Then you cross-multiply and solve the resulting equation. 14x = (9)(56) 14x = 504 x = 504/14 x = 36)

Solve the proportion (find the value of x): 9:14 :: x:56

1 ( Remember your order of operations: Complete operations within parentheses first. Calculate exponents. Then multiply and divide in order from left to right. Then add and subtract in order from left to right. 2 − 8 ÷ (24 ÷ 2) = 2 − 8 ÷ (16 ÷ 2) = 2 − 8 ÷ 8 = 2 − 1 = 1 )

Solve: 2 − 8 ÷ (2^4 ÷ 2) =

902 (Count up from 99 to 100 (+1) and from 100 to 1001 (+901). The answer is the sum of 901 and 1.)

Subtract: 1001 − 99 =

7,675.6

Subtract: 8,674.5 − 998.9 =

5/12 (If there are 48 total, and 28 study French, then 20 study Spanish. The ratio of 20 to 48 = 20/48 = 10/24 = 5/12.)

There are 48 students studying foreign language at the community college. If the only two foreign languages offered are French and Spanish, and 28 students are studying French, which of the following represents the ratio of students studying Spanish to the total number of foreign language students?

4,394 (If 34% of the marbles are white, then 66% must be black. (0.66)(6,657) = 4,393.62)

There are 6,657 marbles in a jar. Approximately 34% are white, and the rest are black. How many black marbles are there?

tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths (Use these place values to line up addition and subtraction problems.)

What are the place values from largest to smallest for six places to the right of the decimal? (tenths to millionths /6 )

1, 5, 10, 50, 100, 500, 1000

What do the Roman Numerals I, V, X, L, C, D, and M represent?

45.50 ( part/whole = %/ 100 ) (Alternatively, directly multiplying 65 by 0.7 will yield the same result.)

What is 70% of 65?

100 Celsius (The boiling point of water is 100° Celsius or 212° Fahrenheit. The freezing point of water is 0° Celsius or 32° Fahrenheit)

What is the boiling point of water?

1/6

What is the reciprocal of 6?

one thousandth, one hundredth, one thousand

What values do the prefixes: milli-, centi-, and kilo- indicate?

0.09% (In order to convert a decimal to a percent you need to move the decimal point two places to the right and add the percent symbol. This is equivalent to dividing the original value by 100.)

Which of the following is equivalent to 0.0009?

45%

Which of the following percentages is equal to 0.45?

125%

Which of these percentages equals 1.25?

MCMVI (n Roman Numerals: M=1000, D=500, C=100, L=50, X=10, V=5, I=1. You must treat ones, tens, hundreds, and thousands as separate items. A smaller item in front of a larger item indicates subtraction. 1000=M 900= CM 6=VI)

Write the number 1906 in Roman numerals.

25 mL

You have orders to give a patient 20 mg of a certain medication. The medication is stored 4 mg per 5-mL dose. How many milliliters will need to be given?

7/15 cups

You need 4/5 cups of water for a recipe. You accidentally put 1/3 cups into the mixing bowl with the dry ingredients. How much more water in cups do you need to add?

132.85

Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens are purchase in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for 12.95. How much will purchasing these products cost?