Mastering Ratios and Proportions

What is a ratio?

• A comparison of two numbers by addition
• A comparison of two numbers by multiplication
• A comparison of two numbers by subtraction
• A comparison of two numbers by division

A bag contains green chips and red chips. The ratio of green chips to purple chips in the bag is 4 to 5. Which of the following statements could be true?

• The bag could contain only red chips.
• There are exactly 20 green chips and 25 purple chips

• The bag could contain 4 purple chips and 5 green chips

• The bag could contain 4 blue chips and 5 purple chips

Answer explanation

NOTE:

Remember only green chips and purple chips are in the bag.

also remember that green chips MUST be less than purple chips.

No other colors must be in the bag.

Which of the following ratios is equivalent to 6:8?

• 3:4

• 9:12

• 12:16

• All of the above

Answer explanation

Which of the following ratios is equivalent to 6:8?

You may use your calculator method and

divide 6 by 8 to get a unit value.

6/8 = 0.75

now divide the other ratios to see which give you the same 0.75

3/4 = 0.75

9/12 = 0.75

12/16 = 0.75

this means all the ratios are equivalent.

The answer is ALL THE ABOVE.

The ratio of blue marbles to red marbles in a bag is 2:3. If there are 18 red marbles, how many blue marbles are there?

• 12

• 24

• 30

• 36

Answer explanation

What is the relationship between red marbles (3) and 18?

18 divide by 3 is equal to 6. Therefore the relationship is 6 because 3 x 6 = 18

therefore 2 x 6 = 12

This means that there are 12 blue marbles in the bag. The answer is 12.

you may also use the BUTTERFLY strategy to find the missing quantity.

2/3 = n / 18

n x 3 = 18 x 2

3n = 36

divide both sides by 3

n = 12

If the ratio of cats to dogs in a pet shop is 3:4, how many cats are there if there are 20 dogs?

• 15

• 25

• 30

• 35

A car travels 300 miles using 10 gallons of gas. What is the unit rate of miles per gallon?

• 30 miles/gallon

• 20 miles/gallon

• 25 miles/gallon

• 35 miles/gallon

Answer explanation

A car travels 300 miles using 10 gallons of gas. What is the unit rate of miles per gallon?

since you are asked to find (per) gallon, you must divide the miles by the GALLON.

300 MILES / 10 GALLON

300/10 = 30 miles per 1 gallon

or 30 miles/gallon

If 5 pencils cost $1.25, how much would 8 pencils cost?

• $1.00

• $2.00

• $2.50

• $2.80

Answer explanation

If 5 pencils cost $1.25, how much would 8 pencils cost?

Find the cost of 1 pencil (unit rate) by dividing the amount of money by the amount of pencils.

$1.25 / 5 = $0.25

The cost for 1 pencil is $0.25

8 pencils is equal to 8 x $0.25 = $2

therefore 8 pencils cost $2

A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to make a half batch, how many cups of flour do you need?

• 1 cup

• 1.5 cups

• 2 cups

• 3 cups

If a map scale shows that 1 inch equals 100 miles, how many miles would 3.5 inches represent?

• 250 miles

• 300 miles

• 350 miles

• 400 miles

A school has a student to teacher ratio of 20:1. If there are 480 students, how many teachers are there?

• 20

• 24

• 26

• 28

Answer explanation

A school has a student to teacher ratio of 20:1. If there are 480 students, how many teachers are there?

What is the relationship between 20 and 240?

480/20 = 24 or 20 x 24 = 480

the relationship is 24

therefore 1 teacher x 24 = 24 teachers