Ratios and Rates

Ratios and Rates

ratio – is a comparison of two numbers or more values.

Example:

1:3

EXAMPLE:

IF WE COMPARE THE NUMBER OF GIRLS WITH THE NUMBER OF BOYS

WE CAN SAY THAT:

THERE IS 1 BOY AND 3 GIRLS , SO:

(FOR EVERY ONE BOY THERE ARE 3 GIRLS)

OR

(THERE ARE 3 GIRLS FOR EVERY ONE BOY)

)

1 : 3

3 : 1

Ratios and RatesThe order of the numbers in a ratio should match the order of the words in a ratio.

apples to oranges

2 to 3

Ratios and RatesRatios can be written in 3

different ways.

3 to 1

3 : 1

3/1

red to black

Ratios and RatesRatios can show comparisons

between:

a) part to partred to green

1 to 2green to red

2 to 1

Ratios and RatesRatios can show comparisons between:

b) part to whole

red to whole

1 to 3

green to whole

2 to 3

Ratios and RatesRatios can show comparisons between:c) whole to part

whole to red

3 to 1

whole to green

3 to 2

Ratios and Rates

Compare octagon to all shapes

1 to 8 1 : 8

1/8

Ratios and RatesCompare all shapes to trapezoid

8 to 1 8 : 1 8/1

Ratios and RatesCompare pentagons to hexagons

2 to 3 2 : 3 2/3

NOW, SOME EXERCISES

Ratios and Rates

Give each ratio in three forms.8 roses out of 24 flowers

24

8

3 dogs out of 12 animals

3 : 12

SOLVE

1) In the following diagram

What is the ratio of orange squares to white squares?

2. WHAT IS THE RATIO OF GREEN BALLS TO RED BALLS?

3. A CLASS OF 32 STUDENTS HAS 12 GIRLS. WHAT IS THE RATIO OF GIRLS TO BOYS?

GIVE EACH RATIO BY SHOWING COMPARISONS BETWEEN :

Part to part

Part to whole

Whole to part

Equivalent RatiosYou can have equivalent ratios by dividing or multiplying the numerator and denominator by by the same value

24

8 ÷ 8

÷ 8=

3

1

4 : 5 is the same as 4×2 : 5×2 = 8

: 10

EXAMPLE: A Recipe for pancakes uses 3 cups of flour

and 2 cups of milk. So the ratio of flour to milk is 3 : 2 To make pancakes for a LOT of people we

might need 4 times the quantity, so we multiply the numbers by 4:

3×4 : 2×4 = 12 : 8 In other words, 12 cups of flour and 8

cups of milk. The ratio is still the same, so the pancakes

should be just as yummy.

Rate – It is a ratio that compares different kinds of units by division to obtain a

unit rate or rate per unit.

Rate

To express a ratio as a rate per unit (1), write the ratio as a fraction and then divide the numerator by the denominator.

395 miles in 5 hours

5

395=

79 miles per hour

miles

hours 1

? miles

hours

Ratios and RatesExpress each ratio as a rate.5 inches of rain in 30 days

30

5=6

1inch of rain per day

120 words in 3 minutes

3

120=

40 words per minute1

? wordsper minute

÷ 5

÷ 5