 # Ratios and Rates. ratio – is a comparison of two numbers or more values. Example: 1:3.

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Ratios and Rates

ratio – is a comparison of two numbers or more values. Example: 1:3

E XAMPLE : I F 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 (T HERE ARE 3 GIRLS FOR EVERY ONE BOY ) ) 1 : 3 3 : 1

Ratios and Rates The 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 Rates Ratios can be written in 3 different ways. 3 to 1 3 : 1 3/13/1 red to black

Ratios and Rates Ratios can show comparisons between: a) part to part red to green 1 to 2 green to red 2 to 1

Ratios and Rates Ratios can show comparisons between: b) part to whole red to whole 1 to 3 green to whole 2 to 3

Ratios and Rates Ratios 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 1/81/8

Ratios and Rates Compare all shapes to trapezoid 8 to 18 : 1 8/18/1

Ratios and Rates Compare pentagons to hexagons 2 to 32 : 32 : 3 2/32/3

N OW, SOME EXERCISES

Ratios and Rates Give each ratio in three forms. 8 roses out of 24 flowers 3 dogs out of 12 animals 3 : 12

S OLVE 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. W HAT IS THE RATIO OF GIRLS TO BOYS ?

G IVE EACH RATIO BY SHOWING COMPARISONS BETWEEN : Part to part Part to whole Whole to part

Equivalent Ratios You can have equivalent ratios by dividing or multiplying the numerator and denominator by the same value ÷ 8 = 4 : 5 is the same as 4 ×2 : 5 ×2 = 8 : 10

E XAMPLE : 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 = 79 miles per hour miles hours miles hours

Ratios and Rates Express each ratio as a rate. 5 inches of rain in 30 days = inch of rain per day 120 words in 3 minutes = 40 words per minute words per minute ÷ 5