8-16th grade math

Ratios and Equivalent Ratios

Objective

• To read and write ratios and equivalent ratios

• Why? To think of ratios as comparisons of two quantities.

California State Standards NS 1.2 : Interpret and use ratios in different

contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (x/y, x to y, x:y)

MR 1.1: Analyze problems by identifying relationships …

Vocabulary• Ratio – A comparison of two quantities• 12 to 9, 12/9, 12:9

• Equivalent ratio– When both terms are multiplied or divided by a

number other than zero. Ratios that represent the same rate or make the same comparison.• 12/9 = 108/81 (x by 9)

How to Compare Ratios1) Cross multiply the

denominator of the first to the numerator of the second. Write the number on top. (IF ratio is written in non-fraction form, re-write into fraction form. Order MATTERS!)

2) Cross multiply the denominator of the second to the numerator of the first. Write the number on top.

3) Compare the two numbers.

14 912 6 84 10814 ↖ ↗ 912 ↗↖ 6

84 < 108

14 < 912 6

Another Way to Compare Ratios

• Make equivalent fractions.

• Compare numerators.• Check for

reasonableness.

14 912 6

14 1812 12

14 < 18

14 < 912 6

To Find the Missing Equivalent Ratio Number1. Cross multiply the

numerator and denominator of the two known numbers.

2. Divide by the last number.

3. Check your work. Does the answer seem reasonable.

4 = 129 X

9 x 12 = 108 27

4 = 129 27

1084

To Find the Missing Equivalent Ratio Number1. Look at the known

numerator and denominator. Decide what number to multiply or divide by to make the equivalence.

2. If ‘moving’ in the same direction, use the same operation as in Step 1.

3. If ‘moving’ in the opposite direction, use the opposite operation in Step 1.

3. Check your work. Does the answer seem reasonable.

4 = 129 X

4 → 12 (by x 3)9 → x 3 = 27

4 = 129 27-----------------------------------------------4 = 12X 27

4 → 12 (by x 3)27 ← ÷ 3 = 9

4 = 129 27

Try It!1) 5 : 8 ___ 15 : 24

2) 3 ____ 9 12 36

3) 4 ____ 16 6 20

4) 9 to 8 ____ 45 to 40

1) 5 = 15 8 24

2) 3 = 9 12 36

3) 4 ≠ 16 6 20

4) 9 = 45 8 40

Objective Review

• To read and write ratios and equivalent ratios

• Why? You can now think of ratios as comparisons of two quantities.

• A ratio is a comparison of two quantities. Order is important in writing a ratio.

Independent Practice

• Complete problems 6-14

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 15-19

• If still more time, work on Accelerated Math.