1. Solving Proportions

2. Unit 5 – Identifying and Writing Proportions

3. Vocabulary
Proportion – An equation stating that two ratios are equivalent.
example: = 6 12
Extremes of a Proportion – The first and last terms in the ratios of a proportion.
example: = 6 12
the numbers 2 and 12 are the extremes
Means of a Proportion – The two middle terms in the ratios of a proportion.
the numbers 4 and 6 are the extremes

4. Determine Whether the Ratios are Proportional
Common Multiplier
Reducing Ratios
Cross Products
2 7 , 6 21
lowest terms
6 21 ÷ 3 3 = 2 7
Yes, 𝑎𝑛𝑑 form a proportion because both ratios reduce to be the same.
2 7 , 6 21
2 7 , 6 21 ×3
×42
×42 ×3
Yes, 𝑎𝑛𝑑 form a proportion because the product of the means and extremes are the same.
Yes, 𝑎𝑛𝑑 form a proportion because both the top terms and bottom terms can be multiplied by the same number.

5. Determine Whether the Ratios are Proportional - Guided Practice
Reducing
Ratios
Common Multiplier
Cross Products
, YES , 3 15 NO
, NO , 3 4 YES
, 10 13 NO
, 24 40
YES

6. Creating Proportions Example
Find a ratio equivalent to each ratio. Then use the ratios to write a proportion.
𝟓 𝟏𝟓
Step 1 – make a ratio that is equivalent to the given ratio. You can multiply or divide by any number as long as you use the same procedure for the numerator and denominator.
5 15 × 2 2 = 10 30
Step 2 – write the two ratios as a proportion.
5 15 = 10 30

7. Creating Proportions Guided Practice
Find a ratio equivalent to each ratio. Then use the ratios to write a proportion.
12 15
Possible Answer: = 24 30
Possible Answer: = 20 50
Possible Answer: = 11 15

8. Comparing Ratios in a Table
Use the data in the table to determine whether the ratios of oats to water are proportional for both serving sizes.
Oats Water →
Yes, the servings are proportional.
Servings of Oatmeal
Cups of Oats
Cups of Water 8 2 4 12 3 6 12 12