1. Proportions
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2. Warm Up Solve each problem. Round to the nearest tenth if necessary.
1). Joe walked 𝟓 𝟕 of a mile in 𝟑 𝟒 of an hour. How far will he walk in one hour?
2). Kim bought 4 pounds of fudge for $ How much did one pound of fudge cost?
3). Ike used 𝟐 𝟑 of a cup of sugar for 𝟏 𝟐 cake. How much sugar would he use for a whole cake?
𝟐𝟎 𝟐𝟏 𝒎𝒑𝒉
$3.64
𝟏 𝟏 𝟑 cup of sugar

3. Proportions Flippable

4. Proportion- two ratios that are equal.
If two ratios are equivalent, they are said to be proportional or in proportion.
How to determine if two ratios are equivalent:
Simplify each ratio to see if they are the same.
Find the common denominator for each ratio and see if they are the same.
Find the cross products and see if they are same.

5. Example 1: Are the two ratios proportional? 𝟐 𝟕 , 𝟔 𝟐𝟏
Yes, they both simplify to 2/7
No, they do not simplify to the same fraction.

6. Solving Proportions
To solve a proportion you set the two fractions equal to each other, cross-multiply, and solve the resulting equation.
Example 3: Find the value of x.
𝟓 𝟖 = 𝒙 𝟐𝟒
Example 4: Find the value of x.
𝒙 𝟔 = 𝟖 𝟏𝟎
x = 15
X=4.8

7. Tell if the ratios are proportional.
Practice
Tell if the ratios are proportional.
1). 𝟏𝟔 𝟐𝟎 𝒂𝒏𝒅 𝟒 𝟓 2). 𝟒 𝟗 𝒂𝒏𝒅 𝟏𝟏 𝟔
Solve each proportion.
3). 𝒙 𝟏𝟒 = 𝟏𝟔 𝟐𝟖 4). 𝟒 𝟕 = 𝒙 𝟏𝟓.𝟒
5). 𝟏.𝟓 𝒙 = 𝟑.𝟕𝟓 𝟏𝟐.𝟓
yes no
𝐗=𝟖
X=8.8
X=5

8. Closure
Tell if the following ratios are proportional. Explain why or why not.
7 boys to every 13 girls.
2184 Boys to every 4056 girls.
Yes, they are proportional, 2184 to 4056 is 7 to 13 when simplified.