Understanding Proportions

What we know…. Ratios are useful ways to compare two quantities. To compare the number of shaded circles to the number of total circles we can use a ratio of 2 to 5, which we often write in the fraction form,. 2 5

The next step is to compare ratios For example, Figure 1 below shows two out of the three circles shaded, and Figure 2 below shows four out of the six circles shaded.

Although Figure 2 has more circles, the ratio of shaded circles to total circles is the same. That is, =. A statement such as this, stating that one ratio is equal to another, is called a proportion

How do ratios and proportions differ? A ratio is a comparison of two quantities by division. A proportion is a statement that two ratios are equal to one another. A proportion is an equation.

To identify proportions… 1) Write each ratio as a fraction. 2) Determine whether the numerator and denominator of the first ratio can both be multiplied (or divided) by the same number to arrive at the second ratio.

Example 1… Are these rates proportional? 24 oz costs $3; 48 oz costs $9 No, because the number of ounces is multiplied by 2, and the cost is multiplied by oz $3 48 oz $9 X2 x3

Example 2… Are these rates proportional? 24 oz costs $3; 72 oz costs $9 Yes, because both the number of ounces and the cost were multiplied by oz $3 72 oz $9 X3 x3

Practice, practice, practice… Determine if each pair of ratios or rates form a proportion. 1) $3 for 2 cookies; $9 for 6 cookies Yes, because both the cost and the number of cookies were multiplied by 3 2) 6 out of 10 students have ; 30 out of 40 students have No, because the number of students that have is multiplied by 5, and the total number of students is multiplied by 4.

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