5-3 Solving Proportions

Transcription

1 Learn to solve proportions by using cross products.

2 5-3 Solving Insert Lesson Proportions Title Here cross product Vocabulary

3 The tall stack of Jenga blocks is 25.8 cm tall. How tall is the shorter stack of blocks? To find the answer you will need to solve a proportion. For two ratios, the product of the numerator in one ratio and the denominator in the other is a cross product. If the cross products of the ratios are equal, then the ratios form a proportion.

4 2 5 = = = 30 CROSS PRODUCT RULE In the proportion a = c, the cross products, b d a d and b c are equal. You can use the cross product rule to solve proportions with variables.

5 Additional Example 1: Solving Proportions Using Cross Products Use cross products to solve the proportion = m 5 15 m = m = 45 15m 15 = m = 3 The cross products are equal. Multiply. Divide each side by 15 to isolate the variable.

6 5-3 Insert Solving Lesson Proportions Title Here Try This: Example 1 Use cross products to solve the proportion. 6 7 = m 14 7 m = m = 84 7m 7 = 84 7 m = 12 The cross products are equal. Multiply. Divide each side by 7 to isolate the variable.

7 When setting up a proportion to solve a problem, use a variable to represent the number you want to find. In proportions that include different units of measurement, either the units in the numerators must be the same and the units in the denominators must be the same or the units within each ratio must be the same. 16 mi 4 hr = 8 mi x hr 16 mi 8 mi = 4 hr x hr

8 Additional Example 2: Problem Solving Application If 3 volumes of Jennifer s encyclopedia takes up 4 inches of space on her shelf, how much space will she need for all 26 volumes? 1 Understand the Problem Rewrite the question as a statement. Find the space needed for 26 volumes of the encyclopedia. List the important information: 3 volumes of the encyclopedia take up 4 inches of space.

9 Additional Example 2 Continued 2 Make a Plan Set up a proportion using the given information. 3 volumes 4 inches = 26 volumes x Let x be the unknown space.

10 3 Additional Example 2 Continued Solve 3 4 = 26 x 3 x = x = 104 3x 3 = x = She needs Write the proportion. The cross products are equal. Multiply. Divide each side by 3 to isolate the variable. inches for all 26 volumes.

11 4 Additional Example 2 Continued Look Back 3 4 = = = 104 The cross products are equal, so answer is the

12 Try This: Example 2 John filled his new radiator with 6 pints of coolant, which is the 10 inch mark. How many pints of coolant would be needed to fill the radiator to the 25 inch level? 1 Understand the Problem Rewrite the question as a statement. Find the number of pints of coolant required to raise the level to the 25 inch level. List the important information: 6 pints is the 10 inch mark.

13 Try This: Example 2 Continued 2 Make a Plan Set up a proportion using the given information. 6 pints 10 inches = x 25 inches Let x be the unknown amount.

14 3 Try This: Example 2 Continued Solve 6 10 = x x = x = x 10 = x = 15 Write the proportion. The cross products are equal. Multiply. Divide each side by 10 to isolate the variable. 15 pints of coolant will fill the radiator to the 25 inch level.

15 4 Try This: Example 2 Continued Look Back 6 10 = = = 150 The cross products are equal, so 15 is the answer.

16 5-3 Solving Insert Lesson Proportions Title Here Lesson Quiz: Part 1 Use cross products to solve the proportion = 45 t 2. x 9 = = r n 10 = 28 8 t = 36 x = 3 r = 24 n = 35

17 5-3 Solving Insert Lesson Proportions Title Here Lesson Quiz: Part 2 5. Carmen bought 3 pounds of bananas for $1.08. June paid $ 1.80 for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy? 5 pounds

18 Homework 5-3 Worksheet Study for 5-1 to 5-4 quiz Tuesday