A ratio is a comparison of two quantities. Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio. 7575 Notes 12 inches = 1 foot 3.

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Presentation transcript:

A ratio is a comparison of two quantities. Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio Notes 12 inches = 1 foot 3 feet = 1 yard 36 inches = 1 yard

Additional Example 1: Writing Ratios in Simplest Form Write the ratio 15 bikes to 9 skateboards in simplest form The ratio of bikes to skateboards is, 5:3, or 5 to 3. = 15 ÷ 3 9 ÷ 3 Write the ratio as a fraction. = = Simplify bikes skateboards

Check It Out! Example 1 Write the ratio 24 shirts to 9 jeans in simplest form The ratio of shirts to jeans is, 8:3, or 8 to 3. = shirts jeans 24 ÷ 3 9 ÷ 3 Write the ratio as a fraction. = = Simplify. 8383

Practice 15 cows to 25 sheep 24 cars to 18 trucks 30 Knives to 27 spoons

When simplifying ratios based on measurements, write the quantities with the same units, if possible.

Write the ratio 3 yards to 12 feet in simplest form. First convert yards to feet. 9 feet 12 feet = 3 yards 12 feet 3434 = 9 ÷ 3 12 ÷ 3 = There are 3 feet in each yard. Additional Example 2: Writing Ratios Based on Measurement 3 yards = 3 ● 3 feet = 9 feet Multiply. Now write the ratio. Simplify. The ratio is, 3:4, or 3 to

Write the ratio 36 inches to 4 feet in simplest form. First convert feet to inches. 36 inches 48 inches = 36 inches 4 feet 3434 = 36 ÷ ÷ 12 = There are 12 inches in each foot. Check It Out! Example 2 4 feet = 4 ● 12 inches = 48 inchesMultiply. Now write the ratio. Simplify. The ratio is, 3:4, or 3 to

Practice 4 feet to 24 inches 3 yards to 12 feet 2 yards to 20 inches

Ratios that make the same comparison are equivalent ratios. Equivalent ratios represent the same point on the number line. To check whether two ratios are equivalent, you can write both in simplest form. Notes

Additional Example 3: Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent B. and A. and 2 18 Since, the ratios are equivalent = = 3 ÷ 3 27 ÷ = 1919 = 2 ÷ 2 18 ÷ = 4545 = 12 ÷ 3 15 ÷ = 3434 = 27 ÷ 9 36 ÷ = Since, the ratios are not equivalent  3434

Practice

Lesson Quiz: Part I Write each ratio in simplest form tigers to 44 lions 2. 5 feet to 14 inches Possible answer:, Possible answer:, Find a ratios that is equivalent to each given ratio

Lesson Quiz: Part II 7. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. Are the ratios of poured juice to starting amount of juice equivalent? and ; yes, both equal =; yes Simplify to tell whether the ratios are equivalent. and and  ; no