Bellwork Grab a book and read silently

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Bellwork Grab a book and read silently If you were absent, turn in your calendar and schedule a test make-up

Ratios and proportions

Ratios compares two different quantities/units Ratio: part-part (# of boys and girls) part-whole (# of boys and class) whole-whole (# of freshmen and sophomores) Ratios can be expressed three ways: fraction bar ( 𝑏𝑜𝑦𝑠 𝑔𝑖𝑟𝑙𝑠 ) colon (boys:girls) “to” (boys to girls)

Examples What is the ratio of boys to girls in Ms. Staggs class? What is the ratio of students to desks? What is the ratio of windows to whiteboards?

Proportions Proportions: two ratios that are equal to each other Examples: 400 𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠 1 𝑏𝑢𝑟𝑔𝑒𝑟 = 1200 𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠 3 𝑏𝑢𝑟𝑔𝑒𝑟𝑠 110 𝑚𝑖𝑙𝑒𝑠 2 ℎ𝑜𝑢𝑟𝑠 = 165 𝑚𝑖𝑙𝑒𝑠 3 ℎ𝑜𝑢𝑟𝑠 two ratios that are equal to each other

Solving Proportions Method 1: Look for a pattern from side-to-side 7 5 = 𝑥 15 7(3) = x x = 21 *3

Solving Proportions Method 2: Look for a pattern from top-to-bottom 28 𝑦 = 36 9 y = 7 y(4) = 28 *4

Solving Proportions Method 3: Cross-multiply and solve *Can ONLY cross-multiply if there is an equal sign* 4 𝑑 = 10 15 4(15) = d(10) 60 = 10d 10 10 6 = d

On Your Own Solve the following (look for patterns or cross-multiply): 4 z = 16 24 8 g = 2 3

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