Ratios and Rates

Unit 4 – Comparing Quantities

Vocabulary Ratio – a comparison of two or more numbers or quantities. It describes the relative sizes of the numbers or quantities. Example: 2:1 or 2 to 1 or 2 1 Term (of a ratio) – the numbers or quantities that are being compared in a ratio.

Writing Ratios Example Write each ratio in all three ways. Compare the number of apples to the number of pears. 𝒂𝒑𝒑𝒍𝒆𝒔 𝒑𝒆𝒂𝒓𝒔 →7 to 5, 7 : 5, 𝟕 𝟓 Compare the number of pears to the number of apples. 𝒑𝒆𝒂𝒓𝒔 𝒂𝒑𝒑𝒍𝒆𝒔 → 5 to 7, 5 : 7, 𝟓 𝟕 Compare the number of apples to the total pieces of fruit. 𝒂𝒑𝒑𝒍𝒆𝒔 𝒕𝒐𝒕𝒂𝒍𝒇𝒓𝒖𝒊𝒕 → 7 to 12, 7 : 12, 𝟕 𝟏𝟐

Writing Ratios Example Write each ratio in all three ways. Compare the number of pencils to the number of erasers. 𝑝𝑒𝑛𝑐𝑖𝑙𝑠 𝑒𝑟𝑎𝑠𝑒𝑟𝑠 → 3 to 8, 3 : 8, 𝟑 𝟖 Compare the number of erasers to the number of pencils. 𝑒𝑟𝑎𝑠𝑒𝑟𝑠 𝑝𝑒𝑛𝑐𝑖𝑙𝑠 → 8 to 3, 8 : 3, 𝟖 𝟑 Compare the number of erasers to the total number of supplies. 𝑒𝑟𝑎𝑠𝑒𝑟𝑠 𝑡𝑜𝑡𝑎𝑙𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑠 → 8 to 11, 8 : 11, 𝟖 𝟏𝟏

Writing Ratios Independent Practice Write each ratio in all three ways. Compare the number of saucers to the number of cups. 𝒔𝒂𝒖𝒄𝒆𝒓𝒔 𝒄𝒖𝒑𝒔 → 9:4, 9 to 4, 𝟗 𝟒 Compare the numbers of cups to the number of saucers. 𝒄𝒖𝒑𝒔 𝒔𝒂𝒖𝒄𝒆𝒓𝒔 → 4:9, 4 to 9, 𝟒 𝟗 Compare the total number of cups and saucers to the number of cups. 𝒕𝒐𝒕𝒂𝒍 𝒄𝒖𝒑𝒔 → 13:4, 13 to 4, 𝟏𝟑 𝟒

Writing Ratios in Word Problems Example There are 31 U.S. stamps and 24 foreign stamps in a collection. Use a model to help you find the ratio. Find the ratio of the number of U.S. stamps to the number of foreign stamps. 𝑼𝑺 𝑭𝒐𝒓𝒆𝒊𝒈𝒏 → 31 to 24 (it didn’t say to write all three so pick the way you prefer) Find the ratio of the number of U.S. stamps to the total number of stamps. 𝑼𝑺 𝑻𝒐𝒕𝒂𝒍 → 31 to 55

Writing Ratios in Word Problems Example Of the 100 people at a concert, 67 are adults and the rest are children. Use a model to help you find the ratio. Find the ratio of the total number of people to the number of adults. 𝒕𝒐𝒕𝒂𝒍 𝒂𝒅𝒖𝒍𝒕𝒔 → 100 to 67 (it didn’t say to write all three so pick the way you prefer) Find the ratio of the number of adults to the number of children. 𝒂𝒅𝒖𝒍𝒕𝒔 𝒄𝒉𝒊𝒍𝒅𝒓𝒆𝒏 → 67 to 33

Writing Ratios in Word Problems Example The ratio of the number of girls to the number of boys at a movie is 5 : 4. Use a model to help you. What fraction of the children at the movie are girls? 𝐠𝐢𝐫𝐥𝐬 𝐭𝐨𝐭𝐚𝐥 → 𝟓 𝟗

Writing Ratios in Word Problems Independent Practice The ratio of the number of red highlighters to the number of blue highlighters is 2 : 3 Use a model to help you. What fraction of the highlighters are red? 𝐫𝐞𝐝 𝐭𝐨𝐭𝐚𝐥 → 𝟐 𝟓 What fraction of the highlighters are blue? 𝐛𝐥𝐮𝐞 𝐭𝐨𝐭𝐚𝐥 → 𝟑 𝟓