Ratios and Rates.

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Presentation transcript:

Ratios and Rates

Unit 4 – Rates & Unit Rates

Vocabulary Rate – A ratio that compares two quantities measured in different units. Unit Rate – a rate which is being compared to 1.

Rate vs. Unit Rate Example Decide if each situation is a rate or unit rate. Lucas drinks 8 glasses of water a day. Unit Rate 2. Peter bought 3 oranges for $5. Rate 3. Jenny can type 280 words in 4 minutes. 4. Mrs. Robinson checks 6 essays in one hour. 5. Lara plays 16 tournaments a year.

Calculating Unit Rates Using Fractions Example Jim walks 900 meters in 5 minutes. At what rate does he walk? Step 1: Write a word ratio. Which ever word will eventually become a 1 should be the denominator. 𝐦𝐞𝐭𝐞𝐫𝐬 𝐦𝐢𝐧𝐮𝐭𝐞𝐬 Step 2: Use the word ratio to write a rate. 𝐦𝐞𝐭𝐞𝐫𝐬 𝐦𝐢𝐧𝐮𝐭𝐞𝐬 → = 𝟗𝟎𝟎 𝟓 Step 3: Divide the numerator and denominator by the denominator so that you end up with a denominator of 1. 𝐦𝐞𝐭𝐞𝐫𝐬 𝐦𝐢𝐧𝐮𝐭𝐞𝐬 → = 𝟗𝟎𝟎 𝟓 ÷ 𝟓 𝟓 = 𝟏𝟖𝟎 𝟏 Step 4: Use the unit rate to write an answer. Jim walks 180 meters per minute

Calculating Unit Rates Using Bar Models Example Jim walks 900 meters in 5 minutes. At what rate does he walk? Step 1: Draw a bar model to represent the story in the question. Step 2: Write the equation from the information given in the bar models. Step 3: Solve for the value of a single box Jim walks 180 meters per minute

The plumber earns $45 per hour Calculating Unit Rates Using Fractions Example A plumber earns $180 for 4 hours of work. How much does the plumber earn per hour? Step 1: Write a word ratio. Which ever word will eventually become a 1 should be the denominator. 𝐝𝐨𝐥𝐥𝐚𝐫𝐬 𝐡𝐨𝐮𝐬 Step 2: Use the word ratio to write a rate. 𝐝𝐨𝐥𝐥𝐚𝐫𝐬 𝐡𝐨𝐮𝐫𝐬 → = 𝟏𝟖𝟎 𝟒 Step 3: Divide the numerator and denominator by the denominator so that you end up with a denominator of 1. 𝐝𝐨𝐥𝐥𝐚𝐫𝐬 𝐡𝐨𝐮𝐫𝐬 → = 𝟏𝟖𝟎 𝟒 ÷ 𝟒 𝟒 = 𝟒𝟓 𝟏 Step 4: Use the unit rate to write an answer. The plumber earns $45 per hour

A plumber makes $45 per hour Calculating Unit Rates Using Bar Models Example A plumber earns $180 for 4 hours of work. How much does the plumber earn per hour? Step 1: Draw a bar model to represent the story in the question. Step 2: Write the equation from the information given in the bar models. Step 3: Solve for the value of a single box A plumber makes $45 per hour