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Ratios 7th Grade Math February, 2011 A ___________ is a comparison of two numbers by division. A ratio must be expressed in __________ . Example #1: There are approximately 600 students at Lewisburg School. There are 30 teachers. What is the student to teacher ratio at Lewisburg School? 600/30 or 20/1 3 ways to write a RATIO! There were 6 chocolate donuts in the box of 12 donuts. 6 Part to Whole = 12 1 = 2 ** This can be expressed as: ** 1 1:2 1 to 2 2 ALL THREE OF THESE MEAN ~ 1 CHOCOLATE DONUT FOR EVERY 2 DONUTS. Equivalent Ratios Two ratios are the same when put in simplest form. Example – Are these two ratios equivalent?: $4 for every 16 ounces $4/16 oz = $10 for every 40 ounces $10/40 oz = These two ratios are equivalent!! Choose a partner and take turns taking each others pulse for 2 minutes. 1. Count the number of beats for each of you. 2. Write the ratio beats to minutes as a fraction. 1st block A ___________ is a ratio that compares two different kinds of units. Example: Heartbeat example Two Units = heartbeats and minutes A ____________ is a ratio that is simplified so that it has a denominator of ONE unit. Examples: 1. I made $300 for 6 hours of work. Write the unit rate. 300/6 = 50/1 2. We drove 220 miles on 8 gallons of gas. Write the unit rate 220/8 = 27.5/1 How to calculate unit rate? Easiest way is to divide BOTH the numerator AND the denominator by the denominator. Example #1: $ 15 3 pounds 15 3 33 $5 1 pound How to calculate unit rate? Easiest way is to divide BOTH the numerator AND the denominator by the denominator. Example #2: 220 heartbeats 4 min utes 220 4 44 55 heartbeats 1 min ute Common Unit Rates Rate Unit Rate Common Unit Rates Rate Unit Rate Number of Miles 1 hour Miles per hour Number of Miles 1 gallon Miles per gallon Number of Dollars Price per pound 1 pound Number of Dollars 1 hour Dollars per hour Different Types of Ratios Different Types of Ratios Ratios Comparing Same Measures Part/Whole (Fraction) Comparing Different Type of Measures Part/Part Rate Different Types of Ratios Part/Whole Examples Ratio Part/Part Examples Ratio Rate Examples Number of red roses to number of flowers in bouquet Number of red roses to number of yellow roses Number of roses per bouquet Number of footballs to number of balls in gym supply Number of footballs to number of soccer balls Number of footballs per class Number of points earned to number of points possible Number of points earned to the number of points not earned Number of points earned per pupil Number of girls to number of student in class Number of girls to number of boys in class Number of students per teacher Rate Different Types of Ratios Part/Whole Examples Ratio Part/Part Examples Ratio Rate Examples Rate Number of red roses to number of flowers in bouquet 6/24 Number of red roses to number of yellow roses 6 to 18 Number of roses per bouquet 12:1 Number of footballs to number of balls in gym supply 5/25 Number of footballs to number of soccer balls 5 to 8 Number of footballs per class 5:5 Number of points earned to number of points possible 80/100 Number of points 80 to 20 earned to the number of points not earned Number of points earned per pupil 1140:15 or 76:1 Number of girls to number of student in class 14/22 Number of girls to number of boys in class Number of students per teacher 22:1 14 to 8 Grocery Store Comparison – UNIT RATE! Four Products: Find the best price!! Let’s try together: http://math.rice.edu/~lanius/proportions/rate.html Practice Small Group: Number your paper from 1-12 Deck of cards LEVEL 0: INDIVIDUAL Deal out cards evenly to each player Answer that problem on your paper Rotate the card (clockwise) to your partner Continue until you’ve answered all cards LEVEL 1: PARTNERS Check your answers with your partners Practice Practice Problems: Glencoe – Rates and Ratios Rotate Problems through groups (5-10 minutes) each