 Ratios Mathematical Relationships

IS IT COLD IN HERE?

LET’S WARM UP How would you demonstrate or write the following pictures in quantitative or numerical form?

 What fraction is black of the total square?  Yellow?  Red?  Green?  Purple?

Objective  By the end of today, seventh grade mathematicians will be able to compare two quantities using ratios and rates.

Ratio  Compares two or more groups of things  9 out of 10 dentists  1 in 1,000,000 people  3 jellyfish to 1 chicken  What others can you think of? Where else have you seen ratio in your own life?

Ratio Note: Order is important! Which would you prefer?  1 in 1,000,000 chance of being struck by lightning  1,000,000 to 1 chance of being struck by lightning

Writing Ratios  James has a 4 in 8 chance of winning a piece of candy. What other ways could you write this ratio? 1. With words: 4 in 8 2. With a colon: 4:8 3. As a fraction: 4/8 4. Simplify it: 4 to 8 = 1 to 2 4:8 = 1:2 4/8 = 1/2 Watch out! A ratio is not a fraction. However, it can look like one, and we simplify it in the same way.

Ratio Example  In a pack of 9 pieces of gum, there are 3 cherry flavored pieces. Write each ratio in simplest terms: 1. Cherry flavored gum to all gum 2. All gum to cherry flavored gum 3. Cherry flavored gum to all other flavors Answers 1. 1:3 2. 3:1 3. 1:2 Remember: Ones are important in ratios. If you end up with a fraction like 3/1, you need to keep the 1 rather than just writing it as 3.

Ratio Example  Using the space in your notes, write down as many ratios as you can think of in our classroom.  Example: number of boys to number of girls

Equivalent Ratios Which school has the largest ratio of boys to girls?  210 boys to 560 girls?  3 boy to 8 girls?  15 boys to 40 girls? They’re all the same!

Equivalent Ratios  Find two equivalent ratios for each of the following: 1. 3: to /7

WE DO  A pastry chef mixes 45 pounds of butter with 60 pounds of butter to make a large batch of desserts. What is the ratio between butter and flour, reduced to its lowest form?

 In the last 30 days we had 14 rainy days. What is the simplified ratio of rainy days to total days?  What is the simplified ratio of sunny days to total days?  What is the simplified ratio of rainy days to sunny days? YOU DO

 Rates Mathematical Relationships

Rates  A rate compares two things with different units. 105 miles in 3 hours Unit #1 = miles (distance) Unit #2 = hours (time)

Unit Rate  A unit rate is where the denominator is miles 3 hours 35 miles 1 hour = We normally see this written as 35 miles per hour

Finding Unit Rate  Goal: End up with 1 as our denominator For every rate you could ever find, this means you divide the numerator and the denominator by the denominator. 105 miles 3 hours 35 miles 1 hour = ÷ 3 Think about it! Why do we need to divide the numerator by the same number?

YOU DO Over the vacation, Mason read a lot of books. He was able to read 8 pages every 4 minutes. How many pages could he read in one minute?

Using Unit Rates  Using his skateboard, Javontae can travel 8 miles in 2 hours.  What is the unit rate of speed for his skateboard?  Answer: 4 miles per hour  At this rate, how far could he travel in 5 hours (assuming he didn’t have to stop to take a break)?  Answer: 20 miles

Using Unit Rates  Using his skateboard, Nathan can travel 10 miles in 3 hours.  What is the unit rate of speed for his skateboard?  Answer: 3.33 miles per hour  Who is faster? Javonate or Nathan?  Answer: Javontae

YOU DO  Mrs. Gupta’s first job was to work at a janitor during the summer. At this job she made about $80 each day. If she worked for 8 hours each day, how much did she make an hour?   If Ms. Gupta worked for 220 hours over the summer at this job, how much money did she make by the end?

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