Lesson 12: Ratios of Fractions and Their Unit Rates Date: 7/23/15 S.49 © 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 Unported License. 7•1 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 12: Ratios of Fractions and Their Unit Rates Classwork During this lesson, you are remodeling a room at your house and need to figure out if you have enough money. You will work individually and with a partner to make a plan of what is needed to solve the problem. After your plan is complete, then you will solve the problem by determining if you have enough money. Example 1: Time to Remodel You have decided to remodel your bathroom and install a tile floor. The bathroom is in the shape of a rectangle and the floor measures 14 feet, 8 inches long by 5 feet, 6 inches wide. The tiles you want to use cost $5 each, and each tile covers 4 ! ! square feet. If you have $100 to spend, do you have enough money to complete the project? Make a Plan: Complete the chart to identify the necessary steps in the plan and find a solution. What I Know What I Want to Find How to Find it Compare your plan with a partner. Using your plans, work together to determine how much money you will need to complete the project and if you have enough money.
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Lesson 12: Ratios of Fractions and Their Unit Rates Date: 7/23/15
S.49
© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported License.
7•1 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 12: Ratios of Fractions and Their Unit Rates
Classwork During this lesson, you are remodeling a room at your house and need to figure out if you have enough money. You will work individually and with a partner to make a plan of what is needed to solve the problem. After your plan is complete, then you will solve the problem by determining if you have enough money.
Example 1: Time to Remodel
You have decided to remodel your bathroom and install a tile floor. The bathroom is in the shape of a rectangle and the floor measures 14 feet, 8 inches long by 5 feet, 6 inches wide. The tiles you want to use cost $5 each, and each tile covers 4 !
! square feet. If you have $100 to spend, do you have enough money to complete the project?
Make a Plan: Complete the chart to identify the necessary steps in the plan and find a solution.
What I Know What I Want to Find How to Find it
Compare your plan with a partner. Using your plans, work together to determine how much money you will need to complete the project and if you have enough money.
Lesson 12: Ratios of Fractions and Their Unit Rates Date: 7/23/15
S.50
© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported License.
7•1 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM
Exercises 1-‐2
1. Which car can travel further on 1 gallon of gas?
Blue Car: travels 18 !! miles using 0.8 gallons of gas
Red Car: travels 17 !! miles using 0.75 gallons of gas
2. Automatic pitching machines throw balls to a batter to practice eye-‐hand coordination. The machine continuously dispenses 9 baseballs into a feeder that empties its contents every 2 !
! minutes. Edin wants to
practice hitting for 10 minutes. What is the unit rate in balls per minute that the pitching machine dispenses balls? Use the unit rate to determine the number of swings Edin can take during the 10 minute interval if he swings once at every ball.
Lesson 12: Ratios of Fractions and Their Unit Rates Date: 7/23/15
S.51
© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported License.
7•1 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson Summary
A fraction whose numerator or denominator is itself a fraction is called a complex fraction.
Recall: A unit rate is a rate, that is expressed as 𝑨𝑩 units of the first quantity per 𝟏 unit of the second quantity for
two quantities 𝑨 and 𝑩.
For example: If a person walks 𝟐 𝟏𝟐 miles in 𝟏 𝟏𝟒 hours at a constant speed, then the unit rate is
𝟐𝟏𝟐𝟏𝟏𝟒=
𝟓𝟐𝟓𝟒
∙ 𝟒𝟓 𝟒𝟓
=𝟒𝟐𝟏= 𝟒
𝟐= 𝟐 𝒐𝒓
𝟐𝟏𝟐𝟏𝟏𝟒=
𝟓𝟐𝟓𝟒
= 𝟓
𝟐∙ 𝟒𝟓= 𝟐 . The person walks 𝟐 mph.
Model Problem The back of a box of pancake mix lists the ingredients and the quantity needed to make various amounts of pancakes. Anita notices that the ratio of the dry mix needed for 20-‐24 pancakes to the ratio of the dry mix needed for 30-‐36 pancakes is 2:3. This ratio has a value of !
!. Anita also noticed that the value of the ratio of
eggs and the value of the ratio of oil between the two batches are also !!. Is the value of the ratio of milk
between the two batches !!?
Solution:
1 122 14
=3294= 32 ÷
94 =
32 ∙49 =
1218 =
23
Yes, the value of the ratio of milk between the two different batches is !
!.
Pancake Ingredients
20-‐24
pancakes
30-‐36
pancakes
Dry Mix 2 𝑐𝑢𝑝𝑠 3 𝑐𝑢𝑝𝑠
Eggs 2 𝑒𝑔𝑔𝑠 3 𝑒𝑔𝑔𝑠
Milk 112 𝑐𝑢𝑝𝑠
2 !
! cups
Oil 4 𝑇𝑎𝑏𝑙𝑒𝑠𝑝𝑜𝑜𝑛𝑠 6 𝑇𝑎𝑏𝑙𝑒𝑠𝑝𝑜𝑜𝑛𝑠
Lesson 12: Ratios of Fractions and Their Unit Rates Date: 7/23/15
S.52
© 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-‐NonCommercial-‐ShareAlike 3.0 Unported License.
7•1 Lesson 12 NYS COMMON CORE MATHEMATICS CURRICULUM
Problem Set 1. You are getting ready for a family vacation. You decide to download as many movies as possible before leaving for
the road trip. If each movie takes 1 !! hours to download and you downloaded for 5 !
! hours, how many movies did
you download?
2. The area of a blackboard is 1 !! square yards. A poster’s area is !
! square yards. Find the unit rate and explain, in
words, what the unit rate means in the context of this problem. Is there more than one unit rate that can be calculated? How do you know?
3. A toy jeep is 12 !! inches long while an actual jeep measures 18 !
! feet long. What is the value of the ratio of the
length of the toy jeep to the length of the actual jeep? What does the ratio mean in this situation?
4. !! cup of flour is used to make 5 dinner rolls.
a. How much flour is needed to make one dinner roll?
b. How many cups of flour are needed to make 3 dozen dinner rolls?
c. How many rolls can you make with 5 !! cups of flour?
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