6th Grade Math Textbook, Fundamentals

Lesson 6-5 for exercise sets. &KDSWHU 

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1.Jack and Li shared the driving during a trip across the country. For every

150 miles that Li drove, Jack drove 200 miles. If the total driving distance

was 2800 miles, how far did each person drive?

2.Discuss and Write Describe the meaning of a part-to-whole ratio.

Pat mixes 5 quarts yellow, 2 quarts orange, and 1 quart white paint. If she wants

to make 16 quarts of this mixture, how many quarts of each color does she need?

1

A proportion can compare parts to parts or parts to the whole quantity.

Method 3 Use Proportions

• Find the sum of the parts to find the total: 5  3  8


• Write a proportion with two part-to-whole ratios for both Leo and Bob.

So the proportions show that Leo received 20 votes and Bob received 12 votes.

Votes for Leo

Let lthe total number of votes for Leo.

Solve: 

5 • 32  8 l Cross multiply.



20 l

Check: Substitute 20 for l.

5 • 32 8 • 20

160  160 Tr u e

Votes for Bob

Let bthe total number of votes for Bob.

Solve: 

3 • 32  8 b Cross multiply.



12 b

Check: Substitute 12 for b.

3 • 32 8 • 12

96  96 Tr u e

part

whole

part

whole

Divide both sides by 8

to isolate b. Simplify.

Divide both sides by 8

to isolate l. Simplify.

96

8

12

1

8

8

1

1

8 b

8

1

1

160 l

8

20

1

b

32

3

8

?



12

32

?

(^38) 
?

?
(^58)  (^2032)
l
32
5
8
Let yquarts of yellow needed

5 • 16  8 y
80  8 y
10 y
part
whole
y
16
5
8
Let oquarts of orange
needed

2 • 16  8 o
32  8 o
4 o
part
whole
o
16
2
8
Let wquarts of white needed

1 • 16  8 w
16  8 w
2 w
part
whole
w
16
1
8
Check:Write and solve an equation.
Let qthe number by which each part is multiplied
to make the correct 16-quart mixture.
5 q 2 qq 16 8 q 16 q 2
So Pat needs 10 quarts of yellow, 4 quarts of orange,
and 2 quarts of white paint to make a 16-quart mixture.
white paint  2
yellow paint 5(2)  10
orange paint 2(2)  4