6th Grade Math Textbook, Fundamentals

 &KDSWHU

6-4

Direct Proportion

Objective To understand and apply the concept of direct proportion

Tracy works at home reading and correcting manuscript
for a small local newsletter publisher. If she works for
5 hours, she earns $70. At that rate, how many hours must
she work to earn $630?

The amount Tracy earns depends directlyon the number
of hours she works.

To find how many hours she must work in order to earn
$630, write and solve a direct proportion.

Two quantities have a relationship when an increase or decrease

in one quantity causes the same kind of changein the other quantity.

Let h the number of hours Tracy must work to earn $630.

direct proportion

Method 1 Use UnlikeUnits for Each Ratio

Solve: 



5 • 630  70 h Multiply.

3150  70 h

45 h

3150 70

70 70

45

1

1

1

 h Divide both sides

by 70 to isolate h.

Use the Cross-Products Rule

to solve for the missing term.

h

630

5

70

h

630

5

70

Check:

5 • 630 70 • 45 Cross multiply.

3150  3150 Tr u e

?

Substitute 45 for hin

the original equation.

?^45

630

5

70



5 hours$70 $630h direct proportion

hours worked

dollars earned

hours worked

dollars earned



5 hoursh $630$70 direct proportion

dollars earned

dollars earned

hours worked

hours worked

Method 2 Use LikeUnits for Each Ratio

Solve: 



5 • 630  70 h Multiply.

3150  70 h

45 h

So Tracy must work 45 hours to earn $630.

5

h

3150 70

70 70

45

1

1

1

 h Divide both sides

by 70 to isolate h.

Use the Cross-Products Rule

to solve for the missing term.

70

630

70

630

5

h

Check:

5 • 630 45 • 70 Cross multiply.

3150  3150 Tr u e

?



Substitute 45 for hin

the original equation.

?

455  63070