6th Grade Math Textbook, Fundamentals

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6-9

Update your skills. See pages 414 XVII, 415 XVIII.

Inverse Proportion

Objective To solve inverse proportions

When an increase or decrease in one quantity causes the oppositekind

of change in the other quantity, an can be formed.

You can use a table to help visualize the concept of inverse proportions.

A farmer has enough food to feed 2 goats for 32 days. If the farmer doubles

the number of goats, what happens to the number of days of available food?

• As the number of goats increases, the number
  of days of available food decreases.


• The number of goats changed by a factor of 2.


• The number of days changed by a factor of.


• The two quantities, goats and days, changed by
  reciprocal factors.


• The two quantities are inverselyproportional.

If the number of goats doubles, the number of days of available food decreases

by a factor of. So if the farmer has enough food for 2 goats for 32 days,

then doubling the goats to 4 means there is only enough food for 16 days.

inverse proportion

1

2

1

2

It takes a group of 4 teenagers a half hour to wash 10 cars.

How long would it take a group of 8 teenagers to wash 10 cars?

Let tthe time it would take 8 teenagers to wash 10 cars.

• Write the two comparisons in words.

4 teenagers work hour 8 teenagers work thours Both groups wash 10 cars

• Write a proportion.



Solve:  Check: Substitute for t.

• 4  8 t Cross multiply. • 4 • 8 Cross multiply.

2  8 t 2  2 Tr u e

 Divide both sides by 8 to isolate t.

t

It would take 8 teenagers hour to wash the same 10 cars.

1

2

8 t

8

8 teenagers

4 teenagers

1

2 hour

t

?^1

4

1

2

1

4

?

1

2

1

4

8

4

1

4

1

2

t

1

4

8

4

2

8

1

2

more teenagers

fewer teenagers

more time

less time

1

Goats Days

232

416

88

16 4

32 2

Think

It would take 8 teenagers less time to

wash 10 cars than it would 4 teenagers.