Inverse proportion

The Maths Habit

Both teams paint the same fence. Which team finishes first?

Team A
Team B✓ Finishes first

How many blocks?

 2 × 5 = 10
 3 × 4 = 12
 4 × 6 = 24

Inverse proportion
When one amount is multiplied, the other is divided by the same number.
4 hours2 workers2 hours4 workers
Block of work
One worker working for one hour.
1 hour1 worker
Total
All the blocks added together.
3 workers

4 workers paint a hall in 5 hours. How many blocks is the job?

5 hours4 workers
1Find the blocks.
4×5=20

2 workers build a shed in 7 hours. How many blocks is the job?

7 hours2 workers
1Find the blocks.
2×7=14

4 workers paint a hall in 5 hours. How many blocks is the job?

5 hours4 workers
1Find the blocks.
4×5=20
1workers×hours=blocks

3 workers tidy a park in 5 hours. How many blocks is the job?

5 hours3 workers
1Find the blocks.
3×5=15

4 workers paint a hall in 5 hours. How many blocks is the job?

5 hours4 workers
1Find the blocks.
4×5=20
1workers×hours=blocks

6 workers dig a pond in 3 hours. How many blocks is the job?

3 hours6 workers
1Find the blocks.
6×3=18

4 workers paint a hall in 5 hours. How many blocks is the job?

5 hours4 workers
1Find the blocks.
4×5=20
1workers×hours=blocks

4 workers lay a path in 6 hours. How many blocks is the job?

6 hours4 workers
1Find the blocks.
4×6=24

Share the blocks equally. How many does each worker get?

12 blocks
3 workers12 ÷ 3 = 4 each
10 blocks
5 workers10 ÷ 5 = 2 each
18 blocks
6 workers18 ÷ 6 = 3 each

4 workers paint a hall in 6 hours. How long do 6 workers take?

6 hours4 workers? hours4 hours6 workers
1Find the blocks.
4×6=24
2Share the blocks.
24÷6=4

3 workers build a shed in 4 hours. How long do 4 workers take?

4 hours3 workers? hours3 hours4 workers
1Find the blocks.
3×4=12
2Share the blocks.
12÷4=3

4 workers paint a hall in 6 hours. How long do 6 workers take?

6 hours4 workers? hours4 hours6 workers
1Find the blocks.
4×6=24
2Share the blocks.
24÷6=4
1workers×hours=blocks2blocks÷new workers=hours

2 workers tidy a park in 5 hours. How long do 5 workers take?

5 hours2 workers? hours2 hours5 workers
1Find the blocks.
2×5=10
2Share the blocks.
10÷5=2

4 workers paint a hall in 6 hours. How long do 6 workers take?

6 hours4 workers? hours4 hours6 workers
1Find the blocks.
4×6=24
2Share the blocks.
24÷6=4
1workers×hours=blocks2blocks÷new workers=hours

4 workers dig a pond in 5 hours. How long do 5 workers take?

5 hours4 workers? hours4 hours5 workers
1Find the blocks.
4×5=20
2Share the blocks.
20÷5=4

4 workers paint a hall in 6 hours. How long do 6 workers take?

6 hours4 workers? hours4 hours6 workers
1Find the blocks.
4×6=24
2Share the blocks.
24÷6=4
1workers×hours=blocks2blocks÷new workers=hours

6 friends tidy a garden in 2 hours. How long do 4 friends take?

2 hours6 friends? hours3 hours4 friends
1Find the blocks.
6×2=12
2Share the blocks.
12÷4=3

Inverse proportion worksheet, page 1

Inverse proportion worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 2 workers take 6 hours, so 4 workers take 3 hours

    Right

  2. 3 workers take 4 hours, so 6 workers take 8 hours

    Wrong: 2 hours

  3. 5 workers take 2 hours, so the job is 10 blocks

    Right

  4. 4 workers take 6 hours, so 8 workers take 2 hours

    Wrong: 3 hours

  5. 6 friends take 2 hours, so 3 friends take 4 hours

    Right

  1. A journey takes 4 hours at 30 mph. How long does it take at 40 mph?

    3 hours

  2. y is inversely proportional to x. When x = 2, y = 18. Find y when x = 6.

    y = 6

  3. 4 machines finish an order in 9 hours. It must be done in 6 hours. How many machines are needed?

    6 machines

  4. 12 cows have enough feed for 10 days. After 4 days, 6 more cows come. How many more days does the feed last?

    4 days

  1. 4 workers paint a fence in 4 hours. How long do 8 workers take?

    2 hours
    4 hours4 workers1Find the blocks.×=2Share the blocks.÷=

  2. 3 workers build a shed in 8 hours. How long do 6 workers take?

    4 hours
    8 hours3 workers1Find the blocks.×=2Share the blocks.÷=

  3. 4 workers dig a pond in 9 hours. How long do 6 workers take?

    6 hours
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