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Working with Fractions

A fraction of what is left

On Monday you spend 1/5 of your money. On Tuesday you spend 3/8 of what is left. How much of all your money is left?

The whole is 5 rows by 8 columns: 40 cells.
Step 1 of 4
  1. The whole is 5 rows by 8 columns: 40 cells.
  2. Monday takes 1 of the 5 rows. 4 rows are left.
  3. Tuesday takes 3 of 8 columns from those 4 rows.
  4. 20 cells are left: 20/40 = 1/2.

Find what is left first

1/2 of your money is left.

Find what is left first. Then take the fraction of that, not of the whole.

After Monday, 1 − 1/5 = 4/5 is left. Tuesday takes 3/8 of 4/5. 3 × 4 = 12 and 8 × 5 = 40, so that is 12/40 = 3/10. Then 4/5 is 8/10, and 8/10 − 3/10 = 5/10 = 1/2 is left.

There is a shorter way. Tuesday takes 3/8, so 5/8 of what was left remains. And 5/8 × 4/5 = 20/40 = 1/2.

Check with ₹200. Monday takes ₹40, so ₹160 is left. Tuesday takes 3/8 of ₹160, which is ₹60. ₹100 is left, which is half of ₹200.

Slide the Day 2 columns in the lab. Aim to leave the goal amount.

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This track

  1. 0 Start here
  2. 1 More than one whole
  3. 2 Renaming until the pieces match
  4. 3 Adding pieces that do not match
  5. 4 Taking one fraction from another
  6. 5 Wholes and parts together
  7. 6 Checkpoint: renaming, adding and taking away
  8. 7 A fraction of a whole number
  9. 8 A fraction of a fraction
  10. 9 When multiplying makes it smaller
  11. 10 The number that undoes a fraction
  12. 11 How many of these fit inside that
  13. 12 Checkpoint: multiplying and dividing
  14. 13 Cancel before you multiply
  15. 14 Share a fraction equally
  16. 15 When dividing makes it bigger
  17. 16 A fraction of what is left
  18. 17 The big picture
  19. 18 Track quiz

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