Working with Fractions
Class 7 · Mathematics
4 ideas in Class 7 Mathematics, explained in plain words, with games and quizzes to practise.
Multiplying fractions
Part of: Tops times tops
A tank grid splits wholes into rows for one part and columns for the other, so parts multiply too. Tops multiply tops, bottoms multiply bottoms: that is Brahmagupta's 628 CE rule from his star-book. Wholes join by wearing ones below, and rectangle areas with fractional sides simply multiply sides. Aaron's walks, tortoise crawls and milk glasses all obey one law.
Why it matters. It turns the child from drawing grids to instant products.
Try it in two minutes
- Recall 20-part tank grid.
- Recall top-top, bottom-bottom.
- Link whole to over-one.
Try at home. Shade half of a third on paper squares.
Cancelling and lowest form
Part of: Shrink first
Old India named lowest terms apavartana, praised by Umasvati near 150 CE. Shared factors divide away ere multiplying: twelves melt, fifteens shrink to thirds. Tap-hours, Somu's plots, board sides, sapling gaps and parcel weights all shrink first. Cancelling is no cheat; the share stays same while digits slim.
Why it matters. It spares the child giant multiplications.
Try it in two minutes
- Recall 12-cut trick.
- Recall tank, land, board trio.
- Link scrap to lowest terms.
Try at home. Halve top and bottom of 6/8.
How big is the product
Part of: Size sense
Two overs multiply past both; two unders sink below both; an under times an over lands between. Times-one holds still. Flip the order, grids stay same. Great ratios obey too: with one leg each side of one, the product tops the under leg yet trails the over leg and one itself.
Why it matters. It lets the child guess size ere computing.
Try it in two minutes
- Recall 35/6 tops both.
- Recall 2/15 trails both.
- Link middle case to straddle.
Try at home. Multiply your age by 1/2.
Dividing fractions
Part of: Flip and multiply
What times the divisor yields the dividend? First flip the divisor: top-bottom swap, product one. Then multiply. Under-one divisors lift quotients past dividends; over-one sink them. Tea cups, Sulba bricks, four fountains, dramma coins and lace bags all yield to one flip.
Why it matters. It hands the child one key for all sharing sums.
Try it in two minutes
- Recall flip-and-multiply.
- Recall under-one lifts.
- Link lace to twelve bags.
Try at home. Share 3/4 cake among 4 fairly.
What your child will practise
- Cancelling and lowest form: Jungle Quest (Flip and Match)
- Cancelling and lowest form: Mission Control Quest (Collect the Answer)
- Dividing fractions: Ocean Quick Fire (Quick Fire)
- How big is the product: Space Puzzle (Clue Puzzle)
- Multiplying fractions: Number Quest (Match It Up)
- Quiz: Cancelling and lowest form (8 questions)
- Quiz: Dividing fractions (8 questions)
- Quiz: How big is the product (8 questions)
- Quiz: Multiplying fractions (8 questions)