Finding fractions of whole numbers

Each target is a product in disguise. Nine halves could come from 9 × 2/4, from 3 × 3/2, from many pairs, and the page offers four candidates with one true match. Working backward like this builds the habit of seeing a whole number times a fraction as a count of unit pieces: 9 × 2/4 is eighteen quarters, and eighteen quarters make nine halves.

The decoys are not random. In question 4, 11 × 4/5 and 9 × 3/8 both look close to 3 until they are multiplied out.

This page works on 5.NF.B.4.a, a fraction times a whole number, and on 4.NF.B.4.b, a multiple of a/b seen as a multiple of 1/b.

The decoys get sneaky in question 3. The target 55/6 shares a 5 with three of the options, so a quick eye may grab 4 × 5/8. Ask, "What do you get if you actually multiply it?" Only one works. 22 × 5/12 reaches 110/12, which simplifies to 55/6.

Problem 8 is the long one: 560 × 15/17 gives 8,400/17, and dividing by 17 leaves 494 2/17.

For parents checking the work: the answer page shows 24/5 for problem 7, but 8 × 4/5 is 32/5. If your child writes 32/5, they are right; say so plainly, then ask, "Where could 24 have come from?"

Players of the 24 Game get four numbers and hunt for a way to reach 24; this page runs the same search with fractions. Turn it into a kitchen game. You name a target like 3 cups, and your child names a whole number and a fraction that make it, such as 12 × 1/4 cup or 6 × 1/2 cup.

Allowance works too. If a $20 allowance gets split and 2/5 goes to savings, how much is saved? Eight dollars.

Point out the checking: "You multiplied every option before you ticked one." Estimating products of fractions and whole numbers comes next.