Multiply three or more fractions and whole numbers

Three fractions multiply exactly like two: numerators together, denominators together. Writing everything in one line, as the example does, keeps the factors visible long enough to cancel. In problem 4, 2 × 5/9 × 3/4 × 1/10 gives 30/360, and dividing both by 30 leaves 1/12.

Problem 7 shows why simplifying early helps. Straight across it reaches 24/3,360; cancel the 4 with the 12 and the 2 with the 8 first, and the numbers stay small on the way to 1/140.

The standard is 5.NF.B.4, multiplying a fraction or whole number by a fraction, stretched here to longer chains of factors.

Two whole numbers sit in problem 5: 5 × 5/10 × 9. Some children multiply only the first one by the fraction and forget the 9. Ask, "Where did the 9 go?" Over 1, it joins the top: 225/10, then 45/2, then 22 1/2.

Heads-up for whoever checks the page: in problem 9 the answer page writes the bottom as 100, but 4 × 8 × 5 is 160. The final 7/20 is right. The boxed example also reads 6 × 3/15 × 3/15 when it means 6 × 1/12 × 3/15.

Before each problem, let your child cross out one common factor out loud.

In One Grain of Rice by Demi, a girl's reward doubles every day, and a long chain of factors becomes a mountain of rice. Fractions run the chain the other way. Half of a half of a half of a pizza is 1/2 × 1/2 × 1/2 = 1/8 of it. Three cuts, eight slices: have your child fold a paper circle to see it.

In the kitchen, a recipe scaled to 2/3, then halved, then made 3 times comes back to 3 × 2/3 × 1/2 = 1 batch.

Finish by naming the habit: "You canceled before you multiplied, and it stayed small." Dividing fractions comes next in 6th grade.