Dividing fractions

Picture two thirds of a pan of brownies cut into sixths. Four pieces come out, so 2/3 ÷ 1/6 = 4. The quotient grows. It grows whenever the divisor is less than 1.

The rule keeps that true without drawing: multiply by the reciprocal. Here is the routine the page rewards:

• keep the first fraction as it is
• flip the divisor, so 1/6 becomes 6/1
• multiply and simplify, 12/3 to 4

The standard is 6.NS.A.1, interpreting and computing quotients of fractions.

A second skill rides along, comparing equivalent fractions, since the right answer may be written in a form your child did not reach.

Flipping the wrong fraction is the trap in problem 3. If your child flips 3/19 instead of 1/4, the result is 19/12, and it sits right there among the choices; multiplying straight across gives 3/76, also on the list. Ask, "Which fraction did you flip?"

A note for parents: problem 4 lists 84/36, 7/3 and 2 1/3, and all three equal the answer. Problem 5 offers both 12/3 and 4. The key ticks the simplest form, which is what "most correct" means here. In problem 1 it ticks 9/15, which is 3/5 left unsimplified.

If your child picks 7/3, ask, "Can you write that as a mixed number?"

The 24 Game hands players four numbers to combine into 24. One famous card, 3, 3, 8, 8, only works with fraction division: 8 ÷ (3 − 8/3) = 8 ÷ 1/3 = 24. Show it after the page. Dividing by a third turns 8 into 24, and the surprise from problem 5 pays off.

At dinner, ask how many 1/4-cup servings sit in a 3/4-cup bowl of rice. Three, and your child can scoop them to prove it.

Put the success into words: "You flipped the second fraction every single time." The series ends with word problems on dividing fractions and mixed numbers.