Dividing fractions and mixed numbers word problems

In a story, the division is hidden. Frank's problem gives the time for 3/4 of a job and asks for the whole job, so 5 1/2 is divided by 3/4. Think it through in fourths. If 3/4 takes 5 1/2 hours, 1/4 takes a third of that, and four fourths take four times as much: 22/3, or 7 1/3 hours.

John's question is a measurement: how many 2/3 pieces fit in 5 1/2? That is 11/2 × 3/2 = 33/4.

The standard is 6.NS.A.1, solving word problems that divide fractions by fractions.

Both stories also need converting mixed numbers to improper fractions before anything else.

Before any numbers, ask, "What is being shared, and into what size?" Your child should name the sand, in 2/3-load bags. Some children write 2/3 ÷ 5 1/2 instead and get 4/33 of a bag; an answer that tiny is a clue the order flipped.

Worth a word at checking time: the answer page says John can fill 8 1/4 bags. The arithmetic is right, but only 8 bags get filled, and the last one is a quarter full. Ask, "Would you count that as a bag?"

Frank's problem asks for a mixed number, so 22/3 must become 7 1/3.

Jon Scieszka and Lane Smith built Math Curse around a student who suddenly sees a math problem in every part of the day. Fraction division fits right in. A 6-foot ribbon cut into 3/4-foot bows makes 8 bows; a 2 1/2-mile walk at 1/2 mile per lap is 5 laps around the park.

Let your child invent the next one from your kitchen, with a bag of flour and a 1/3-cup scoop.

Give the effort its due: "You asked what was being shared, then divided." Next, 6th grade moves on to integers, starting with understanding integers.