Multiplication of fractions word problems

In every problem the second fraction is a part of the first part, not a part of the whole. Of the half of the students on the playground, 3/4 wear sport uniforms, so the fraction of all students is 1/2 × 3/4 = 3/8. Of means times.

The layout trains that reading. Each solution lists the two fractions in a small table, then multiplies across. Bob eats 2/4 of the 4/6 left, and 8/24 simplifies to 1/3.

The standard is 5.NF.B.6, solving real-world problems with multiplication of fractions and mixed numbers, here with fractions only.

Try a short exchange before problem 2.

• You: "How much cake was left?"
• Your child: "Four-sixths."
• You: "Did Bob eat 2/4 of the whole cake?"

That last question matters, because the problem literally says 2/4 of the cake, and the answer page reads it as 2/4 of the leftover 4/6. Talk it through until your child can say which whole the 2/4 belongs to.

In problem 3, 5/10 of the 2/3 who like fruit prefer oranges, so 10/30, or 1/3, of the members do. The answer page labels those fractions women members and vegetarian women, which the story never mentions; the numbers and the final 1/3 are still right.

Math Curse by Jon Scieszka and Lane Smith follows a student who finds a problem in every part of the day, and this page invites the same habit. At breakfast, if 3/4 of the juice carton is left and your child pours 1/3 of that, what fraction of the full carton went into the glass? One quarter.

At the park, half of 20 kids are on the swings and 3/5 of those wear hats. How many hats? Six.

Notice the reading, and say so: "You found which part the fraction was of." Multiplying three or more fractions and whole numbers closes the series.