Solve Real-World Problems Multiplying Mixed Numbers

Students apply mixed number multiplication to solve real-world problems such as calculating distances, areas, or quantities in cooking and construction contexts. They estimate first, calculate, and verify that answers are reasonable.

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Grade 5 · Multiplying Fractions in Real-World Problems · question 1 of 3

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20 rungs. A star at the top.

Leo serves 2 bowls of soup. Each bowl holds 1 3/4 cups. How many cups does he serve?

How it is taught

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Convert mixed numbers before you multiply.

Then convert the improper product back.

Read it: Mixed numbers in a story

3 bottles of 1 1/4 liters is 3 × 1 1/4. Split 1 1/4 into 1 + 1/4: 3 × 1 = 3 and 3 × 1/4 = 3/4, so 3 3/4 liters in all.

Find the two amounts in the story and write them as a product.
Split each mixed number into its whole and its fraction, and multiply part by part.
Add the parts, and answer the story's question in simplest form.

Equal groups of a mixed number are a product: 3 bottles of 1 1/4 liters is 3 × 1 1/4.

1 1/4 is 1 + 1/4, so 3 × 1 1/4 is 3 × 1 and 3 × 1/4, added: 3 + 3/4.

A side times a side is an area, and mixed sides split the same way.

A story's product of mixed numbers: split each into parts, multiply part by part, then add.

Multiplying the whole number by the whole part only: 3 × 1 = 3 liters.

The 1/4 is multiplied too: 3 × 1/4 = 3/4, so 3 + 3/4 = 3 3/4 liters.

Ava fills 2 planters. Each planter needs 3 1/2 scoops of mulch. How many scoops does she use? — 7. 2 × 3 1/2 = 7: every part of one number times every part of the other, added.

2½ × 1¾ cups of flour

A muffin recipe needs two and a half cups of flour. We're making one and three-fourths batches. How much flour do we need?

Grade 5 · Scaling a recipe with mixed numbers

First let's estimate. Two and a half is close to three, and one and three-fourths is close to two. So our answer should be near six cups.

Let's write the problem: two and one-half times one and three-fourths.

Change two and one-half to an improper fraction. Two times two is four, plus one is five. That's five-halves.

Now one and three-fourths. One times four is four, plus three is seven. That's seven-fourths.

Multiply the numerators: five times seven is thirty-five.

Multiply the denominators: two times four is eight.

Our product is thirty-five eighths.

Change back to a mixed number. Thirty-five divided by eight is four, with three left over.

Four and three-eighths cups. That's close to our estimate of six — actually a bit less, which makes sense.

We need four and three-eighths cups of flour. Time to bake!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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