Lesson 10: Divide Mixed Numbers6.NOS.1

I can…

I can explain what dividing with mixed numbers means, rewrite them as improper fractions, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Key words

• Divide Mixed Numbers — Change both to improper fractions. Then divide the fractions.
• Mixed Number — A whole number and a fraction together, like 2 1/2.
• Improper Fraction — A fraction that is 1 or more, like 5/2.
• Convert — Change to a new unit or form; the amount stays the same.
• Simplify — Write it in a smaller form with the same value.
• Reciprocal — A fraction turned upside down.

Steps

1. Agent Chen has a 3 1/2-mile route cut into 1/4-mile segments. I want 3 1/2 ÷ 1/4.
2. First I convert 3 1/2. Multiply the whole by the bottom: 3 × 2 = 6. Add the top: 6 + 1 = 7. So 3 1/2 = 7/2.
3. Now I ask how many 1/4s fit in 7/2. In fourths, 7/2 = 14/4, and 14 fourths ÷ 1 fourth = 14 — the common-denominator method.
4. The reciprocal shortcut gives the same answer: 7/2 × 4/1 = 28/2 = 14.
5. Check by multiplying: 14 × 1/4 = 14/4 = 3 1/2. So 3 1/2 ÷ 1/4 = 14 segments.

Try it

What is 3 3/4 ÷ 3/4? (Think: how many 3/4-cup scoops are in 3 3/4 cups of flour?)

Check your answer

5

3 3/4 = 15/4. Then 15/4 ÷ 3/4 = 15/4 × 4/3 = 60/12 = 5. Check by multiplying: 5 × 3/4 = 15/4 = 3 3/4.

Sentence starter

I know ___ because ___.

Goal: I can explain my steps and why they work, using the words mixed number, improper fraction, convert, reciprocal, and simplify.