Stuck? Start here. Read the steps, try the problem, then check your answer.
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 mixed numbers to improper fractions, then multiply by the reciprocal.
Mixed Number — A whole number plus a fraction, like 2 1/3.
Improper Fraction — A fraction where the top is bigger than or equal to the bottom, like 7/4.
Convert — To change a number to a new form but keep the same value.
Simplify — To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2.
Reciprocal — A fraction turned upside down. Dividing by a fraction gives the same answer as multiplying by its reciprocal.
Steps
Agent Chen has a 3 1/2-mile route cut into 1/4-mile segments. I want 3 1/2 ÷ 1/4.
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.
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.
The reciprocal shortcut gives the same answer: 7/2 × 4/1 = 28/2 = 14.
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?)