Student Help Card

Lesson 2: Division Expressions with Fractions and Mixed Numbers6.NOS.1

Stuck? Start here. Read the steps, try the problem, then check your answer.

I can…

I can explain what dividing a fraction by a fraction means, find the quotient with common denominators or by multiplying by the reciprocal, and check it by multiplying.

Key words

Divide Fractions — Multiply the first fraction by the reciprocal of the second fraction.
Dividend — The total number being divided into equal groups (the number inside the division bracket).
Divisor — The number of equal groups you are dividing into (the number outside the division bracket).
Reciprocal — A fraction turned upside down.
Quotient — The answer when you divide.
Simplify — To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2.
Mixed number — A whole number and a fraction written together, like 2 1/2. It must be rewritten as an improper fraction before dividing.
Improper fraction — A fraction whose numerator is greater than or equal to its denominator, like 5/2.

Steps

Agent Rivera has 3/4 pound and each portion is 1/8 pound. I want 3/4 ÷ 1/8.
It asks how many 1/8-pound portions fit in 3/4 pound. I rename 3/4 in eighths: 3/4 = 6/8.
6 eighths ÷ 1 eighth = 6, the same way 6 apples ÷ 1 apple = 6. That is the common-denominator method.
The reciprocal shortcut gives the same answer: 3/4 × 8/1 = 24/4 = 6, because each pound holds 8 eighths. Check: 6 × 1/8 = 6/8 = 3/4. She can make 6 portions.
One more move to know: mixed number → improper fraction: multiply the bottom by the whole number, add the top, keep the same bottom. 3 1/2 → (2 × 3) + 1 = 7 → 7/2.

Try it

A family has 2/3 of a pizza left and cuts it into slices that are each 1/9 of a whole pizza. What is 2/3 ÷ 1/9 — how many slices?

Check your answer

2/3 ÷ 1/9 = 6. Using the reciprocal, 2/3 × 9/1 = 18/3 = 6. Since 2/3 = 6/9, six 1/9-size slices fit. Check: 6 × 1/9 = 6/9 = 2/3.

Sentence starter

I know ___ because ___.

Goal: I can explain why multiplying by the reciprocal works, using the words reciprocal, improper fraction, mixed number, and simplify.