Fractions as Division

5th Grade MathOperations with Fractions4 pages

About this worksheet

This 5th grade math worksheet works on 5.NF.3, the Common Core standard that reads a fraction as division of the numerator by the denominator. A table has students rewrite quotients such as 7 ÷ 2 and 26 ÷ 5 as fractions and mixed numbers, then four sharing stories follow: 3 pizzas for 4 friends, an 18-foot roll of bulletin board paper cut for 5 groups, a 36-liter cooler split by 8 runners, and a 50-pound bag of potatoes for 9 campers. A boxed example proving 4 × (3/4) = 3 sets up the reasoning questions, and the sheet closes on Marcus's claim that 8 ÷ 3 equals 3/8.

Remix for free

$Fractions as Division: Operations with Fractions - page 1$

$Fractions as Division: Operations with Fractions - page 2$

$Fractions as Division: Operations with Fractions - page 3$

$Fractions as Division: Operations with Fractions - page 4$

Curriculum objectives covered

5.NF.3

“Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?”

Every question applies it: the Part 1 table rewrites quotients as fractions, the four sharing stories land on 3/4, 3 3/5, 4 1/2 and 5 5/9, and question 4 restages the standard's own 50-pound-sack example with potatoes and 9 campers.

What's inside this worksheet

Part 1: Rewrite and Estimate

Students complete a table that turns division problems into fractions and mixed numbers: 3 ÷ 4 stays at 3/4, while 7/2, 11/3 and 26/5 become 3 1/2, 3 2/3 and 5 1/5, each pinned between two whole numbers.

Part 2: Real-World Sharing Problems

Four stories ask for a division equation and a fraction answer: 3 pizzas shared by 4 friends, 18 feet of paper for 5 groups (3 3/5 feet each), 36 liters of water for 8 runners, and 50 pounds of potatoes for 9 campers (5 5/9 pounds).

Part 3: Visual Thinking and Reasoning

A worked box shows that 4 shares of 3/4 rebuild 3 wholes. Students then write the matching equation 6 × (5/6) = 5 for trail mix shared by 6 hikers, and question 6 asks them to explain why Marcus's 8 ÷ 3 = 3/8 swaps the dividend and divisor.

Answer key

Solutions give every quotient in both forms, including 36 ÷ 8 = 4 1/2 liters, and spell out that 8 ÷ 3 must equal 8/3, which is 2 2/3.

How teachers use it

Introducing 5.NF.3

Work the boxed 4 × (3/4) = 3 example together before releasing Part 1. The multiplication check is what makes fraction-as-division click, so do not let students skip question 5.

Spotting the classic reversal

Question 6 exposes the students who write 3/8 for 8 ÷ 3. Collect answers to that one question and you have your small group for tomorrow.

Estimation practice

The between-which-whole-numbers column doubles as an estimation drill. Ask students to fill that column first, before converting anything, and check answers against it afterward.

More 5th Grade Math worksheets

Place Value and Decimals Measurement and Data Geometry Order of Operations

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