Adding and Subtracting Fractions with Unlike Denominators

5th Grade MathOperations with Fractions4 pages

About this worksheet

This 5th grade math worksheet drills adding and subtracting fractions with unlike denominators (Common Core 5.NF.1 and 5.NF.2). Guided fill-ins rename 1/4 + 2/3 as twelfths, then independent problems climb from 3/5 + 1/2 to the double-regrouping subtraction 4 1/2 - 1 3/5. Part 3 hands students Marcus's homework mistake, 2/5 + 1/2 = 3/7, to demolish with the 1/2 benchmark. Two word problems finish the sheet: Maya mixing two milks for muffins and Leo cutting a 5 1/4-foot board.

Remix for free

$Adding and Subtracting Fractions with Unlike Denominators: Operations with Fractions - page 1$

$Adding and Subtracting Fractions with Unlike Denominators: Operations with Fractions - page 2$

$Adding and Subtracting Fractions with Unlike Denominators: Operations with Fractions - page 3$

$Adding and Subtracting Fractions with Unlike Denominators: Operations with Fractions - page 4$

Curriculum objectives covered

5.NF.1

“Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)”

Questions 1 to 6 practice the renaming itself, over denominators of 12, 6, 10 and 8, with regrouping arriving in question 6.

5.NF.2

“Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 <1/2.”

Question 7 restages the standard's own example (2/5 + 1/2 = 3/7) as Marcus's homework, and questions 8 and 9 apply the skill to milk and lumber.

What's inside this worksheet

Part 1: Rename with Common Denominators

Students fill in blanks to convert 1/4 + 2/3 into twelfths and 5/6 - 1/2 into sixths, writing the simplified result 1/3 at the end of the second chain.

Part 2: Compute

Four problems each start with a Common denominator blank: 3/5 + 1/2 lands over 10 at 1 1/10, 7/8 - 3/4 over 8, the mixed sum 2 1/3 + 1 1/6 simplifies to 3 1/2, and 4 1/2 - 1 3/5 requires regrouping into 3 15/10.

Part 3: Number Sense and Error Analysis

A boxed sample of Marcus's work shows 2/5 + 1/2 = 3/7. Students explain why the sum must exceed 1/2 and then compute the correct answer of 9/10.

Part 4: Word Problems

Maya combines 3/4 cup of whole milk with 2/3 cup of almond milk for 1 5/12 cups, and Leo cuts 2 5/6 feet from a 5 1/4-foot board, leaving 2 5/12 feet.

Answer key

Every solution shows the renamed fractions, including the regrouping chain 5 3/12 = 4 15/12 in the board problem.

How teachers use it

Guided-to-independent lesson

Part 1's fill-in blanks make the gradual release explicit. Do question 1 under the document camera, let pairs do question 2, then release Part 2 as solo work.

Catching numerator-adders

Question 7 is Marcus adding tops and bottoms. Students who cannot articulate why 3/7 is impossible are still pattern-matching, so pull them before question 9's regrouping.

Quick homework check

Mark only the Common denominator lines in Part 2 at the door. Ten seconds per paper tells you who needs the renaming reteach before the next lesson.

More 5th Grade Math worksheets

Place Value and Decimals Measurement and Data Geometry Order of Operations

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