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Dividing FractionsFREEWorksheet Generator(Grades 6-8)

Dividing Fractions worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 6โ€“8.

๐ŸŽฏ Fraction Division Cluster:Switch to Multiplying Fractions โž”
Fraction รท WholeGrade 5Whole รท FractionGrade 5Mixed NumbersGrade 6Master Generator
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๐Ÿ“„ Sheet #1โ€ข10 Problems
PanMaths.comDividing Fractions Worksheets โ€ข Worksheet #1
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 10
1.
45รท13= ย ______
Workspace:
2.
56รท23= ย ______
Workspace:
3.
25รท13= ย ______
Workspace:
4.
15รท23= ย ______
Workspace:
5.
37รท45= ย ______
Workspace:
6.
46รท24= ย ______
Workspace:
7.
13รท27= ย ______
Workspace:
8.
25รท23= ย ______
Workspace:
9.
23รท24= ย ______
Workspace:
10.
12รท18= ย ______
Workspace:
PanMaths.com โ€ข Free Math Worksheet GeneratorPage 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Worksheet #1
Answer Key
Total Problems: 10
1.
45รท13= 12/5
1. Keep First Fraction: 4/5
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 1/3 โ†’ 3/1
4. Multiply Across: (4 ร— 3) / (5 ร— 1) = 12/5
5. Already in Lowest Terms: 12/5
2.
56รท23= 5/4
1. Keep First Fraction: 5/6
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 2/3 โ†’ 3/2
4. Multiply Across: (5 ร— 3) / (6 ร— 2) = 15/12
5. Simplify by Greatest Common Divisor (3): 15 รท 3 / 12 รท 3 = 5/4
3.
25รท13= 6/5
1. Keep First Fraction: 2/5
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 1/3 โ†’ 3/1
4. Multiply Across: (2 ร— 3) / (5 ร— 1) = 6/5
5. Already in Lowest Terms: 6/5
4.
15รท23= 3/10
1. Keep First Fraction: 1/5
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 2/3 โ†’ 3/2
4. Multiply Across: (1 ร— 3) / (5 ร— 2) = 3/10
5. Already in Lowest Terms: 3/10
5.
37รท45= 15/28
1. Keep First Fraction: 3/7
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 4/5 โ†’ 5/4
4. Multiply Across: (3 ร— 5) / (7 ร— 4) = 15/28
5. Already in Lowest Terms: 15/28
6.
46รท24= 4/3
1. Keep First Fraction: 4/6
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 2/4 โ†’ 4/2
4. Multiply Across: (4 ร— 4) / (6 ร— 2) = 16/12
5. Simplify by Greatest Common Divisor (4): 16 รท 4 / 12 รท 4 = 4/3
7.
13รท27= 7/6
1. Keep First Fraction: 1/3
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 2/7 โ†’ 7/2
4. Multiply Across: (1 ร— 7) / (3 ร— 2) = 7/6
5. Already in Lowest Terms: 7/6
8.
25รท23= 3/5
1. Keep First Fraction: 2/5
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 2/3 โ†’ 3/2
4. Multiply Across: (2 ร— 3) / (5 ร— 2) = 6/10
5. Simplify by Greatest Common Divisor (2): 6 รท 2 / 10 รท 2 = 3/5
9.
23รท24= 4/3
1. Keep First Fraction: 2/3
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 2/4 โ†’ 4/2
4. Multiply Across: (2 ร— 4) / (3 ร— 2) = 8/6
5. Simplify by Greatest Common Divisor (2): 8 รท 2 / 6 รท 2 = 4/3
10.
12รท18= 4
1. Keep First Fraction: 1/2
2. Change Operation to Multiplication: รท โ†’ ร—
3. Flip Second Fraction (Reciprocal): 1/8 โ†’ 8/1
4. Multiply Across: (1 ร— 8) / (2 ร— 1) = 8/2
5. Simplify by Greatest Common Divisor (2): 8 รท 2 / 2 รท 2 = 4
PanMaths.com โ€ข Answer Key & Worked SolutionsPage 2 of 2
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Worksheet Info

Categoryfractions
Grade LevelGrades 5-7
Difficultymedium
Time10-15 min

Skills Practiced

  • โœ“ Dividing Fractions fluency
  • โœ“ Mental math speed
  • โœ“ Step-by-step problem solving

Key Strategies

  • Keep-Change-Flip (KCF): Keep the 1st fraction, change รท to ร—, flip the 2nd fraction to its reciprocal.
  • Inverse Multiplication Proof: Multiply the calculated quotient by the divisor to confirm it equals the dividend.
  • Reciprocal Inversion: Invert numerator and denominator (e.g. 3/5 โ†’ 5/3) before multiplying.
๐ŸŽฎ Interactive Warm-Up

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Strategies

  • Keep-Change-Flip (KCF): Keep the 1st fraction, change รท to ร—, flip the 2nd fraction to its reciprocal.
  • Inverse Multiplication Proof: Multiply the calculated quotient by the divisor to confirm it equals the dividend.
  • Reciprocal Inversion: Invert numerator and denominator (e.g. 3/5 โ†’ 5/3) before multiplying.

Mastering Dividing Fractions: Core Concepts & Mental Models

Dividing Fractions worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 6โ€“8.

๐Ÿ’ก Essential Strategies for Dividing Fractions

Keep-Change-Flip (KCF)

Keep the 1st fraction, change รท to ร—, flip the 2nd fraction to its reciprocal.

Inverse Multiplication Proof

Multiply the calculated quotient by the divisor to confirm it equals the dividend.

Reciprocal Inversion

Invert numerator and denominator (e.g. 3/5 โ†’ 5/3) before multiplying.

โš ๏ธ Common Mistakes & Teacher Fixes

โš ๏ธFlipping the First Fraction Instead of the Second

Why students stumble: Students remember that a fraction must be inverted, but flip the dividend (left fraction) rather than the divisor (right fraction).

Teacher Fix: Follow the "KCF" chant: Keep the FIRST, Change the SIGN, Flip the SECOND.
Example: For 2/3 รท 4/5: Keep 2/3, Change to ร—, Flip to 5/4 โ†’ 2/3 ร— 5/4 = 10/12 = 5/6.
โš ๏ธForgetting to Change Division to Multiplication

Why students stumble: Students flip the second fraction but leave the division symbol unchanged (e.g. 2/3 รท 5/4).

Teacher Fix: Flipping the fraction requires inverting the operation: รท must become ร— immediately.
Example: 2/3 รท 4/5 becomes 2/3 ร— 5/4.
โš ๏ธFlipping Both Fractions (Double Inversion)

Why students stumble: Students over-apply the reciprocal rule and invert both fractions (e.g. 3/2 ร— 5/4).

Teacher Fix: Only the divisor (the number you are dividing by) is inverted. The first number never changes.
Example: Only flip the fraction after the รท sign.

โ“ Frequently Asked Questions

What does "Keep, Change, Flip" mean?

It is a mnemonic for fraction division: Keep the first fraction, Change division (รท) to multiplication (ร—), and Flip the second fraction upside down (its reciprocal).

Why do we only flip the second fraction?

Because the second fraction is the divisor (the quantity being divided by). In algebra, dividing by a quantity is mathematically defined as multiplying by its reciprocal.

Do the answer keys show step-by-step KCF transformations?

Yes. Every generated answer key displays the original problem, the KCF multiplication step, the unreduced product, and the final simplified fraction.

Can I print fresh worksheets with new randomized fractions?

Yes. You can toggle between Sets A, B, C, and D on the showcase page or launch the Studio to generate unlimited fresh PDF sheets.

The "Keep, Change, Flip" (KCF) Rule for Dividing Fractions

Dividing fractions is computed by multiplying by the reciprocal of the divisor:

  1. 1. KEEP: Leave the first fraction (dividend) unchanged: a/b.
  2. 2. CHANGE: Change the division symbol (รท) into a multiplication symbol (ร—).
  3. 3. FLIP: Invert the second fraction (divisor) to its reciprocal: c/d โ†’ d/c.
  4. 4. MULTIPLY & REDUCE: Multiply straight across: (a ร— d) / (b ร— c), then simplify to lowest terms.

Why Multiplying by the Reciprocal Works Mathematically

Division asks: "How many times does the second quantity fit into the first?"

Consider 2 รท 1/3: How many one-third slices are in 2 whole pizzas? Since each whole pizza has 3 thirds, 2 pizzas have 2 ร— 3 = 6 thirds. Dividing by 1/3 is mathematically identical to multiplying by 3/1.

Converting Mixed Fractions and Whole Numbers for Division

Before applying the Keep-Change-Flip rule, ensure all numbers are formatted as simple fractions:

  • Whole Numbers: Write whole numbers over 1 (e.g. 4 โ†’ 4/1). For 4 รท 2/3, calculate 4/1 ร— 3/2 = 12/2 = 6.
  • Unit Fraction Differences: Dividing 1/2 รท 1/6 equals 1/2 ร— 6/1 = 6/2 = 3.

Worksheet Facts by Grade Level

Grade LevelCommon Core StandardTarget Operations & ComplexityRecommended Drills
Grade 5CCSS.MATH.CONTENT.5.NF.B.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractionsSet A (Standard 10 Problems)
Grade 6CCSS.MATH.CONTENT.6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving fraction divisionSet B & Set C (Proper & Unlike Fractions)
Grade 7CCSS.MATH.CONTENT.7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbersSet C (Challenging Drills)
Grade 7CCSS.MATH.CONTENT.7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficientsSet C & Unlimited Studio drills

The "Keep, Change, Flip" (KCF) Rule for Dividing Fractions

Dividing fractions is computed by multiplying by the reciprocal of the divisor:

  1. 1. KEEP: Leave the first fraction (dividend) unchanged: a/b.
  2. 2. CHANGE: Change the division symbol (รท) into a multiplication symbol (ร—).
  3. 3. FLIP: Invert the second fraction (divisor) to its reciprocal: c/d โ†’ d/c.
  4. 4. MULTIPLY & REDUCE: Multiply straight across: (a ร— d) / (b ร— c), then simplify to lowest terms.

Why Multiplying by the Reciprocal Works Mathematically

Division asks: "How many times does the second quantity fit into the first?"

Consider 2 รท 1/3: How many one-third slices are in 2 whole pizzas? Since each whole pizza has 3 thirds, 2 pizzas have 2 ร— 3 = 6 thirds. Dividing by 1/3 is mathematically identical to multiplying by 3/1.

Converting Mixed Fractions and Whole Numbers for Division

Before applying the Keep-Change-Flip rule, ensure all numbers are formatted as simple fractions:

  • Whole Numbers: Write whole numbers over 1 (e.g. 4 โ†’ 4/1). For 4 รท 2/3, calculate 4/1 ร— 3/2 = 12/2 = 6.
  • Unit Fraction Differences: Dividing 1/2 รท 1/6 equals 1/2 ร— 6/1 = 6/2 = 3.
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Benefits of Mastery

๐Ÿ”„ Reciprocal Fluency

Master the concept of multiplicative inverses essential for high school algebra.

โšก Fast Algorithmic Execution

Convert division into straightforward multiplication in 1 second.

๐ŸŽฏ CCSS Standard Aligned

Directly targets Common Core 5.NF.B.7 and 6.NS.A.1 benchmarks.

โœ… Step-by-Step Answer Keys

Every generated PDF details the full KCF transformation, intermediate product, and GCD reduction.