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Dividing Integers by Fractions WORKSHEET
Suitable for Grades: 5th Grade, 6th Grade
CCSS: 5.NF.B.7, 6.NS.A.1
CCSS Description: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Dividing Integers by Fractions WORKSHEET DESCRIPTION
This worksheet develops understanding of dividing integers by fractions through visual models, reasoning, and problem solving.
In Section A, students use bar models to divide whole numbers by unit fractions and recognise the connection between division and multiplication.
Section B extends to non-unit fractions, using diagrams and reasoning to identify when results are whole numbers.
Section C explores mixed-number quotients, challenging learners to interpret remainders within bar models and to correct common misconceptions such as misreading fractional remainders.
Finally, Section D promotes deeper reasoning with prediction, error-spotting, and equation-forming problems that require generalisation and pattern recognition.
In Section A, students use bar models to divide whole numbers by unit fractions and recognise the connection between division and multiplication.
Section B extends to non-unit fractions, using diagrams and reasoning to identify when results are whole numbers.
Section C explores mixed-number quotients, challenging learners to interpret remainders within bar models and to correct common misconceptions such as misreading fractional remainders.
Finally, Section D promotes deeper reasoning with prediction, error-spotting, and equation-forming problems that require generalisation and pattern recognition.
All worksheets are created by the team of experienced teachers at Cazoom Math.
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This dividing integers by fractions worksheet is designed for students in 5th Grade and 6th Grade and aligns with Common Core State Standards.