Great Inheritance Mathematics Term A · Independent learning

Dividing a Fraction by a Whole Number

Learning target: Share a proper fraction among whole-number groups and verify using multiplication.

Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.

Opening task

Explore · fraction sharing

Divide 3/5 of a liter of juice into 2 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 3/10 L

How it works: Sharing model: (3/5) ÷ 2 = 3/(5×2) = 3/10 L per portion. Check 2×3/10=3/5.

Lesson-specific prerequisite checkpoint

Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.

What is 3/4 of 12 counters?

Show answer and worked explanation

Answer: 9 counters

How it works: 12 ÷ 4 × 3 = 9; this is of-a-set, not yet sharing.

Understand the idea

Share a proper fraction among whole-number groups and verify using multiplication.

To divide a proper fraction among equal groups, begin with the fraction as a quantity on one consistent whole. Split that shaded quantity equally, then check by rebuilding all groups. A fractional share may simplify by common factors.

Vocabulary focus: sharing interpretation, measurement interpretation, inverse multiplication. Make a small labeled model, work through the arithmetic, and explain the result in words.

Watch for: Dividing only the numerator even when a visual explanation is required.

Model to study: Equal-part fraction strip.

Worked examples

Worked examples 1 · fraction sharing

Divide 3/8 of a liter of juice into 2 equal portions. How many liters per portion?

Solution: 3/16 L

Why: Sharing model: (3/8) ÷ 2 = 3/(8×2) = 3/16 L per portion. Check 2×3/16=3/8.

Worked examples 2 · fraction sharing

Divide 2/5 of a liter of juice into 3 equal portions. How many liters per portion?

Solution: 2/15 L

Why: Sharing model: (2/5) ÷ 3 = 2/(5×3) = 2/15 L per portion. Check 3×2/15=2/5.

Worked examples 3 · fraction sharing

Divide 2/4 of a liter of juice into 4 equal portions. How many liters per portion?

Solution: 1/8 L

Why: Sharing model: (2/4) ÷ 4 = 2/(4×4) = 1/8 L per portion. Check 4×1/8=1/2.

Check understanding

Check understanding 1 · fraction sharing

Divide 4/6 of a liter of juice into 3 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 2/9 L

How it works: Sharing model: (4/6) ÷ 3 = 4/(6×3) = 2/9 L per portion. Check 3×2/9=2/3.

Check understanding 2 · fraction sharing

Divide 5/6 of a liter of juice into 4 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 5/24 L

How it works: Sharing model: (5/6) ÷ 4 = 5/(6×4) = 5/24 L per portion. Check 4×5/24=5/6.

Guided practice

Guided practice 1 · fraction sharing

Divide 2/6 of a liter of juice into 3 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 1/9 L

How it works: Sharing model: (2/6) ÷ 3 = 2/(6×3) = 1/9 L per portion. Check 3×1/9=1/3.

Guided practice 2 · fraction sharing

Divide 3/4 of a liter of juice into 3 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 1/4 L

How it works: Sharing model: (3/4) ÷ 3 = 3/(4×3) = 1/4 L per portion. Check 3×1/4=3/4.

Guided practice 3 · fraction sharing

Divide 5/6 of a liter of juice into 3 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 5/18 L

How it works: Sharing model: (5/6) ÷ 3 = 5/(6×3) = 5/18 L per portion. Check 3×5/18=5/6.

Independent practice

Independent practice 1 · fraction sharing

Divide 3/4 of a liter of juice into 4 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 3/16 L

How it works: Sharing model: (3/4) ÷ 4 = 3/(4×4) = 3/16 L per portion. Check 4×3/16=3/4.

Independent practice 2 · fraction sharing

Divide 6/8 of a liter of juice into 2 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 3/8 L

How it works: Sharing model: (6/8) ÷ 2 = 6/(8×2) = 3/8 L per portion. Check 2×3/8=3/4.

Independent practice 3 · fraction sharing

Divide 4/5 of a liter of juice into 5 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 4/25 L

How it works: Sharing model: (4/5) ÷ 5 = 4/(5×5) = 4/25 L per portion. Check 5×4/25=4/5.

Independent practice 4 · fraction sharing

Divide 7/8 of a liter of juice into 3 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 7/24 L

How it works: Sharing model: (7/8) ÷ 3 = 7/(8×3) = 7/24 L per portion. Check 3×7/24=7/8.

Independent practice 5 · fraction sharing

Divide 7/8 of a liter of juice into 2 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 7/16 L

How it works: Sharing model: (7/8) ÷ 2 = 7/(8×2) = 7/16 L per portion. Check 2×7/16=7/8.

Challenge and error analysis

Challenge and error analysis 1 · worked-error diagnosis

Error-analysis notebook: Learner notebook (LESSON): “Dividing 3/4 by 4 means multiplying, so I wrote 3 instead of finding the right group size.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Divide 6/8 of a liter of juice into 4 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 3/16 L

How it works: Wrong step/assumption: Learner notebook (LESSON): “Dividing 3/4 by 4 means multiplying, so I wrote 3 instead of finding the right group size.” Diagnosis: Differentiate equal sharing from measuring group count, and check the inverse multiplication with the correct quotient unit. Correct computation: Sharing model: (6/8) ÷ 4 = 6/(8×4) = 3/16 L per portion. Check 4×3/16=3/4.

Challenge and error analysis 2 · reasoning transfer

Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Divide 3/4 of a liter of juice into 2 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 3/8 L

How it works: Sharing model: (3/4) ÷ 2 = 3/(4×2) = 3/8 L per portion. Check 2×3/8=3/4. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.

Exit check

Exit check 1 · fraction sharing

Divide 2/8 of a liter of juice into 2 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 1/8 L

How it works: Sharing model: (2/8) ÷ 2 = 2/(8×2) = 1/8 L per portion. Check 2×1/8=1/4.

Exit check 2 · fraction sharing

Divide 2/4 of a liter of juice into 3 equal portions. How many liters per portion?

Show answer and worked explanation

Answer: 1/6 L

How it works: Sharing model: (2/4) ÷ 3 = 2/(4×3) = 1/6 L per portion. Check 3×1/6=1/2.

Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.