Grade 5 Mathematics - Fractions (Subtracting Unlike Denominators)

Big Idea: Key Concept

When subtracting fractions with different denominators, we cannot subtract directly because the pieces are different sizes. Just like you can't subtract 3 apples from 5 oranges without first converting them to the same unit (fruit), we must convert fractions to have the same denominator. This process uses equivalent fractions - different-looking fractions that represent the same amount. Once both fractions have a common denominator, we can subtract the numerators while keeping the denominator the same.

🧪 Interactive
Simulation

How-To Methods

Find the LCD: Identify the Least Common Denominator by finding the smallest number both denominators divide into evenly
Convert to Equivalent Fractions: Multiply numerator and denominator of each fraction by the same number to create fractions with the LCD
Subtract the Numerators: Keep the common denominator and subtract only the top numbers (numerators)
Simplify if Needed: Check if the answer can be reduced by dividing both numerator and denominator by their greatest common factor
Verify Your Answer: Convert back to see if the result makes sense - the difference should be smaller than the original fraction

Worked Example:

Problem: Subtract: 5/6 - 1/4

Find the LCD: Multiples of 6: 6, 12, 18... Multiples of 4: 4, 8, 12... LCD = 12

Convert 5/6 to denominator 12: 6 × 2 = 12, so multiply: (5 × 2)/(6 × 2) = 10/12

Convert 1/4 to denominator 12: 4 × 3 = 12, so multiply: (1 × 3)/(4 × 3) = 3/12

Subtract numerators: 10/12 - 3/12 = 7/12

Check if simplifiable: 7 and 12 share no common factors, so 7/12 is in simplest form

Answer: 5/6 - 1/4 = 7/12

(B) Basic Practice

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Problem 6 Apply ★★★ [12 pts]

Maya had 7/8 of a pizza. She gave 1/4 of the whole pizza to her brother. What fraction of the pizza does Maya have left?

A. 6/8

B. 5/8

C. 3/4

D. 1/2

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Problem 7 Apply ★★★ [12 pts]

A recipe calls for 3/4 cup of flour. You need to use 1/3 cup less. How much flour should you use?

A. 5/12 cup

B. 2/7 cup

C. 1/2 cup

D. 9/12 cup

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Problem 8 Apply ★★★ [12 pts]

Alex walked 9/10 of a mile to school. On the way home, he took a shortcut that was 2/5 of a mile shorter. How long was the walk home?

A. 1/2 mile

B. 7/10 mile

C. 7/15 mile

D. 5/10 mile

(D) Advanced Challenge (Higher-Order Thinking)

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Problem 10 Apply ★★★★ [14 pts]

A carpenter has a board that is 5/6 of a meter long. He cuts off 1/8 of a meter. How much of the board remains?

A. 4/6 meter

B. 1/2 meter

C. 9/24 meter

D. 17/24 meter

(E) Mini Quiz - Check Your Understanding!

Mini Quiz

E1. Subtract: 1/2 - 1/4

A. 1/4

B. 0

C. 2/4

D. 1/6

E2. Subtract: 4/5 - 1/2

A. 3/3

B. 3/10

C. 1/5

D. 2/5

E3. Emma drank 3/4 of a bottle of water. Her friend drank 1/3 of the same bottle. How much more did Emma drink than her friend?

A. 5/12

B. 2/7

C. 1/2

D. 7/12

Self-Reflection

How did you feel about this topic?
Confident / Okay / Confused - Circle one

What is one thing you must remember?

Problem-Solving Strategy (4-Step Process)

Challenge Problem: A baker used 7/8 cup of sugar for cookies and 2/3 cup of sugar for a cake. How much more sugar did the cookies need compared to the cake? Express your answer as a simplified fraction.

1. Understand:

2. Plan:

3. Execute:

4. Check:

(F) Answer Key & Detailed Explanations

#	Answer	Type	Solution
1	B	Apply	final_step: LCD = 12. Answer: B step_1: List multiples of 4: 4, 8, 12, 16... step_2: List multiples of 6: 6, 12, 18... step_3: The smallest common multiple is 12
2	A	Apply	final_step: Answer: A (1/4) step_1: Convert to common denominator 4: 3/4 stays as 3/4, 1/2 becomes 2/4 step_2: Subtract: 3/4 - 2/4 = 1/4
3	C	Apply	final_step: Answer: C (5/12) step_1: Need to find: 2/3 - 1/4 step_2: LCD of 3 and 4 is 12 step_3: Convert: 2/3 = 8/12, 1/4 = 3/12 step_4: Subtract: 8/12 - 3/12 = 5/12
4	D	Apply	final_step: Answer: D (1/2) step_1: Need to find: 5/6 - 1/3 step_2: LCD of 6 and 3 is 6 step_3: Convert: 5/6 stays 5/6, 1/3 = 2/6 step_4: Subtract: 5/6 - 2/6 = 3/6 = 1/2
5	B	Apply	final_step: Answer: B (3/10) step_1: Need to find: 7/10 - 2/5 step_2: LCD of 10 and 5 is 10 step_3: Convert: 7/10 stays 7/10, 2/5 = 4/10 step_4: Subtract: 7/10 - 4/10 = 3/10
6	B	Apply	final_step: Maya has 5/8 of the pizza left. Answer: B step_1: Convert 1/4 to eighths: 1/4 = 2/8 step_2: Subtract: 7/8 - 2/8 = 5/8
7	A	Apply	final_step: Answer: A (5/12 cup) step_1: Need to find: 3/4 - 1/3 step_2: LCD of 4 and 3 is 12 step_3: Convert: 3/4 = 9/12, 1/3 = 4/12 step_4: Subtract: 9/12 - 4/12 = 5/12
8	A	Apply	final_step: Answer: A (1/2 mile) step_1: Need to find: 9/10 - 2/5 step_2: LCD of 10 and 5 is 10 step_3: Convert: 9/10 stays 9/10, 2/5 = 4/10 step_4: Subtract: 9/10 - 4/10 = 5/10 = 1/2
9	C	Apply	final_step: Answer: C (7/24) step_1: LCD of 12 and 8 is 24 step_2: Convert: 11/12 = 22/24, 5/8 = 15/24 step_3: Subtract: 22/24 - 15/24 = 7/24 step_4: Check simplification: 7 and 24 have no common factors
10	D	Apply	final_step: Answer: D (17/24 meter remains) step_1: Need to find: 5/6 - 1/8 step_2: LCD of 6 and 8 is 24 step_3: Convert: 5/6 = 20/24, 1/8 = 3/24 step_4: Subtract: 20/24 - 3/24 = 17/24

(G) Mini Quiz Answers

Multiple Choice:

E1. A

E2. B

E3. A

Self-Reflection:

I feel pretty confident about subtracting fractions now. One thing I must remember is to always find the LCD first before subtracting, and I should check if my answer can be simplified by dividing both the numerator and denominator by their greatest common factor.

Problem-Solving Strategy (4-Step):

1. Understand: We need to subtract two fractions: 11/12 - 5/8. The fractions have different denominators (12 and 8), so we cannot subtract them directly. We must find a common denominator.

2. Plan: Find the LCD of 12 and 8, which is 24. Convert both fractions to equivalent fractions with denominator 24, then subtract the numerators and simplify if possible.

3. Execute: Step 1: LCD of 12 and 8 is 24. Step 2: Convert 11/12 to 24ths: (11 × 2)/(12 × 2) = 22/24. Step 3: Convert 5/8 to 24ths: (5 × 3)/(8 × 3) = 15/24. Step 4: Subtract: 22/24 - 15/24 = 7/24. Step 5: Check if 7/24 can be simplified - 7 and 24 have no common factors, so it's already in lowest terms.

4. Check: Verify by converting to decimals: 11/12 ≈ 0.917, 5/8 = 0.625, difference ≈ 0.292. And 7/24 ≈ 0.292. The answer checks out!

(I) Review Schedule

Review this worksheet on these dates for maximum retention:

Today (Initial Learning)
Tomorrow (Day 2)
Day 3 (Short-term consolidation)
Week 13 (1 week later)
Month 1 (Long-term retention)

Why this works: Ebbinghaus forgetting curve research shows spaced repetition increases retention by 200%+

학부모 가이드 (Parent Guide)

분모가 다른 분수의 뺄셈
아이에게 'Why do we need a common denominator to subtract fractions?'이라고 물어보며 같은 크기 조각의 중요성을 생각하게 해주세요.
피자나 케이크를 예시로 'How can we compare 1/4 and 1/6 pieces?'라고 물으며 시각화를 도와주세요.
분수를 통분할 때 'What number do both denominators go into?'라고 물어보며 최소공배수 찾기를 연습하세요.
실생활 상황을 만들어 'If you have 3/4 cup of milk and use 1/2 cup, how much is left?'처럼 문제를 만들어보세요.

Problem #	My Score	Error Type	What I Learned / How to Improve
#9	0/15	Concept	"I forgot to check my answer. Next time I will verify my solution."

Learning Objectives (What You'll Master Today)

(A) Mathematical Concepts - Self-Learning Guide

Big Idea: Key Concept

How-To Methods

Key Formula/Rule:

Worked Example:

Why This Matters

(B) Basic Practice

(C) Problem Solving (Real-World Applications)

(D) Advanced Challenge (Higher-Order Thinking)

(E) Mini Quiz - Check Your Understanding!

Mini Quiz

Problem-Solving Strategy (4-Step Process)

(F) Answer Key & Detailed Explanations

(G) Mini Quiz Answers

(H) Error Analysis Notebook (Growth Mindset Tool)

(I) Review Schedule

학부모 가이드 (Parent Guide)