Fractions — Addition, Subtraction, Mixed Numbers

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Recall what a fraction is and identify its parts (numerator and denominator)
Identify types of fractions: proper, improper, mixed, unit, like, and unlike
Find equivalent fractions by multiplying or dividing both parts
Simplify (reduce) fractions to their lowest terms using HCF
Compare fractions using LCM of denominators or cross multiplication
Convert between improper fractions and mixed numbers
Add like and unlike fractions (including mixed numbers)
Subtract like and unlike fractions (including mixed numbers)
Solve word problems involving addition and subtraction of fractions

Introduction — Fractions in Daily Life

Imagine you are at a birthday party. Meena's mother cuts a pizza into 8 equal slices. Meena eats 3 slices and Arjun eats 2 slices. How much of the pizza did each person eat? Meena ate 3/8 (three-eighths) and Arjun ate 2/8 (two-eighths) of the pizza. Together, they ate 5/8 of the pizza. This is an example of adding fractions!

Fractions are everywhere in our daily life:

Sharing rotis equally at dinner — "Each person gets 2 and a half rotis" = 2½
Measuring ingredients for kheer — "Add ¾ cup of sugar"
Telling time — "It's quarter past three" = ¼ of an hour past 3
Distance — "We have covered ⅔ of the journey from Delhi to Agra"
Marks in a test — "Priya scored 17 out of 20" = 17/20

In Class 4, you learned about types of fractions and how to compare them. In Class 5, we will learn how to add and subtract fractions — including fractions with different denominators (unlike fractions) and mixed numbers!

Revision — What is a Fraction?

A fraction represents a part of a whole. When we divide something into equal parts and take some of those parts, we get a fraction.

A fraction is written as:

Numerator / Denominator

Numerator (top number) = How many parts we have taken
Denominator (bottom number) = How many equal parts the whole is divided into

Example: If a chocolate bar is divided into 5 equal parts and Ravi eats 2 parts, then Ravi has eaten 2/5 (two-fifths) of the chocolate.
Here: Numerator = 2, Denominator = 5

Image needed: A visual showing what a fraction means — a rectangle divided into 5 equal parts with 2 parts shaded in colour. The fraction 2/5 labelled with arrows pointing to numerator (2) and denominator (5). Also show a circle divided into 8 parts with 3 shaded = 3/8.
Style: Clean flat illustration, bright colours, child-friendly, labelled clearly
Size: 700×350px

Remember: The denominator can NEVER be zero! You cannot divide something into 0 equal parts. So fractions like 5/0 do not exist.

Types of Fractions

Let us revise and learn all the different types of fractions:

Type	Definition	Examples
Proper Fraction	Numerator is less than the denominator. Value is less than 1.	1/2, 3/7, 5/9, 2/11
Improper Fraction	Numerator is greater than or equal to the denominator. Value is 1 or more.	7/3, 11/5, 9/4, 6/6
Mixed Number	A whole number + a proper fraction written together.	2⅓, 5¾, 1½, 3⅖
Unit Fraction	A fraction with numerator = 1.	1/2, 1/3, 1/5, 1/10
Like Fractions	Fractions with the same denominator.	2/7, 5/7, 1/7, 6/7
Unlike Fractions	Fractions with different denominators.	1/3, 2/5, 3/8, 4/9

Image needed: Visual showing 3 types of fractions using pie charts: (1) Proper fraction — circle with less than half shaded (3/8), (2) Improper fraction — one full circle + part of another shaded (7/4), (3) Mixed number — 1 full circle + 3/4 of another = 1 and 3/4. Each labelled clearly.
Style: Colourful pie diagrams, labelled, child-friendly
Size: 750×350px

Quick Check — Identify the type:
• 5/8 → Proper (5 < 8)
• 12/5 → Improper (12 > 5)
• 3¼ → Mixed number
• 1/6 → Unit fraction (numerator = 1)
• 3/7 and 5/7 → Like fractions (same denominator 7)
• 2/3 and 4/5 → Unlike fractions (different denominators)

Equivalent Fractions

Equivalent fractions are fractions that look different but represent the same value. They are equal in size even though they have different numerators and denominators.

How to Make Equivalent Fractions

Multiply both the numerator and denominator by the same number (not zero).
Divide both the numerator and denominator by the same number (their common factor).

Rule: If you multiply or divide BOTH parts of a fraction by the same number, the value of the fraction does not change.

Example 1: Find 3 equivalent fractions of 2/3.

Multiply by 2: 2/3 = (2×2)/(3×2) = 4/6
Multiply by 3: 2/3 = (2×3)/(3×3) = 6/9
Multiply by 4: 2/3 = (2×4)/(3×4) = 8/12

So, 2/3 = 4/6 = 6/9 = 8/12 (all equivalent!)

Example 2: Are 3/4 and 9/12 equivalent?

Method 1 (Cross multiply): 3 × 12 = 36 and 4 × 9 = 36. Since both are equal, YES, they are equivalent.

Method 2 (Simplify): 9/12 = (9÷3)/(12÷3) = 3/4. Since we get 3/4, YES, they are equivalent.

Image needed: A fraction wall showing equivalent fractions visually — horizontal bars divided into different numbers of equal parts. Show 1/2 = 2/4 = 3/6 = 4/8 and 1/3 = 2/6 = 3/9 = 4/12 with shaded portions aligned to show equality. Colourful bars.
Style: Fraction wall diagram, horizontal bars, colour-coded, clearly labelled
Size: 750×450px

Think About It: Can you find an equivalent fraction of 1/2 with denominator 100? Yes! 1/2 = 50/100. This means half is the same as 50 out of 100 — which is also 50%!

Simplifying Fractions (Reducing to Lowest Terms)

A fraction is in its lowest terms (or simplest form) when the numerator and denominator have no common factor other than 1. This means their HCF (Highest Common Factor) is 1.

Steps to Simplify a Fraction

Step 1: Find the HCF of the numerator and the denominator.
Step 2: Divide both the numerator and the denominator by their HCF.
Step 3: The result is the fraction in its simplest form.

Example 1: Simplify 12/18.

Step 1: Find HCF of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
HCF = 6

Step 2: Divide both by 6.
12/18 = (12÷6)/(18÷6) = 2/3

So, 12/18 in lowest terms = 2/3

Example 2: Simplify 15/25.

HCF of 15 and 25 = 5
15/25 = (15÷5)/(25÷5) = 3/5

Example 3: Simplify 8/24.

HCF of 8 and 24 = 8
8/24 = (8÷8)/(24÷8) = 1/3

Example 4: Is 7/11 already in simplest form?

Factors of 7: 1, 7
Factors of 11: 1, 11
HCF = 1
Since HCF = 1, YES, 7/11 is already in its simplest form.

Comparing Fractions

To compare fractions means to find which one is greater, smaller, or if they are equal. The method depends on whether the fractions are like or unlike.

Case 1: Like Fractions (Same Denominator)

When fractions have the same denominator, simply compare the numerators. The fraction with the greater numerator is greater.

Example: Compare 3/7 and 5/7.
Same denominator (7). Compare numerators: 3 < 5.
So, 3/7 < 5/7

Case 2: Unlike Fractions (Different Denominators)

When fractions have different denominators, we must first make them like fractions (same denominator), then compare.

Method: Using LCM of Denominators

Step 1: Find the LCM of the two denominators.
Step 2: Convert both fractions to equivalent fractions with the LCM as denominator.
Step 3: Compare the numerators of the new like fractions.

Example 1: Compare 2/3 and 3/4.

Step 1: LCM of 3 and 4 = 12
Step 2: Convert both to denominator 12.
• 2/3 = (2×4)/(3×4) = 8/12
• 3/4 = (3×3)/(4×3) = 9/12
Step 3: Compare: 8/12 < 9/12
So, 2/3 < 3/4

Example 2: Compare 5/6 and 7/9.

LCM of 6 and 9 = 18
• 5/6 = (5×3)/(6×3) = 15/18
• 7/9 = (7×2)/(9×2) = 14/18
Compare: 15/18 > 14/18
So, 5/6 > 7/9

Cross Multiplication Method (Quick Check)

To compare a/b and c/d: multiply a×d and b×c.

Example: Compare 3/5 and 4/7.
3 × 7 = 21 and 5 × 4 = 20
Since 21 > 20, we get 3/5 > 4/7

Converting Between Improper Fractions and Mixed Numbers

Every improper fraction can be written as a mixed number, and every mixed number can be written as an improper fraction. These are two different ways of writing the same value.

Improper Fraction → Mixed Number

Steps

Divide the numerator by the denominator.
The quotient becomes the whole number part.
The remainder becomes the new numerator.
The denominator stays the same.

Formula: Numerator ÷ Denominator = Quotient (remainder R) → Mixed number = Quotient R/Denominator

Example 1: Convert 17/5 to a mixed number.

17 ÷ 5 = 3 remainder 2
So, 17/5 = 3⅖ (three and two-fifths)

Example 2: Convert 23/4 to a mixed number.

23 ÷ 4 = 5 remainder 3
So, 23/4 = 5¾ (five and three-quarters)

Example 3: Convert 9/9 to a mixed number.

9 ÷ 9 = 1 remainder 0
So, 9/9 = 1 (a whole number — no fraction part!)

Mixed Number → Improper Fraction

Steps

Multiply the whole number by the denominator.
Add the numerator to the result.
Write the answer over the same denominator.

Formula: Whole × Denominator + Numerator / Denominator

Example 1: Convert 3⅖ to an improper fraction.

(3 × 5) + 2 = 15 + 2 = 17
So, 3⅖ = 17/5

Example 2: Convert 4&frac37; to an improper fraction.

(4 × 7) + 3 = 28 + 3 = 31
So, 4&frac37; = 31/7

Example 3: Convert 2⅙ to an improper fraction.

(2 × 6) + 1 = 12 + 1 = 13
So, 2⅙ = 13/6

Addition of Fractions

Adding fractions is one of the most important skills in Class 5 Mathematics. The method depends on whether the fractions are like or unlike.

Adding Like Fractions (Same Denominator)

Rule

Keep the denominator the same.
Add the numerators.
Simplify if possible.

Formula: a/d + b/d = (a + b)/d

Example 1: 2/7 + 3/7
= (2 + 3)/7 = 5/7

Example 2: 5/9 + 7/9
= (5 + 7)/9 = 12/9 = 1&frac39; = 1⅓ (simplified)

Example 3: 3/8 + 1/8 + 2/8
= (3 + 1 + 2)/8 = 6/8 = 3/4 (simplified: 6÷2 / 8÷2)

Adding Unlike Fractions (Different Denominators)

When denominators are different, we cannot simply add the numerators. We must first convert the fractions to like fractions (same denominator) using the LCM.

Steps to Add Unlike Fractions

Step 1: Find the LCM of the denominators.
Step 2: Convert each fraction to an equivalent fraction with the LCM as denominator.
Step 3: Add the numerators (denominators are now the same).
Step 4: Simplify if needed. Convert to mixed number if improper.

Image needed: A step-by-step visual showing the addition of 1/3 + 1/4. Step 1: Two bars — one divided into 3 parts (1 shaded), another into 4 parts (1 shaded). Step 2: Both bars redrawn divided into 12 parts — first shows 4/12 shaded, second shows 3/12 shaded. Step 3: Combined bar showing 7/12 shaded. Clear labels at each step.
Style: Step-by-step visual with coloured bars, arrows between steps, labelled
Size: 800×450px

Example 1: Add 1/3 + 1/4

Step 1: LCM of 3 and 4 = 12
Step 2: Convert to denominator 12.
• 1/3 = (1×4)/(3×4) = 4/12
• 1/4 = (1×3)/(4×3) = 3/12
Step 3: Add: 4/12 + 3/12 = 7/12

Answer: 1/3 + 1/4 = 7/12

Example 2: Add 2/5 + 3/4

LCM of 5 and 4 = 20
• 2/5 = (2×4)/(5×4) = 8/20
• 3/4 = (3×5)/(4×5) = 15/20
Add: 8/20 + 15/20 = 23/20 = 1 3/20 (mixed number)

Example 3: Add 5/6 + 2/9

LCM of 6 and 9 = 18
• 5/6 = (5×3)/(6×3) = 15/18
• 2/9 = (2×2)/(9×2) = 4/18
Add: 15/18 + 4/18 = 19/18 = 1 1/18

Adding Mixed Numbers

To add mixed numbers, you can use two methods:

Method 1: Add Whole Numbers and Fractions Separately

Add the whole number parts together.
Add the fraction parts together (find LCM if unlike).
Combine the results. If the fraction part is improper, convert and add to the whole number.

Example 4: Add 2⅓ + 3¼

Whole numbers: 2 + 3 = 5
Fractions: 1/3 + 1/4 = 4/12 + 3/12 = 7/12
Combined: 5 7/12

Example 5: Add 3⅚ + 2¾

Whole numbers: 3 + 2 = 5
Fractions: 5/6 + 3/4. LCM of 6 and 4 = 12
• 5/6 = 10/12 and 3/4 = 9/12
• 10/12 + 9/12 = 19/12 = 1 7/12
Combined: 5 + 1 7/12 = 6 7/12

Method 2: Convert to Improper Fractions First

Convert both mixed numbers to improper fractions.
Find LCM and add as unlike fractions.
Convert the result back to a mixed number.

Example 6: Add 2⅓ + 3¼ (using Method 2)

Convert: 2⅓ = 7/3 and 3¼ = 13/4
LCM of 3 and 4 = 12
• 7/3 = 28/12 and 13/4 = 39/12
• 28/12 + 39/12 = 67/12
Convert back: 67 ÷ 12 = 5 remainder 7
Answer: 5 7/12 (same answer as Method 1!)

Subtraction of Fractions

Subtracting fractions works just like addition — the only difference is we subtract the numerators instead of adding them.

Subtracting Like Fractions (Same Denominator)

Rule

Keep the denominator the same.
Subtract the numerators.
Simplify if possible.

Formula: a/d − b/d = (a − b)/d

Example 1: 7/9 − 4/9
= (7 − 4)/9 = 3/9 = 1/3 (simplified)

Example 2: 11/12 − 5/12
= (11 − 5)/12 = 6/12 = 1/2 (simplified)

Subtracting Unlike Fractions (Different Denominators)

Steps to Subtract Unlike Fractions

Step 1: Find the LCM of the denominators.
Step 2: Convert each fraction to equivalent fractions with the LCM as denominator.
Step 3: Subtract the numerators.
Step 4: Simplify if needed.

Example 3: Subtract 3/4 − 1/3

LCM of 4 and 3 = 12
• 3/4 = (3×3)/(4×3) = 9/12
• 1/3 = (1×4)/(3×4) = 4/12
Subtract: 9/12 − 4/12 = 5/12

Example 4: Subtract 5/6 − 2/5

LCM of 6 and 5 = 30
• 5/6 = (5×5)/(6×5) = 25/30
• 2/5 = (2×6)/(5×6) = 12/30
Subtract: 25/30 − 12/30 = 13/30
Answer: 13/30 (already in simplest form)

Example 5: Subtract 7/8 − 1/6

LCM of 8 and 6 = 24
• 7/8 = (7×3)/(8×3) = 21/24
• 1/6 = (1×4)/(6×4) = 4/24
Subtract: 21/24 − 4/24 = 17/24
Answer: 17/24

Subtracting a Fraction from a Whole Number

To subtract a fraction from a whole number, write the whole number as a fraction with the same denominator.

Example 6: 5 − 2/3

Write 5 as a fraction with denominator 3: 5 = 15/3
Now subtract: 15/3 − 2/3 = 13/3 = 4⅓

Example 7: 3 − 5/8

Write 3 as 24/8
Subtract: 24/8 − 5/8 = 19/8 = 2⅜

Subtracting Mixed Numbers

Method: Subtract Whole Numbers and Fractions Separately

Subtract the whole number parts.
Subtract the fraction parts (find LCM if unlike).
If the fraction being subtracted is larger, borrow 1 from the whole number.

Example 8: 5¾ − 2¼

Whole numbers: 5 − 2 = 3
Fractions: 3/4 − 1/4 = 2/4 = 1/2
Combined: 3½

Example 9: 4⅓ − 1⅚ (fraction part needs borrowing!)

Fractions: 1/3 − 5/6. LCM of 3 and 6 = 6.
1/3 = 2/6. But 2/6 − 5/6 gives a negative! We need to borrow.

Borrow 1 from 4: Now we have 3 and (1 + 1/3) = 3 and 4/3 = 3 and 8/6
Now subtract: 8/6 − 5/6 = 3/6 = 1/2
Whole numbers: 3 − 1 = 2
Answer: 2½

Example 10 (Improper fraction method): 4⅓ − 1⅚

Convert to improper: 4⅓ = 13/3 and 1⅚ = 11/6
LCM of 3 and 6 = 6
• 13/3 = 26/6 and 11/6 = 11/6
Subtract: 26/6 − 11/6 = 15/6 = 5/2 = 2½ (same answer!)

Word Problems — Fractions in Real Life

Let us solve some word problems using addition and subtraction of fractions. Notice how fractions appear in everyday situations!

Problem 1: Sita spent 1/4 of her pocket money on a book and 2/5 on stationery. What fraction of her money did she spend in total?

Solution: Total spent = 1/4 + 2/5
LCM of 4 and 5 = 20
1/4 = 5/20 and 2/5 = 8/20
Total = 5/20 + 8/20 = 13/20
Sita spent 13/20 of her pocket money.

Problem 2: Arjun's family drove from Delhi to Agra (a journey of 240 km). They covered 2/3 of the distance before stopping for lunch. How far did they still have to go?

Solution: Fraction remaining = 1 − 2/3 = 3/3 − 2/3 = 1/3
Distance remaining = 1/3 × 240 = 80 km

Problem 3: Meena's recipe for kheer needs 3½ cups of milk. She has only 1¾ cups. How much more milk does she need?

Solution: More milk needed = 3½ − 1¾
Convert to improper: 3½ = 7/2 and 1¾ = 7/4
LCM of 2 and 4 = 4
7/2 = 14/4 and 7/4 = 7/4
Subtract: 14/4 − 7/4 = 7/4 = 1¾ cups
Meena needs 1¾ more cups of milk.

Problem 4: Ravi studied for 2⅓ hours in the morning and 1⅚ hours in the evening. How many hours did he study in total?

Solution: Total = 2⅓ + 1⅚
Convert: 2⅓ = 7/3 and 1⅚ = 11/6
LCM of 3 and 6 = 6
7/3 = 14/6 and 11/6 = 11/6
Add: 14/6 + 11/6 = 25/6 = 4⅙ hours

Problem 5: A water tank is 7/8 full. If 1/3 of the water is used for washing clothes, what fraction of the tank still has water?

Solution: Water remaining = 7/8 − 1/3
LCM of 8 and 3 = 24
7/8 = 21/24 and 1/3 = 8/24
Subtract: 21/24 − 8/24 = 13/24
The tank is 13/24 full.

Image needed: Real-life fraction scenarios illustrated: (1) A pizza cut into 8 slices with some taken, (2) A measuring cup showing 3/4 mark for recipe, (3) A clock face showing quarter past (1/4 hour), (4) A road with a car at 2/3 distance mark between Delhi and Agra signs.
Style: Four small illustrations in a 2×2 grid, colourful, child-friendly, labelled
Size: 750×500px

Key Words

Term	Meaning
Fraction	A part of a whole, written as numerator/denominator
Numerator	Top number — how many parts are taken
Denominator	Bottom number — how many equal parts the whole is divided into
Proper Fraction	Numerator less than denominator (value < 1)
Improper Fraction	Numerator greater than or equal to denominator (value ≥ 1)
Mixed Number	Whole number + proper fraction (e.g., 3½)
Equivalent Fractions	Fractions with same value but different numerators/denominators
Simplest Form	Fraction where HCF of numerator and denominator is 1
Like Fractions	Fractions with the same denominator
Unlike Fractions	Fractions with different denominators
LCM	Least Common Multiple — used to find common denominator
HCF	Highest Common Factor — used to simplify fractions

Key Points to Remember

A fraction = Numerator ÷ Denominator. The denominator can never be zero.
Proper fraction: numerator < denominator. Improper: numerator ≥ denominator.
To find equivalent fractions, multiply or divide both parts by the same number.
To simplify: divide both numerator and denominator by their HCF.
To compare unlike fractions: find LCM of denominators, convert, then compare numerators.
Improper → Mixed: Divide numerator by denominator. Quotient = whole, Remainder = new numerator.
Mixed → Improper: (Whole × Denominator + Numerator) / Denominator.
Adding like fractions: Add numerators, keep denominator same.
Adding unlike fractions: Find LCM → convert to like → add numerators.
Subtracting fractions: Same as addition, but subtract numerators instead.
When subtracting mixed numbers, borrow 1 from the whole number if the fraction part is too small.
Always simplify your final answer and convert improper fractions to mixed numbers.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. What is 2/3 + 1/6?

2/3 = 4/6, so 4/6 + 1/6 = 5/6.

2. The mixed number for 23/5 is:

23 ÷ 5 = 4 remainder 3, so 23/5 = 4⅗.

3. Which pair are like fractions?

Like fractions have the same denominator. 3/7 and 5/7 both have 7.

4. 5¼ − 2¾ = ?

5¼ = 21/4, 2¾ = 11/4. 21/4 − 11/4 = 10/4 = 2½.

5. Add the like fractions: 3/8 + 5/8 = (write in lowest terms)

3/8 + 5/8 = 8/8 = 1.

6. Reduce to lowest terms: 6/18 =

6 and 18 share a factor of 6. 6÷6 = 1, 18÷6 = 3, so 6/18 = 1/3.

7. Compare using >, < or = : 3/5 ___ 4/7

3/5 = 21/35 and 4/7 = 20/35. Since 21/35 > 20/35, we get 3/5 > 4/7.

8. Convert to a mixed number: 19/4 =

19 ÷ 4 = 4 remainder 3, so 19/4 = 4¾ (written 4 3/4).

Practice Questions

A. Identify the type of fraction:

1. 5/9 →

2. 11/4 →

3. 3⅖ →

4. 1/8 →

5. 7/7 →

6. 15/4 →

B. Find 3 equivalent fractions for each:

1. 3/5 = = =

2. 2/7 = = =

3. 4/9 = = =

4. 5/6 = = =

C. Reduce to lowest terms:

1. 6/18 =

2. 14/21 =

3. 20/35 =

4. 9/27 =

5. 24/36 =

D. Compare using >, < or =

1. 3/5 4/7

2. 5/8 7/12

3. 2/3 8/12

4. 4/9 5/11

5. 7/10 3/4

E. Convert improper to mixed and vice versa:

1. 19/4 =

2. 25/7 =

3. 33/8 =

4. 4⅗ =

5. 6&frac27; =

6. 2&frac59; =

F. Add the fractions:

1. 3/8 + 5/8 =

2. 2/5 + 1/3 =

3. 3/4 + 5/6 =

4. 1/2 + 2/7 =

5. 4/9 + 5/6 =

6. 2⅓ + 1¼ =

7. 3⅖ + 2¾ =

8. 1⅚ + 4⅔ =

G. Subtract the fractions:

1. 7/9 − 4/9 =

2. 5/6 − 1/4 =

3. 3/4 − 2/5 =

4. 7/8 − 1/3 =

5. 4 − 3/7 =

6. 5½ − 2¼ =

7. 6⅓ − 3¾ =

8. 8⅙ − 5⅔ =

H. True or False:

1. 3/4 and 9/12 are equivalent fractions.

2. An improper fraction is always greater than 1.

3. To add unlike fractions, we must first find the LCM of the denominators.

4. 5/5 is a proper fraction.

5. The fraction 7/21 in simplest form is 1/3.

I. Choose the correct answer (MCQ):

1. What is 2/3 + 1/6?

a) 3/9 b) 5/6 c) 3/6 d) 1/2

2. The mixed number for 23/5 is:

a) 4⅕ b) 4⅗ c) 5⅗ d) 3⅘

3. Which pair are like fractions?

a) 2/3 and 2/5 b) 3/7 and 5/7 c) 1/4 and 3/8 d) 5/6 and 6/5

4. 5¼ − 2¾ = ?

a) 3½ b) 2½ c) 2¼ d) 3¼

J. Word Problems:

1. Priya read 2/5 of a storybook on Monday and 1/4 of the book on Tuesday. What fraction of the book has she read in total?

2. A recipe for mango lassi needs 3½ cups of yoghurt. Ravi has 1¾ cups. How much more yoghurt does he need?

3. Arjun walked 5/6 km to school. Meena walked 3/4 km. Who walked more? By how much?

4. A water tank was 7/8 full. After using water for cooking, it became 1/2 full. What fraction of water was used?

5. Sita spent 1½ hours on maths homework and 2¼ hours on a science project. How much total time did she spend studying?

Activity — Fraction Pizza Party!

Get a piece of paper and follow these steps:

Draw 3 circles of the same size (use a plate or compass). These are your "pizzas."
Pizza 1: Divide into 4 equal slices. Colour 1/4 red and 2/4 yellow. Write the addition: 1/4 + 2/4 = 3/4
Pizza 2: Divide into 8 equal slices. Colour 3/8 green and 2/8 blue. Write: 3/8 + 2/8 = 5/8
Pizza 3 (Challenge!): Draw one circle divided into 3 parts and another into 6 parts. Colour 1/3 of the first and 1/6 of the second. Can you show that 1/3 + 1/6 = 3/6 = 1/2? (Hint: 1/3 = 2/6)

Bonus: Share your pizzas with family and explain how you added fractions with pictures!

Want to review the lesson again?

Mathematics

Fractions — Addition, Subtraction, Mixed Numbers

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Identify types of fractions: proper, improper, mixed, like, unlike
Find equivalent fractions and simplify to lowest terms
Compare fractions using LCM
Convert between improper fractions and mixed numbers
Add and subtract like and unlike fractions (including mixed numbers)
Solve word problems on fractions

What is a Fraction?

A fraction represents a part of a whole. It is written as Numerator/Denominator.

Numerator (top) = parts taken. Denominator (bottom) = total equal parts. Denominator can never be 0.

Example: If a chocolate has 5 equal parts and Ravi eats 2, he ate 2/5 of it.

[Image: Visual showing fraction concept — rectangle divided into 5 parts with 2 shaded = 2/5, and circle divided into 8 parts with 3 shaded = 3/8]

Types of Fractions

Type	Definition	Examples
Proper	Numerator < Denominator (value < 1)	1/2, 3/7, 5/9
Improper	Numerator ≥ Denominator (value ≥ 1)	7/3, 11/5, 9/4
Mixed Number	Whole number + proper fraction	2⅓, 5¾
Unit Fraction	Numerator = 1	1/2, 1/5, 1/10
Like Fractions	Same denominator	2/7, 5/7, 1/7
Unlike Fractions	Different denominators	1/3, 2/5, 3/8

[Image: Types of fractions as pie charts — proper (3/8), improper (7/4 shown as 1 full + 3/4), mixed number (1 and 3/4)]

Equivalent Fractions

Rule: Multiply or divide BOTH numerator and denominator by the same number → value stays the same.

Example: 3 equivalent fractions of 2/3:
2/3 = (2×2)/(3×2) = 4/6 = (2×3)/(3×3) = 6/9 = (2×4)/(3×4) = 8/12

Check: Are 3/4 and 9/12 equivalent? Cross multiply: 3×12=36 and 4×9=36. Equal! YES.

[Image: Fraction wall showing 1/2 = 2/4 = 3/6 = 4/8 and 1/3 = 2/6 = 3/9 with coloured bars aligned]

Simplifying Fractions (Lowest Terms)

Steps: (1) Find HCF of numerator and denominator. (2) Divide both by HCF.

Ex 1: 12/18 → HCF(12,18) = 6 → 12÷6 / 18÷6 = 2/3
Ex 2: 15/25 → HCF = 5 → 3/5
Ex 3: 8/24 → HCF = 8 → 1/3
Ex 4: 7/11 → HCF = 1 → already in simplest form!

Comparing Fractions

Like fractions: Compare numerators directly. Unlike fractions: Find LCM → convert → compare.

Ex 1: Compare 2/3 and 3/4. LCM(3,4)=12. 2/3=8/12, 3/4=9/12. 8<9 → 2/3 < 3/4
Ex 2: Compare 5/6 and 7/9. LCM(6,9)=18. 5/6=15/18, 7/9=14/18. 15>14 → 5/6 > 7/9
Cross multiply: 3/5 vs 4/7 → 3×7=21, 5×4=20 → 21>20 → 3/5 > 4/7

Converting Improper Fractions and Mixed Numbers

Improper → Mixed: Divide numerator by denominator. Quotient = whole, Remainder = numerator.
Mixed → Improper: (Whole × Denominator + Numerator) / Denominator

Improper → Mixed: 17/5 → 17÷5 = 3 rem 2 → 3⅖ | 23/4 → 23÷4 = 5 rem 3 → 5¾
Mixed → Improper: 3⅖ → (3×5+2)/5 = 17/5 | 4&frac37; → (4×7+3)/7 = 31/7

Addition of Like Fractions

Rule: a/d + b/d = (a+b)/d — Keep denominator, add numerators. Simplify.

2/7 + 3/7 = 5/7 | 5/9 + 7/9 = 12/9 = 1⅓ | 3/8 + 1/8 + 2/8 = 6/8 = 3/4

Addition of Unlike Fractions

Steps: (1) Find LCM of denominators. (2) Convert to like fractions. (3) Add numerators. (4) Simplify.

[Image: Step-by-step visual of adding 1/3 + 1/4 — bars divided into 3 and 4, then redrawn as 12ths showing 4/12 + 3/12 = 7/12]

Ex 1: 1/3 + 1/4. LCM(3,4)=12. 1/3=4/12, 1/4=3/12. Answer: 7/12
Ex 2: 2/5 + 3/4. LCM(5,4)=20. 2/5=8/20, 3/4=15/20. Answer: 23/20 = 1 3/20
Ex 3: 5/6 + 2/9. LCM(6,9)=18. 5/6=15/18, 2/9=4/18. Answer: 19/18 = 1 1/18

Adding Mixed Numbers

Method 1: Add whole numbers separately + Add fractions separately (find LCM if unlike). Combine.
Method 2: Convert both to improper fractions → add → convert back.

Ex 1: 2⅓ + 3¼ → Wholes: 2+3=5, Fractions: 1/3+1/4=4/12+3/12=7/12 → 5 7/12
Ex 2: 3⅚ + 2¾ → Wholes: 5, Fractions: 5/6+3/4, LCM=12: 10/12+9/12=19/12=1 7/12 → 6 7/12

Subtraction of Like Fractions

Rule: a/d − b/d = (a−b)/d — Keep denominator, subtract numerators. Simplify.

7/9 − 4/9 = 3/9 = 1/3 | 11/12 − 5/12 = 6/12 = 1/2

Subtraction of Unlike Fractions

Steps: (1) Find LCM. (2) Convert to like fractions. (3) Subtract numerators. (4) Simplify.

Ex 1: 3/4 − 1/3. LCM(4,3)=12. 3/4=9/12, 1/3=4/12. Answer: 5/12
Ex 2: 5/6 − 2/5. LCM(6,5)=30. 5/6=25/30, 2/5=12/30. Answer: 13/30
From whole number: 5 − 2/3 = 15/3 − 2/3 = 13/3 = 4⅓

Subtracting Mixed Numbers

Method: Subtract wholes and fractions separately. If fraction part too small, borrow 1 from whole.

Ex 1: 5¾ − 2¼ → Wholes: 5−2=3, Fractions: 3/4−1/4=2/4=1/2 → 3½
Ex 2 (Borrowing): 4⅓ − 1⅚ → Convert: 13/3 − 11/6, LCM=6: 26/6 − 11/6 = 15/6 = 5/2 = 2½

Word Problems

1. Sita spent 1/4 on a book + 2/5 on stationery. Total = 5/20+8/20 = 13/20 of money.
2. Meena needs 3½ cups milk, has 1¾. More needed: 7/2−7/4=14/4−7/4=7/4 = 1¾ cups
3. Ravi studied 2⅓ + 1⅚ hrs = 14/6+11/6 = 25/6 = 4⅙ hours
4. Tank 7/8 full, used 1/3. Remaining: 21/24−8/24 = 13/24

[Image: Real-life fractions — pizza slices, measuring cup at 3/4, clock showing quarter past, car at 2/3 of Delhi-Agra road]

Key Words

Term	Meaning
Numerator	Top number (parts taken)
Denominator	Bottom number (total equal parts)
Equivalent	Same value, different form
Simplest Form	HCF of num. and den. is 1
LCM	Least Common Multiple (for common denominator)
HCF	Highest Common Factor (for simplifying)

Key Points:
• Like fractions: add/subtract numerators, keep denominator.
• Unlike fractions: find LCM → convert to like → then add/subtract.
• Improper → Mixed: divide. Mixed → Improper: multiply whole × den + num.
• When subtracting mixed numbers, borrow 1 if fraction part too small.
• Always simplify final answer. Convert improper results to mixed numbers.

Practice Questions

A. Identify the type of fraction:

1. 5/9 →

2. 11/4 →

3. 3⅖ →

4. 1/8 →

5. 7/7 →

6. 15/4 →

B. Find 3 equivalent fractions for each:

1. 3/5 = = =

2. 2/7 = = =

3. 4/9 = = =

4. 5/6 = = =

C. Reduce to lowest terms:

1. 6/18 =

2. 14/21 =

3. 20/35 =

4. 9/27 =

5. 24/36 =

D. Compare using >, < or =

1. 3/5 4/7

2. 5/8 7/12

3. 2/3 8/12

4. 4/9 5/11

5. 7/10 3/4

E. Convert improper to mixed and vice versa:

1. 19/4 =

2. 25/7 =

3. 33/8 =

4. 4⅗ =

5. 6&frac27; =

6. 2&frac59; =

F. Add the fractions:

1. 3/8 + 5/8 =

2. 2/5 + 1/3 =

3. 3/4 + 5/6 =

4. 1/2 + 2/7 =

5. 4/9 + 5/6 =

6. 2⅓ + 1¼ =

7. 3⅖ + 2¾ =

8. 1⅚ + 4⅔ =

G. Subtract the fractions:

1. 7/9 − 4/9 =

2. 5/6 − 1/4 =

3. 3/4 − 2/5 =

4. 7/8 − 1/3 =

5. 4 − 3/7 =

6. 5½ − 2¼ =

7. 6⅓ − 3¾ =

8. 8⅙ − 5⅔ =

H. True or False:

1. 3/4 and 9/12 are equivalent fractions.

2. An improper fraction is always greater than 1.

3. To add unlike fractions, we must find LCM of denominators.

4. 5/5 is a proper fraction.

5. 7/21 in simplest form is 1/3.

I. Choose the correct answer (MCQ):

1. What is 2/3 + 1/6?

a) 3/9 b) 5/6 c) 3/6 d) 1/2

2. The mixed number for 23/5 is:

a) 4⅕ b) 4⅗ c) 5⅗ d) 3⅘

3. Which pair are like fractions?

a) 2/3, 2/5 b) 3/7, 5/7 c) 1/4, 3/8 d) 5/6, 6/5

4. 5¼ − 2¾ = ?

a) 3½ b) 2½ c) 2¼ d) 3¼

J. Word Problems:

1. Priya read 2/5 of a book on Monday and 1/4 on Tuesday. What fraction has she read in total?

2. A recipe needs 3½ cups of yoghurt. Ravi has 1¾ cups. How much more does he need?

3. Arjun walked 5/6 km, Meena walked 3/4 km. Who walked more? By how much?

4. A tank was 7/8 full, now it is 1/2 full. What fraction of water was used?

5. Sita spent 1½ hours on maths and 2¼ hours on science. Total study time?

Activity — Fraction Pizza Party!

Draw 3 circles (pizzas). Divide Pizza 1 into 4 slices — colour 1/4 + 2/4 = 3/4. Divide Pizza 2 into 8 slices — colour 3/8 + 2/8 = 5/8. Pizza 3 (Challenge): Show 1/3 + 1/6 = 1/2 using equivalent fractions!

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