Class 5 Maths Notes Chapter Fractions and LCM

📊 Complete Guide to LCM and Fractions

Class 5 Mathematics - Chapter 4

🔢Understanding Fractions

A fractional number or fraction indicates a part or parts of a whole. Fractions can represent:

• Part of a whole: 5/8 means 5 parts out of 8 equal parts
• Part of a collection: 3/4 of 12 apples means 9 apples
• Division: Any fraction can be expressed as division

💡 Key Point: A fraction a/b means a ÷ b, where a is the numerator and b is the denominator.

📂Types of Fractions

🔗 Like Fractions

Fractions with the same denominators

2/7, 3/7, 4/7, 5/7

🔀 Unlike Fractions

Fractions with different denominators

2/3, 5/6, 7/8, 8/9

1️⃣ Unit Fractions

Fractions with numerator 1

1/2, 1/4, 1/5

✅ Proper Fractions

Numerator < Denominator

3/4, 7/9, 13/16

❌ Improper Fractions

Numerator > Denominator

8/5, 9/4, 15/7

= Equivalent Fractions

Different fractions with same value

1/2 = 2/4 = 4/8

⚖️LCM in Fraction Operations

The Least Common Multiple (LCM) is crucial for working with unlike fractions. Here's how we use it:

Converting Unlike Fractions to Like Fractions

Example: Convert 2/3 and 4/5 to like fractions

Find LCM of denominators: LCM of 3 and 5 = 15

Convert 2/3: (2 × 5)/(3 × 5) = 10/15

Convert 4/5: (4 × 3)/(5 × 3) = 12/15

Result: 10/15 and 12/15 are like fractions

🎯 Testing Time 4.1 - Fractional Part of a Collection

1. Look at the figure given below and answer the questions that follow:

1. How many cups are there in all?
2. Find 1/4 of the total number of buttons.
3. Find 1/6 of the total number of buttons.

2. What fractional part of the collection of 24 cups do the following crossed cups represent?

(a) [Figure reference]

(b) [Figure reference]

3. Find 2/4 of a collection of:

(a) 8 stars

(b) 12 tables

(c) 18 apples

(d) 42 dogs

(e) 56 pencils

(f) 72 pens

4. Find 2/7 of a collection of:

(a) 14 mangoes

(b) 28 toffees

(c) 35 pens

(d) 49 toys

(e) 63 birds

(f) 77 kites

5. Find 3/5 of a collection of:

(a) 10 balls

(b) 15 dolls

(c) 25 balloons

(d) 45 coins

(e) 50 birds

(f) 70 marbles

🎯 Testing Time 4.2 - Fraction as Division

1. Write each of the following as a fraction:

(a) 8÷2

(b) 12÷3

(c) 45÷5

(d) 48÷8

(e) 63÷7

(f) 78÷13

(g) 84÷21

(h) 150÷25

2. Write each of the following as a division:

(a) 3/5

(b) 6/11

(c) 9/13

(d) 7/22

(e) 18/19

(f) 25/29

(g) 32/48

(h) 105/105

🎯 Testing Time 4.3 - Types of Fractions

1. Which of the following are groups of like fractions?

1. 1/7, 2/7, 3/7, 5/7, 6/7
2. 1/11, 7/11, 4/7, 8/13, 13/6
3. 2/8, 5/15, 13/9, 6/7, 4/15
4. 4/13, 2/13, 7/13, 5/13, 8/13
5. 3/8, 5/8, 1/8, 7/8, 9/8
6. 4/9, 3/10, 5/8, 3/5, 7/10

2. Which of the following fractions are proper fractions?

(a) 5/8

(b) 12/24

(c) 13/42

(d) 17/8

(e) 27/38

3. Which of the following fractions are improper fractions?

(a) 9/10

(b) 22/14

(c) 2/3

(d) 16/20

(e) 43/38

4. Which of the following are unit fractions?

(a) 6/9

(b) 2/5

(c) 1/6

(d) 1/15

(e) 1/8

5. Check whether the given fractions are equivalent:

(a) 5/28, 4/20

(b) 5/9, 36/42

(c) 10/7, 3/21

(d) 4/11, 24/55

(e) 6/13, 30/65

(f) 8/15, 60/32

6. Replace □ in each of the following by the correct number:

(a) 5/6 = □/12

(b) 4/13 = □/39

(c) 8/11 = □/44

(d) 3/15 = □/60

(e) 1/5 = □/15

(f) 3/8 = □/24

7. Find the equivalent fraction of:

1. 4/7 having numerator 12
2. 5/8 having denominator 32
3. 9/11 having denominator 99
4. 8/14 having numerator 4
5. 20/60 having numerator 2
6. 20/35 having denominator 7

🎯 Testing Time 4.4 - Fractions in Lowest Terms

1. Which of the following fractions are in lowest terms?

(a) 8/9

(b) 12/14

(c) 3/7

(d) 25/40

2. Reduce each of the following fractions to lowest terms:

(a) 9/33

(b) 12/28

(c) 32/40

(d) 56/70

(e) 108/220

(f) 116/312

(g) 75/80

(h) 91/260

(i) 75/120

(j) 162/54

(k) 140/245

(l) 156/346

🎯 Testing Time 4.5 - Fractional Part of a Number/Quantity

1. Determine the value of the following:

(a) 1/4 of 8

(b) 2/3 of 24

(c) 5/11 of 48

(d) 5/9 of 9

(e) 8/16 of 16

(f) 2/3 of 27

(g) 5/18 of 54

(h) 2/5 of 50

(i) 5/25 of 1000

2. Find:

(a) 5/7 of ₹35

(b) 7/12 of 50 paise

(c) 3/8 of ₹420

(d) 9/5 of 40 m

(e) 7/3 of 63 km

(f) 6/13 of 26 kg

(g) 3/4 of 3 kg (in grams)

(h) 5/3 of a day (in hours)

(i) 9/4 of an hour (in minutes)

3. Fill in the blanks with fractions in lowest terms:

1. 4 hours is ___ of a day.
2. 200 g is ___ of 1 kg.
3. 5 years is ___ of a decade.
4. 50 paise is ___ of one rupee.
5. 40 cm is ___ of a metre.
6. 9 months is ___ of one year.
7. 15 seconds is ___ of a minute.

4. A class has 56 students. 4/7 of the class went on a picnic. How many students went on the picnic?

5. Rinku bought 30 balloons. She distributed 4/5 of the balloons among her friends. How many balloons did she distribute?

6. A shopkeeper bought 550 candles. He found that 1/11 of the candles were defective and he did not sell them. How many candles did he sell?

🎯 Testing Time 4.6 - Comparison and Order of Fractions

1. Compare each pair given below using > or < or =:

(a) 2/3 □ 1/2

(b) 1/4 □ 1/7

(c) 2/5 □ 3/8

(d) 4/7 □ 2/5

(e) 5/6 □ 6/1

(f) 3/9 □ 1/11

(g) 6/14 □ 1/15

(h) 17/18 □ 13/18

(i) 11/23 □ 17/4

(j) 11/46 □ 13/49

(k) 18/18 □ 13/19

(l) 17/15 □ 18/15

2. Arrange the following fractions in ascending order:

1. 3/8, 5/9, 2/4, 17/3, 8/8
2. 3/15, 5/15, 2/15, 17/2, 10/10
3. 5/4, 5/8, 5/12, 5/16
4. 7/8, 7/15, 7/16, 7/12
5. 5/9, 3/10, 1/3, 4/15
6. 3/8, 1/16, 5/18, 7/4

3. Arrange the following fractions in descending order:

1. 7/9, 3/9, 1/9, 5/9, 2/9
2. 13/30, 9/30, 11/30, 17/30, 15/30
3. 8/15, 2/15, 14/15, 7/15, 1/15
4. 12/17, 11/17, 9/17, 16/17, 8/17
5. 3/8, 3/5, 3/6, 3/4
6. 1/4, 1/2, 1/8, 3/37

🎯 Testing Time 4.7 - Addition of Fractions

1. Find the equivalent fractions with lowest common denominator:

(a) 3/4 and 2/3

(b) 7/8 and 5/9

(c) 4/9 and 7/12

(d) 8/35 and 6/4

(e) 2/10 and 7/3

(f) 7/25 and 2/8

(g) 3/10 and 1/6

(h) 2/3 and 11/5

2. Add:

(a) 3/4 and 2/3

(b) 8/3 and 5/2

(c) 3/4 and 8/3

(d) 2/3 and 5/6

(e) 7/10 and 3/7

(f) 2/3 and 11/5

(g) 1/6 and 2/3

(h) 5/3 and 11/8

3. Find the sum:

1. 2/3 + 3/4
2. 3/10 + 1/5 + 1/2
3. 5/8 + 9/16 + 13/24
4. 3/4 + 5/12
5. 5/10 + 2/10 + 7/20
6. 1/2 + 1/6 + 1/22
7. 1/4 + 1/5 + 1/7
8. 1/6 + 1/12
9. 2/3 + 1/7 + 4/3 + 2/4
10. 5/7 + 7/7 + 6/14

🎯 Testing Time 4.8 - Subtraction of Fractions

1. Solve:

(a) 5/7 - 6/7

(b) 6/13 - 1/4

(c) 3/5 - 1/12

(d) 6/11 - 2/4 - 1/28

(e) 1/5 - 1/12

(f) 4/6 - 5/10

2. Subtract:

(a) 2/4 from 5/3

(b) 5/20 from 7/15

(c) 7/12 from 5/8

(d) 9/8 from 5/9

(e) 1/42 from 1/4

(f) 1/24 from 2/4

3. Find the difference between:

(a) 4/5 and 4/5

(b) 4/6 and 2/7

(c) 3/4 and 1/7

(d) 21/7 and 2/9

(e) 4/13 and 3/4

(f) 18/15 and 5/4

(g) 4/9 and 7/25

(h) 23/4 and 15/12

(i) 7/22 and 18/18

✖️Multiplication and Division

Multiplication

(a/b) × (c/d) = (a × c) / (b × d)

Example: 3/7 × 5/9 = (3 × 5)/(7 × 9) = 15/63 = 5/21

Finding fractional part of a number

3/8 of 40 = 3/8 × 40 = (3 × 40)/8 = 120/8 = 15

Division (Reciprocal Method)

To divide fractions, multiply by the reciprocal of the divisor.

Reciprocal of a/b is b/a

📋Quick Reference

🔍 To find LCM quickly:

• List multiples of each number
• Find the smallest common multiple
• Or use prime factorization method

✅ Key Formulas:

• Mixed to Improper: (whole × denominator + numerator)/denominator
• Addition: Convert to like fractions using LCM
• Comparison: Convert to like fractions

🎓 Master Fractions with Practice!

Remember: LCM is your best friend when working with unlike fractions. Practice regularly to build confidence!

© 2025 by Abhinav Anand Maths Abhinav Sir | Class 5 - Chapter 4: Fractions