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\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

Mind Map Creative Thinking
math
FRACTIONS

Types of Fractions Comparing and Ordering Fractions Multiplication of Fractions

1 1 1
Unit fractions: , , , etc. For like fractions: The fraction with Multiplication of a fraction by a whole
3 9 12 the larger numerator is greater. number:
3
1 2 4 11
Proper fractions: , , , , etc. E.g., > 2 Product of a fraction and a whole
5
5
2 3 7 13 For unlike fractions: Numerator × Whole Number
4 5 11 19
2
2
3
Improper fractions: , , , , etc. E.g., > as, = 2 × 4 = 8 and number = Denominator
3 2 7 8 4 5 5 5 × 4 20 E.g., × 12 = 3 × 12 = 36 = 9
3
1
5
3
Mixed fractions: 2 , 3 , 7 8 , 5 , etc. 3 = 3 × 5 = 15 Since 15 > 8, 4 4 4
4 × 5
4
20
7 4 11 9 we get: 15 > 8 or > 2 Multiplication of a fraction by another
3
2 1 4 5
Like fractions: , , , , etc. 20 20 4 5 fraction:
7 7 7 7 Fractions in ascending order: Product of two fractions
2
7
1
1 2 4 5
Unlike fractions: , , , , etc. E.g., < < < 5 Product of numerators
6
2
3
9
8 9 10 7 Fractions in descending order: = Product of denominators
2
1
2
5
2 4 6 8
3
Equivalent fractions: , , , , etc. E.g., > > > 3 E.g., × = 2 × 3 = 6 = 3
3 6 9 12 8 5 3 10 7 4 7 × 4 28 14
Addition and Subtraction of Fractions Division of Fractions
For like fractions: Division of fraction by a whole number:
Addition of fractions = Sum of numerators Fraction ÷ Whole number = Fraction × Reciprocal of
Common denominator whole number.
1
3
E.g., + = 3 + 1 = 4 E.g., ÷ 3
1
5 5 5 5 3
Subtraction of fractions = Difference of numerators 1 1 1
Common denominator
3
2
1
3
3
E.g., – = = 1 = × = 9
4 4 4 2 Division of a whole number by a fraction:
For unlike fractions: Convert the fractions into like fractions Whole number ÷ Fraction = Whole number × Reciprocal
first, and then add and subtract as like fractions. of fraction.
Addition of unlike fractions: E.g., 4 ÷ 1
3
3
7
E.g., + = 7 × 8 + 3 × 9 (As, LCM of 8, 9 is 72)
9 × 8
8 × 9
8
9
= 56 + 27 = 56 + 27 = 83 = 1 11 = 4 × 3 = 12
Division of a fraction by another fraction:
72 72 72 72 72
st
st
nd
nd
Subtraction of unlike fractions: 1 fraction ÷ 2 fraction = 1 fraction × Reciprocal of 2
5
4
E.g., – = 5 × 3 – 4 × 2 (As, LCM of 6, 9 is 18) fraction
2
4
2
6 9 6 × 3 9 × 2 E.g., ÷ = × Multiplicative inverse of 4
8
7
= 15 – 18 = 15 – 8 = 18 2 7 5 5 10 7 5 5
18
18
= × =
7 4 28 = 14
Challenge Question Critical Thinking
1. One-fourth of a herd of deer have gone to the forest and one-third of the total are
grazing in a field. The remaining 25 are drinking water on a river. What is the total
number of deer in the herd?
1
6
2. Find the fraction obtained when 6 is taken 4 times and then is added.
2 7
Mathematics-5 97