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\\November 22, 2023 3:12 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Encapsulate
math
FrACtIONS

Multiplication of Fractions types of Fractions Comparing and Ordering Fractions
Multiplication of a fraction by a whole Unit fractions: , , , etc. For like fractions: The fraction with
1 1 1
number: 3 9 12 the larger numerator is greater.
3
1 2 4 11
Product of a fraction and a whole Proper fractions: , , , , etc. E.g., > 2
5
5
2 3 7 13
number = Numerator × Whole Number For unlike fractions:
4 5 11 19
Denominator Improper fractions: , , , , etc. E.g., > As, = 2 × 4 = 8 and
2
2
3
8
3 2 7
5 × 4
20
4
3
E.g., × 12 = 3 × 12 = 36 = 9 Mixed fractions: 2 , 3 , 7 8 , 5 , etc. 3 = 3 × 5 5 = 15 5 Since 15 > 8,
4
4
4
5
1
3
4
4 × 5
Multiplication of fraction by another 7 4 11 9 We get, 15 > 20 8 or > 2
3
2 1 4 5
fraction: Like fractions: , , , , etc. 20 20 4 5
Product of two fractions 7 7 7 7 Fractions in ascending order:
1
5
7
2
1 2 4 5
9
3
2
= Product of numerators Unlike fractions: , , , , etc. E.g., < < < 6
8 9 10 7
Product of denominators Fractions in descending order:
2
5
2 4 6 8
1
3
2
E.g., × = 2 × 3 = 6 = 3 Equivalent fractions: , , , , etc. E.g., > > > 3
7 4 7 × 4 28 14 3 6 9 12 8 5 3 10
division of Fractions Addition and Subtraction of Fractions
division of fraction by a whole number: For like fractions:
Fraction ÷ Whole number = Fraction × Reciprocal of Addition of fractions = Sum of numerators
whole number. 3 1 3 + 1 4 Common denominator
1
E.g., ÷ 3 E.g., + = 5 = 5
5
5
3 Difference of numerators
1
1
= × = 1 Subtraction of fractions = Common denominator
1
1
2
3
3
3
9
E.g., – = =
division of a whole number by a fraction: 4 4 4 2
Whole number ÷ Fraction = Whole number × Reciprocal For unlike fractions: Convert the fractions into like fractions
of the fraction. first, and then add and subtract as same as like fractions.
E.g., 4 ÷ 1 Addition of unlike fractions:
3
3
7
E.g., + = 7 × 8 + 3 × 9 (As, LCM of 8, 9 is 72)
9 × 8
8
8 × 9
9
= 4 × 3 = 12 56 27 56 + 27 83 11
division of a fraction by another fraction: = 72 + 72 = 72 = 72 = 1 72
st
nd
st
1 fraction ÷ 2 fraction = 1 fraction × Reciprocal of the Subtraction of unlike fractions:
nd
2 fraction E.g., – = 5 × 3 – 4 × 2 (As, LCM of 6, 9 is 18)
4
5
2
2
4
E.g., ÷ = × Multiplicative inverse of 4 6 9 6 × 3 9 × 2
7 5 7 5 = 15 – 8 = 15 – 8 = 7
2
5
= × = 10 = 5 18 18 18 18
7 4 28 14
Brain Sizzlers
1. One-fourths 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 which goes 4 times 6 and a remainder of .
2 7
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