Question

Add : (a) 1 upon 10+ 4 upon 5 with LCM.
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Answer 1

Answer:

So, we convert the given fractions into equivalent fractions with denominator 30.

7/10 = (7× 3)/(10 × 3) = 21/30 , and 2/15 = (2 × 2)/(15 × 2) = 4/30

Therefore, 7/10 + 2/15

= 21/30 + 4/30

= (21 + 4)/30

=

= 5/6

(ii) 2²/₃3 + 3¹/₂

= (2 × 3 + 2)/3 + (3 × 2 + 1)/2

= 8/3 +7/2

= (8× 2)/(3× 2)+ (7× 3)/(2× 3)

[Since least common multiple (LCM) of 3 and 2 is 6; so, convert each fraction to an equivalent fraction with denominator 6]

= 16/6 + 21/6

= (16 + 21)/6

= 37/6

2. Simplify:

(i) 15/16 – 11/12

(ii) 11/15 – 7/20

(i) 15/16 – 11/12

Least common multiple (LCM) of 16 and 12 = (4 × 4 × 3) = 48.

= (15 × 3)/(16 × 3) – (11 × 4)/(12 × 4)

[Converting each fraction to an equivalent fraction with denominator 48]

= 45/48 – 44/48

= (45 – 44)/48

= 1/48

(ii) 11/15 – 7/20

Least common multiple (LCM) of 15 and 12 = 5 × 3 × 4 = 60

= (11 × 4)/(15 × 4) – (7 × 3)/(20 × 3)

[Converting each fraction to an equivalent fraction with denominator 60]

= 44/60 – 21/60

= (44 – 21)/60

= 23/60

3. Simplify: 4⁵/₆ – 2³/₈ + 3⁷/₁₂

Solution:

4⁵/₆ – 2³/₈ + 3⁷/₁₂

= (6 × 4 + 5)/6 – (2 × 8 + 3)/8 + (3 × 12 + 7)/12

= 29/6 – 19/8 + 43/12

= 29/6 – 19/8 + 43/12

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Step-by-step explanation:

= (29 × 4)/(6 × 4) – (19 × 3)/(8 × 3) + (43 × 2)/(12 × 2)

[Since, LCM of 6, 8, 12 is 2 × 3 × 2 × 2 = 24]

= 116/24 – 57/24 + 86/24

= (116 – 57 + 86)/24

= (202 – 57)/24

= 145/24

Answer 2

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