write in the simplest form 6 by 2 over 3 : 7 by 1 over 2
Answers
Step-by-step explanation:
= (5 + 2)/8
= 7/8
(ii) 11/5 – 7/15
= (11 – 7)/15
= 4/15
(iii) 16/5 – 3/5 + 2/5 – 9/5
= (16 – 3 + 2 - 9)/5
= (18 – 12)/5
= 6/5
(iv) 4²/₃ + 1/3 – 4¹/₃
= (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3
= 14/3 + 1/3 – 13/3
= (14 + 1 - 13)/3
= (15 - 13)/3
= 2/3
In order to add and subtract unlike fractions, we follow the following steps:
STEP I: Obtain the fractions and their denominators.
STEP II: Find the LCM of the denominators.
STEP III: Convert each of the fraction into an equivalent fraction having its denominator equal to the Least Common Multiple (LCM) obtained in step II.
STEP IV: Add or subtract like fractions obtained in step III.
Examples on addition or subtraction with unlike fractions;
1. Add:
(i) 7/10 + 2/15
(ii) 2²/₃ + 3¹/₂
Solution:
(i) 7/10 + 2/15
LCM of 10 and 15 is (5 × 2 × 3) = 30.
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
= (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
Step-by-step explanation:
राइट इन सिंपलेस्ट फॉर्म 6 एटॉमिक टू बाय 3 डिवाइड 7 अपॉन वन बाय टू