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Answers
Answer:
a. –40/21
b. 47/504
c. 59/20
Step-by-step explanation:
a. (-2/7 -2/7) +(-2/3 -2/3)
⇒ -2(2/7) -2(2/3)
⇒ -4/7 -4/3
⇒ (-12-28)/21
⇒ –40/21
b. (5/6+2/7) (1/3-1/4)
⇒ {(35+12)/42} {(4-3)/12}
⇒ 47/42× 1/12
⇒47/504
c. (4/7÷16/49) + (5/6×36/25)
⇒ (4/7 × 49/16) + 6/5 [Cross multiplication]
⇒ 7/4 + 6/5 [Cross multiplication]
⇒ (35+24)/20
⇒59/20
Answer:
(a) -40/21
(b) 47/504
(c) 59/20
Step-by-step explanation:
(a)
((-2/7) - (2/7)) + ((-2/3) - (2/3))
= ((-2/7) + (-2/7)) + ((-2/3) + (-2/3))
= ((-2 - 2)/7) + ((-2 - 2)/3)
= (-4/7) + (-4/3)
Now, to add two or more fractions, they must be like or in simple terms their denominator must be equal, so we take their LCM
Thus,
LCM (7, 3) = 21
So,
(-4/7) × (3/3) = (-12/21)
(-4/3) × (7/7) = (-28/21)
Adding them we get,
(-12/21) + (-28/21)
= (-12 - 28)/21
= -40/21
Thus,
((-2/7) - (2/7)) + ((-2/3) - (2/3)) = (-40/21)
(b)
((5/6) + (2/7)) × ((1/3) - (1/4))
Similarly,
To add, their denominator must be equal,
LCM (6, 7) = 42
So,
(5/6) × (7/7) = (35/42)
(2/7) × (6/6) = (12/42)
Thus,
((5/6) + (2/7)) = (35/42) + (12/42)
= (35 + 12)/42
= 47/42
Now,
Similarly,
LCM (3, 4) = 12
So,
(1/3) × (4/4) = (4/12)
(1/4) × (3/3) = (3/12)
Thus,
((1/3) - (1/4)) = (4/12) - (3/12)
= (4 - 3)/12
= (1/12)
Thus,
((5/6) + (2/7)) × ((1/3) - (1/4)) = (47/42) × (1/12)
= (47 × 1)/(42 × 12)
= 47/504
Remember, for Multiplication and Division we need not require like fractions.
(c)
((4/7) ÷ (16/49)) + ((5/6) × (36/25))
We know that,
(a/b) ÷ (c/d) = (a/b) × (d/c)
So,
= ((4/7) × (49/16)) + ((5/6) × (36/25))
Cancelling terms out we get,
= (7/4) + (6/5)
Taking LCM we get,
LCM (4, 5) = 20
So,
(7/4) × (5/5) = (35/20)
(6/5) × (4/4) = (24/20)
Adding we get,
= (35/20) + (24/20)
= (35 + 24)/20
= 59/20
Thus,
((4/7) ÷ (16/49)) + ((5/6) × (36/25)) = 59/20
Hope it helped and you understood it........All the best