Answer:
139/42
Explanation:
Simplify the following:
(3/8 + 1 + 5/9)/(7/12)
Hint: | Write (3/8 + 1 + 5/9)/(7/12) as a single fraction.
Multiply the numerator of (3/8 + 1 + 5/9)/(7/12) by the reciprocal of the denominator. (3/8 + 1 + 5/9)/(7/12) = ((3/8 + 1 + 5/9)×12)/7:
((3/8 + 1 + 5/9)×12)/7
Hint: | Put the fractions in 3/8 + 1 + 5/9 over a common denominator.
Put 3/8 + 1 + 5/9 over the common denominator 72. 3/8 + 1 + 5/9 = (9×3)/72 + 72/72 + (8×5)/72:
((9×3)/72 + 72/72 + (8×5)/72 12)/7
Hint: | Multiply 9 and 3 together.
9×3 = 27:
((27/72 + 72/72 + (8×5)/72)×12)/7
Hint: | Multiply 8 and 5 together.
8×5 = 40:
((27/72 + 72/72 + 40/72)×12)/7
Hint: | Add the fractions over a common denominator to a single fraction.
27/72 + 72/72 + 40/72 = (27 + 72 + 40)/72:
((27 + 72 + 40)/72×12)/7
Hint: | Evaluate 27 + 72 + 40 using long addition.
| 7 | 2
| 4 | 0
+ | 2 | 7
1 | 3 | 9:
(139/72×12)/7
Hint: | Express 139/72×12 as a single fraction.
139/72×12 = (139×12)/72:
((139×12)/72)/7
Hint: | Express ((139×12)/72)/7 as a single fraction.
((139×12)/72)/7 = (139×12)/(72×7):
(139×12)/(72×7)
Hint: | In (139×12)/(72×7), divide 72 in the denominator by 12 in the numerator.
12/72 = 12/(12×6) = 1/6:
139/(6×7)
Hint: | Multiply 6 and 7 together.
6×7 = 42:
Answer: 139/42