Q:

please awnser i fraction form 4 3/4 times 3 3/5 times 15

Accepted Solution

A:
Simplify the following:
(4 + 3/4) (3 + 3/5)Γ—15

Put 3 + 3/5 over the common denominator 5. 3 + 3/5 = (5Γ—3)/5 + 3/5:
(4 + 3/4) (5Γ—3)/5 + 3/5 15

5Γ—3 = 15:
(4 + 3/4) (15/5 + 3/5)Γ—15

15/5 + 3/5 = (15 + 3)/5:
(4 + 3/4) (15 + 3)/5Γ—15

15 + 3 = 18:
(4 + 3/4)Γ—18/5Γ—15

Put 4 + 3/4 over the common denominator 4. 4 + 3/4 = (4Γ—4)/4 + 3/4:
(18Γ—15)/5 (4Γ—4)/4 + 3/4

4Γ—4 = 16:
((16/4 + 3/4)Γ—18Γ—15)/5

16/4 + 3/4 = (16 + 3)/4:
(18Γ—15)/5 (16 + 3)/4

16 + 3 = 19:
19/4Γ—18/5Γ—15

19/4Γ—18/5Γ—15 = (19Γ—18Γ—15)/(4Γ—5):
(19Γ—18Γ—15)/(4Γ—5)

15/5 = (5Γ—3)/5 = 3:
(19Γ—18Γ—3)/4
The gcd of 18 and 4 is 2, so (19Γ—18Γ—3)/4 = (19 (2Γ—9) 3)/(2Γ—2) = 2/2Γ—(19Γ—9Γ—3)/2 = (19Γ—9Γ—3)/2:
(19Γ—9Γ—3)/2

19Γ—9 = 171:

(171Γ—3)/2

171Γ—3 = 513:

Answer: 513/2