SOLUTION: I can't figure this problem out! "Laura started with 7/10 feet of rope. If she received 9/12 from Jane and gave 5/7 to jerome, then how many feet of rope did laura have in the end?

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Question 610224: I can't figure this problem out! "Laura started with 7/10 feet of rope. If she received 9/12 from Jane and gave 5/7 to jerome, then how many feet of rope did laura have in the end?" The answer must be be a fraction in simplest terms
I keep getting 0.7357 as a decimal??? Is that right-what is that in a fraction?
Thanks for any help
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Add the first two fractions:
7/10 + 9/12

(7/10)*(6/6) + 9/12

(7*6)/(10*6) + 9/12

42/60 + 9/12

42/60 + (9/12)*(5/5)

42/60 + (9*5)/(12*5)

42/60 + 45/60

(42+45)/60

87/60

So after receiving 9/12 ft of rope from Jane, she now has 87/60 ft of rope

Now subtract off 5/7 (since she's giving this amount to Jerome)

87/60 - 5/7

(87/60)*(7/7) - 5/7

(87*7)/(60*7) - 5/7

609/420 - 5/7

609/420 - (5/7)*(60/60)

609/420 - (5*60)/(7*60)

609/420 - 300/420

(609-300)/420

309/420

(3*103)/(3*140)

103/140

So she has 103/140 ft of rope in the end.

Note: 103/140 = 0.7357, which helps confirm that you were on the right track (you just needed to convert to fraction form)

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Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the LCD for 10, 4, and 7 is 2*5*2*7

98/140 + 105/140 - 100/140

your decimal is a correct approximation