Answer:
5 13/24
Step-by-step explanation:
(10 5/12) - (4 7/8) = (10 +5/12) -(4 +7/8)
... = (10 -4) +(5/12 -7/8)
... = 6 + (5/12 -7/8) . . . . . read on for how to simplify this
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Adding fractions
Adding fractions can be done in a mechanical sort of way using the formula ...
... a/b + c/d = (ad +bc)/(bd)
Here, we have a=5, b=12, c=-7, d=8, so the sum is ...
... (5·8 +12(-7))/(12·8) = (40 -84)/96 = -44/96
The numerator and denoinator of this fraction are both multiples of 4, so we can reduce the fraction.
... -44/96 = 4(-11)/(4·24) = -11/24
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Back to the problem at hand
... 6 + (5/12 -7/8) = 6 - 11/24
Now, we know that 1 = 24/24, so when we subtract 11/24 from 1, we get ...
... 1 - 11/24 = 24/24 - 11/24 = (24 -11)/24 = 13/24
So, our expression 6 - 11/24 can be rewritten as ...
... 6 -11/24 = (5 + 1) - 11/24 = 5 + (1 -11/24) = 5 13/24
Summary
... (10 5/12) - (4 7/8) = 5 13/24
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Another way to add fractions
The way to add fractions that is commonly taught is to first find a common denominator. Here that means you want to find the smallest number that is a multiple of both 12 and 8, the two denominators. You may recognize that number as being 24 = 12·2 = 3·8. (The methods of finding the common denominator (least common multiple) for numbers not in your memorized multiplication tables are not easy to describe.)
The next step in this method is to rewrite the fractions so they each have this denominator. The multipliers in the above equation are helpful for that purpose.
... 5/12 = (5·2)/(12·2) = 10/24
... 7/8 = (7·3)/(8·3) = 21/24
Now, the subtraction can proceed easilly:
... 10/24 - 21/24 = (10 -21)/24 = -11/24 . . . . . same result as above
