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Question
What should be added to `(-3)/32` to get `53/96`?
Solution
To find what should be added to `(-3)/32` to get `53/96`, let the required number be x. The equation becomes:
`(-3)/32 +x = 53/96`
Rearrange the equation to isolate x
`x=53/96-(-3)/32`
Subtracting a negative is the same as adding
`x=53/96 + 3/32`
The denominators are 96 and 32. The least common denominator (LCD) is 96.
Rewrite `3/32` with a denominator of 96:
`3/32 = (3xx3)/(32xx3) = 9/96`
Now the equation becomes: `x = 53/96+9/96`
Since the denominators are the same, add the numerators:
`x=(53+9)/96=62/96`
Simplify `62/96` by dividing both numerator and denominator by their greatest common divisor (2):
`x = (62÷2)/(96div2)`
`= 31/48`
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