Question

What should be added to `(-3)/32` to get `53/96`?

Answer 1

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`