Question

Match each expression on the left with its sum on the right. Some answer options on the right will not be used.

Answer 1

To match the expression with the sum, what you have to do is solve each sum.

Remember that to sum/subtract two fractions, both of them should be expressed using the same denominator,

1)

`-(2)/(3)+(5)/(6)`

The denominators of these fractions are "3" and "6", the least common denominator between both values is 6. To express the first fraction as its equivalent with denominator 6, you have to multiply it by 2:

`-(2\cdot2)/(3\cdot2)+(5)/(6)=-(4)/(6)+(5)/(6)`

Now you can proceed to add both fractions:

`-(4)/(6)+(5)/(6)=(-4+5)/(6)=(1)/(6)`

The result for this sum is 1/6

2)

`(7)/(12)+(-(3)/(4))`

First, simplify both symbols, when a plus symbol and a minus symbol and next to each other, the plus sign gets canceled:

`(7)/(12)+(-(3)/(4))=(7)/(12)-(3)/(4)`

To subtract both fractions the first step is to express them using the same denominator. The least common denominator between 12 and 4 is 12, to express -3/4 as its equivalent with denominator 12, you have to multiply the fraction by 3:

`(7)/(12)-(3\cdot3)/(4\cdot3)=(7)/(12)-(9)/(12)`

Next, subtract both fractions:

`(7)/(12)-(9)/(12)=(7-9)/(12)=-(2)/(12)`

The result is no in its simplest form, 2 and 12 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator by 2:

`-(2/2)/(12/2)=-(1)/(6)`

The result for this expression is -1/6

3)

`-(1)/(4)+(3)/(8)`

Same as before, the first step is to express both fractions with the same denominator. the least common denominator for both fractions is 8. To express -1/4 as its equivalent with denominator 8, you have to multiply the fraction by 2

`-(1\cdot2)/(4\cdot2)+(3)/(8)=-(2)/(8)+(3)/(8)`

Next, add both fractions:

`-(2)/(8)+(3)/(8)=(-2+3)/(8)=(1)/(8)`

The result for this sum is 1/8

So the corresponding matches are:

`\begin{gathered} 1)-(2)/(3)+(5)/(6)=(1)/(6) \\ 2)(7)/(12)+(-(3)/(4))=-(1)/(6) \\ 3)-(1)/(4)+(3)/(8)=(1)/(8) \end{gathered}`