Question

Find 7 3/4 + ( - 2 1/3) + ( - 5/6)Find

Answer 1

To solve the operation:

`7(3)/(4)+(-2(1)/(3))+(-(5)/(6))`

First, simplify the signs, when + and - are next to each other, the plus sign is canceled so that:

`7(3)/(4)-2(1)/(3)-(5)/(6)`

Second, you have to express the mixed numbers as fractions:

For 7 3/4

Divide the whole number by 1 to express it as a fraction and add 3/4

`(7)/(1)+(3)/(4)`

Multiply 7/1 by 4 to express it using the same denominator as 3/4, then add both fractions:

`\begin{gathered} (7\cdot4)/(1\cdot4)+(3)/(4) \\ (28)/(4)+(3)/(4) \\ (28+3)/(4)=(31)/(4) \end{gathered}`

For 2 1/3

Same as before, the first step is to divide the whole number by 1 to express it as a fraction and add 1/3

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

Multiply the first fraction by 3 to express both fractions using the same denominator and add them:

`(2\cdot3)/(1\cdot3)+(1)/(3)=(6)/(3)+(1)/(3)=(6+1)/(3)=(7)/(3)`

Now you can write the operation between fractions as follows:

`(31)/(4)-(7)/(3)-(5)/(6)`

The next step is to solve the subtraction, to do so you have to express the three fractions using the same denominator. For the numbers "4", "3", and "6", the least common denominator is 12, so you have to multiply each fraction for a corresponding value so that as a result each one is expressed with denominator 12.

-Multiply 31/4 by 3

-Multiply 7/3 by 4

-Multiply 5/6 by 2

`\begin{gathered} (31\cdot3)/(4\cdot3)-(7\cdot4)/(3\cdot4)-(5\cdot2)/(6\cdot2) \\ (93)/(12)-(28)/(12)-(10)/(12) \end{gathered}`

Now, you can subtract the fractions:

`(93)/(12)-(28)/(12)-(10)/(12)=(93-28-10)/(12)=(55)/(12)`

Now that we have solved the subtractions, what's left is to express the fraction as a mixed number, to do so you have to divide 55 by 12, the whole number will be the result of the division and the decimal values will represent the fraction of the mixed number:

`55/12=4.58\bar{3}`

This result indicates that 55/12 expressed as a mixed number has 4 whole numbers and 0.583 remaining.

You know that the remaining fraction will have denominator 12, to determine its numerator, you have to multiply the decimal value 0.583 by the denominator, that is:

`0.58\bar{3}\cdot12=7`

This means that the decimal value 0.583 expressed as a fraction is 7/12

And the result of the subtraction expressed as a mixed value is equal to:

`(55)/(12)=4(7)/(12)`

The correct option is the first one.