What is the answer to - 2 5/6 + ( - 7/8) divided by 5 1/4 ( I got -3 and I don't think I got it right. Could somebody also explain how they got it? Thank you!)

Conversion a mixed number 2 5/

6

to a improper fraction: 2 5/6 = 2 5/

6

= 2 · 6 + 5/

6

= 12 + 5/

6

= 17/

6

To find new numerator:

a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/

6

= 12/

6

b) Add the answer from previous step 12 to the numerator 5. New numerator is 12 + 5 = 17

c) Write a previous answer (new numerator 17) over the denominator 6.

Two and five sixths is seventeen sixths

Unary minus: -17/

6

= -17/

6

Conversion a mixed number 5 1/

4

to a improper fraction: 5 1/4 = 5 1/

4

= 5 · 4 + 1/

4

= 20 + 1/

4

= 21/

4

To find new numerator:

a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/

4

= 20/

4

b) Add the answer from previous step 20 to the numerator 1. New numerator is 20 + 1 = 21

c) Write a previous answer (new numerator 21) over the denominator 4.

Five and one quarter is twenty-one quarters

Divide: -7/

8

: 21/

4

= -7/

8

· 4/

21

= -7 · 4/

8 · 21

= -28/

168

= 28 · (-1)/

28 · 6

= -1/

6

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 21/

4

is 4/

21

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - minus seven eighths divided by twenty-one quarters = minus one sixth.

Add: the result of step No. 2 + the result of step No. 4 = -17/

6

+ (-1/

6

) = -17 + (-1)/

6

= -18/

6

= 6 · -3/

6 · 1

= -3

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 6) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 6 = 36.

In words - minus seventeen sixths plus minus one sixth = minus three.