Answer:
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.
