1/6 + 1/7 + 1/8
Find the LCD
This is a long process, so let us just get the LCM of the three denominators.
This will be 168, which means the LCD is also 168.
Then 168 will be our denominator.
Divide the common denominator by each of the denominator then multiply by the numerator.
168 / 6 x 1 =?
168 / 7 x 1 =?
168 / 8 x 1 =?
28
24
21
Add 28, 24, and 21, this will be the numerator.
28 + 24 + 21 = 73
So therefore, 1/6 + 1/7 + 1/8 = 73/168. It is already reduced.
9 and 3/8 - 78/168
This is a subtraction problem, so we need to find two equivalent fractions that have the same denominators. Then we can subtract the numerators.
The first fraction needs to be converted to improper form. Plug in the values of the first fraction into the formula:
9 × 8 + 3 = 75
Re-writing the first fraction, we get 75/8.
Now we know 168 is the least common denominator of 75/8 and 78/168.
Plug in the values of the first fraction into the formula:
(168 ÷ 8) × 75 = 1575
Plug in the values of the second fraction into the formula:
(168 ÷ 168) x 78 = 78
First Fraction: 1575/168
Second Fraction: 78/168
Subtract the first numerator and the second numerator:
1575 - 78 = 1497
So therefore, we got 1497/168 as the answer. But it is not yet reduced,
3 is the largest factor of both 1497 and 168, so we need to divide both the numerator and denominator by 3.
Numerator: 1497 ÷ 3 = 499
Denominator: 168 ÷ 3 = 56
499/56 is the new fraction.
Converting into mixed number, The quotient, 8, is the whole part of the mixed number. The remainder, 51, is the numerator of the fraction. Putting it all together, we get:
8 and 51/56
