Simplify 3/8 * 1/4 / 3/4 + 1/5
(3/8 * 1/4) / (3/4 + 1/5)
= (3/32) / (19/20)
= 60/608
= 15/152
As written, using PEMDAS and treating the fractions as single units,
3/8 * 1/4 / 3/4 + 1/5
= 3/32 / 3/4 + 1/5
= 1/8 + 1/5
= 9/40
following BEDMAS
3/8 * 1/4 / 3/4 + 1/5
= 3/32 / 3/5 + 1/5
= 1/8 + 1/5
= 13/40
To simplify the expression (3/8 * 1/4) / (3/4) + 1/5, follow these steps:
Step 1: Simplify the multiplication of fractions.
Multiply the numerators (top numbers) to get the new numerator, and multiply the denominators (bottom numbers) to get the new denominator.
(3/8 * 1/4) = (3 * 1) / (8 * 4) = 3/32
Step 2: Simplify the division of fractions.
Division of fractions is the same as multiplying by the reciprocal of the second fraction.
Divide the first fraction by the second fraction: (3/32) / (3/4).
To take the reciprocal of a fraction, swap the numerator and the denominator.
(3/32) / (3/4) = (3/32) * (4/3) = (3 * 4) / (32 * 3) = 12/96 = 1/8
Step 3: Add the remaining fraction.
Further simplify the expression by adding the remaining fraction 1/5.
1/8 + 1/5
To add fractions, they need to have a common denominator.
Step 4: Find the least common multiple (LCM) of the denominators, which is 40.
The LCM of 8 and 5 is 40.
Step 5: Rewrite the fractions with the common denominator of 40.
1/8 = (1/8) * (5/5) = 5/40
1/5 = (1/5) * (8/8) = 8/40
Step 6: Add the fractions.
Now that both fractions have a common denominator of 40, add them together.
5/40 + 8/40 = (5 + 8) / 40 = 13/40
Therefore, the simplified expression is 13/40.