simplify 3/4 + 5/8 over 3/4 - 1/2
Make the denominators the same
6/8 + 5/8 over 6/8 - 4/8
6/8 + 5/8 = 11/8
6/8 - 4/8 = 2/8
(11/8) / (2/8) = 11/8 * 8/2
=11/2
You need to clarify if that is
(3/4 + 5/8) over (3/4 - 1/2)
or
3/4 + (5/8 over 3/4) - 1/2
The answers will be different.
To simplify the expression (3/4 + 5/8) / (3/4 - 1/2), follow these steps:
Step 1: Simplify the numerator (3/4 + 5/8):
To add fractions with different denominators, you need to find a common denominator. In this case, the least common multiple (LCM) of 4 and 8 is 8.
Multiplying the numerator and denominator of 3/4 by 2, we get (3/4) * (2/2) = 6/8.
Now, the expression becomes (6/8 + 5/8) / (3/4 - 1/2).
Combining the numerators, we have (6 + 5)/8 = 11/8.
Step 2: Simplify the denominator (3/4 - 1/2):
To subtract fractions with different denominators, just like in Step 1, we need to find a common denominator. The LCM of 4 and 2 is 4.
Multiplying the numerator and denominator of 1/2 by 2, we get (1/2) * (2/2) = 2/4.
Now, the expression becomes (11/8) / (3/4 - 2/4).
Simplifying the denominator, we have (11/8) / (1/4).
Step 3: Flip the denominator and multiply:
To divide by a fraction, we flip the fraction and multiply.
Now, the expression becomes (11/8) * (4/1) = (11 * 4) / (8 * 1) = 44/8.
Step 4: Simplify the resulting fraction:
To simplify the final fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which in this case is 4.
Dividing 44 by 4 and dividing 8 by 4, we get 11/2.
Therefore, the simplified form of (3/4 + 5/8) / (3/4 - 1/2) is 11/2.