Simplify: 5/8 divided by 15/16 + 1/2
If your problem is
(5/8) / (15/16) + 1/2
(5/8) * (16)/15) + 1/2
(80/120) + (60/120) = 140/120 = 1 1/6
5/8 / (15/16+8/16) ??? is that what you mean?
5/8 / (23/16)
10/16 / (23/16)
10/23
To simplify the expression 5/8 divided by 15/16 + 1/2, we need to convert the division problem into a multiplication problem:
5/8 ÷ 15/16 can be written as 5/8 * 16/15.
Now, let's multiply the fractions:
(5/8) * (16/15) = (5 * 16) / (8 * 15) = 80/120.
Next, we need to simplify the fraction 80/120:
The greatest common divisor (GCD) of 80 and 120 is 40.
Dividing both the numerator and the denominator by 40, we get:
80/120 = (80 ÷ 40) / (120 ÷ 40) = 2/3.
So, the simplified expression becomes:
2/3 + 1/2.
To add these fractions, we need a common denominator, which is 6:
(2/3) * (2/2) = 4/6.
Now, we can add the fractions:
4/6 + 1/2 = 4/6 + 3/6 = (4 + 3) / 6 = 7/6.
Therefore, the simplified expression is 7/6.
To simplify the expression 5/8 divided by 15/16 + 1/2, we follow a specific order of operations known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Step 1: Simplify 5/8 divided by 15/16.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
5/8 divided by 15/16 = (5/8) * (16/15)
Step 2: Simplify (5/8) * (16/15).
To multiply fractions, we multiply the numerators together and the denominators together.
(5/8) * (16/15) = (5 * 16) / (8 * 15)
Step 3: Simplify (5 * 16) / (8 * 15).
By multiplying the numerator and the denominator, we get:
(5 * 16) / (8 * 15) = 80 / 120
Step 4: Simplify 80 / 120.
We can simplify this fraction by finding the greatest common divisor of the numerator and the denominator, which is 40.
80 / 120 = (80 ÷ 40) / (120 ÷ 40) = 2/3
Step 5: Add 1/2 to 2/3.
To add fractions, we need to have a common denominator. The least common multiple (LCM) of 2 and 3 is 6. So, we rewrite 1/2 and 2/3 by multiplying each fraction by an appropriate form of 1.
(1/2) * (3/3) = 3/6
(2/3) * (2/2) = 4/6
Now, we can add the fractions with the same denominator:
3/6 + 4/6 = 7/6
Therefore, the simplified expression is 7/6.