simplify 24 divided by 1/2 +5/8*6/7
To simplify the expression 24 divided by 1/2 + 5/8 * 6/7, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
Let's break it down step by step:
Step 1: Simplify the multiplication component.
5/8 * 6/7
To multiply fractions, multiply the numerators together and multiply the denominators together:
(5 * 6) / (8 * 7) = 30 / 56
30/56 is not simplified yet. We can divide both the numerator and the denominator by their greatest common divisor, which is 2:
30 / 56 = (30 ÷ 2) / (56 ÷ 2) = 15/28
Step 2: Perform the division operation.
24 divided by 1/2 + 15/28
To divide by a fraction, we multiply by its reciprocal.
24 ÷ 1/2 = 24 * 2/1 = 24 * 2 = 48
Step 3: Perform the addition.
48 + 15/28
In this case, we need to find a common denominator for the addition.
The common denominator for 28 and 1 is 28.
To convert 48 to a fraction with a denominator of 28, we multiply the numerator and denominator by 28:
48/1 = 48 * 28/1 * 28 = 1344/28
Now we can add the fractions:
1344/28 + 15/28 = (1344+15)/28 = 1359/28
So, the simplified expression is 1359/28.