Solving the Mathematical Expression: 1 1/2 divided by 1/6 - 7/8
In this article, we will tackle the mathematical expression 1 1/2 divided by 1/6 - 7/8. To solve this expression, we need to follow the order of operations (PEMDAS) and break it down step by step.
Step 1: Convert Mixed Numbers to Improper Fractions
First, let's convert the mixed number 1 1/2 to an improper fraction. To do this, we multiply the whole number part (1) by the denominator (2) and then add the numerator (1).
1 1/2 = (1 × 2) + 1 = 3/2
So, the expression becomes:
(3/2) ÷ (1/6) - 7/8
Step 2: Divide 3/2 by 1/6
To divide two fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
(3/2) ÷ (1/6) = (3/2) × (6/1) = 18/2 = 9
Now, the expression becomes:
9 - 7/8
Step 3: Subtract 7/8 from 9
To subtract a fraction from a whole number, we need to convert the whole number to a fraction with a denominator of 8.
9 = 72/8
Now, subtract 7/8 from 72/8:
(72 - 7)/8 = 65/8
Therefore, the final answer is:
65/8
In conclusion, the solution to the mathematical expression 1 1/2 divided by 1/6 - 7/8 is 65/8.
