Math

Question Subtract the mixed numbers 8188 \frac{1}{8} and 1581 \frac{5}{8}. Give the answer as a mixed number or proper fraction.

Studdy Solution

STEP 1

Assumptions
1. We are subtracting two mixed numbers: 8188 \frac{1}{8} and 1581 \frac{5}{8}.
2. The result should be expressed as a mixed number or a proper fraction, not as an improper fraction.

STEP 2

First, let's write down the mixed numbers to be subtracted.
8181588 \frac{1}{8} - 1 \frac{5}{8}

STEP 3

To subtract mixed numbers, we subtract the whole numbers and the fractions separately.

STEP 4

Subtract the whole numbers.
81=78 - 1 = 7

STEP 5

Now, subtract the fractions.
1858\frac{1}{8} - \frac{5}{8}

STEP 6

Since the fractions have the same denominator, we can subtract the numerators directly.
158\frac{1 - 5}{8}

STEP 7

Calculate the difference of the numerators.
15=41 - 5 = -4

STEP 8

Write the result of the subtraction of the fractions.
48\frac{-4}{8}

STEP 9

Since we have a negative fraction, we need to borrow 1 from the whole number part to make the fraction positive.

STEP 10

Subtract 1 from the whole number part.
71=67 - 1 = 6

STEP 11

Convert the 1 we subtracted into eighths since the denominator of our fraction is 8.
1=881 = \frac{8}{8}

STEP 12

Add this to the negative fraction to make it positive.
88+48=848\frac{8}{8} + \frac{-4}{8} = \frac{8 - 4}{8}

STEP 13

Calculate the sum of the fractions.
848=48\frac{8 - 4}{8} = \frac{4}{8}

STEP 14

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
48=4÷48÷4\frac{4}{8} = \frac{4 \div 4}{8 \div 4}

STEP 15

Calculate the simplified fraction.
4÷48÷4=12\frac{4 \div 4}{8 \div 4} = \frac{1}{2}

STEP 16

Combine the whole number part and the simplified fraction to get the final answer.
6126 \frac{1}{2}
The result of subtracting 8188 \frac{1}{8} by 1581 \frac{5}{8} is 6126 \frac{1}{2}.

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