157/8 divided by 1/2 in Fraction Form
The result of 157/8 divided by 1/2 is: 39 1/4
Step-by-Step Solution
Step 1: Understand the Problem
We need to divide the fraction \(\frac1578\) by \(\frac12\).
Step 2: Use the Division Rule
To divide fractions, we multiply by the reciprocal of the second fraction:
\(\frac1578 \div \frac12 = \frac1578 \times \frac21\)
Step 3: Multiply the Fractions
Multiply the numerators: 157 × 2 = 314
Multiply the denominators: 8 × 1 = 8
Step 4: Simplify the Fraction
We can simplify \(\frac3148\) to its lowest form.
The greatest common divisor (GCD) of 314 and 8 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac1574\).
Step 5: Convert to Mixed Number
The fraction \(\frac1574\) can be written as the mixed number \(39\frac14\).
Final Answer
The result of 157/8 divided by 1/2 is:
Understanding Fraction Division
How to Divide Fractions
To divide fractions, you multiply by the reciprocal of the divisor:
\( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc} \)
This technique is often remembered as "keep, change, flip" - keep the first fraction, change division to multiplication, and flip the second fraction.
Why Simplify Fractions?
Simplifying fractions makes them easier to work with and understand. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
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