37/8 divided by 2/3 in Fraction Form
The result of 37/8 divided by 2/3 is: 6 15/16
Step-by-Step Solution
Step 1: Understand the Problem
We need to divide the fraction \(\frac378\) by \(\frac23\).
Step 2: Use the Division Rule
To divide fractions, we multiply by the reciprocal of the second fraction:
\(\frac378 \div \frac23 = \frac378 \times \frac32\)
Step 3: Multiply the Fractions
Multiply the numerators: 37 × 3 = 111
Multiply the denominators: 8 × 2 = 16
Step 4: Convert to Mixed Number
The fraction \(\frac11116\) can be written as the mixed number \(6\frac1516\).
Final Answer
The result of 37/8 divided by 2/3 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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