Question Simplify the expression $5/6 \div 1/2$ and reduce to lowest terms if possible.

Studdy Solution

STEP 1

Assumptions
1. We are given the fraction $\frac{5}{6}$ and we need to divide it by the fraction $\frac{1}{2}$ .
2. To divide by a fraction, we multiply by its reciprocal.

STEP 2

Write the division of two fractions as the multiplication of the first fraction by the reciprocal of the second fraction.
$\frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \times \frac{2}{1}$

STEP 3

Now, multiply the numerators of the two fractions to get the numerator of the result.
$Numerator = 5 \times 2$

STEP 4

Calculate the numerator.
$Numerator = 5 \times 2 = 10$

STEP 5

Multiply the denominators of the two fractions to get the denominator of the result.
$Denominator = 6 \times 1$

STEP 6

Calculate the denominator.
$Denominator = 6 \times 1 = 6$

STEP 7

Combine the numerator and denominator to form the resulting fraction.
$Resulting\, fraction = \frac{Numerator}{Denominator} = \frac{10}{6}$

STEP 8

Reduce the resulting fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 10 and 6 is 2.

STEP 9

Divide both the numerator and the denominator by the GCD to reduce the fraction.
$\frac{10}{6} = \frac{10 \div 2}{6 \div 2}$

STEP 10

Calculate the reduced fraction.
$\frac{10 \div 2}{6 \div 2} = \frac{5}{3}$
The reduced form of $\frac{5}{6} \div \frac{1}{2}$ is $\frac{5}{3}$ .

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