Question

find the value of the expression
$g \div \frac{1}{2}$
for $g = 2 \frac{7}{8}$.
write your answer as a fraction or as a whole or mixed number.

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \( g = 2\frac{7}{8} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 2\frac{7}{8} \), we have \( a = 2 \), \( b = 7 \), \( c = 8 \). Then \( 2\times8 + 7 = 16 + 7 = 23 \), so \( 2\frac{7}{8}=\frac{23}{8} \).

Step2: Divide by a fraction (multiply by reciprocal)

The expression is \( g\div\frac{1}{2} \), and dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{1}{2} \) is \( 2 \) (or \( \frac{2}{1} \)). So we have \( \frac{23}{8}\div\frac{1}{2}=\frac{23}{8}\times2 \).

Step3: Multiply the fractions

Multiply \( \frac{23}{8} \) by \( 2 \). We can write \( 2 \) as \( \frac{2}{1} \), so \( \frac{23}{8}\times\frac{2}{1}=\frac{23\times2}{8\times1}=\frac{46}{8} \).

Step4: Simplify the fraction

Simplify \( \frac{46}{8} \). We can divide both the numerator and the denominator by their greatest common divisor, which is \( 2 \). So \( \frac{46\div2}{8\div2}=\frac{23}{4} \). Then convert \( \frac{23}{4} \) back to a mixed number. \( 23\div4 = 5 \) with a remainder of \( 3 \), so \( \frac{23}{4}=5\frac{3}{4} \).

Answer:

\( 5\frac{3}{4} \)