To solve [tex]\( 48 \div 1 \frac{1}{5} \)[/tex], follow these steps:
1. Convert the Mixed Number to an Improper Fraction: - Start with the mixed number [tex]\(1 \frac{1}{5}\)[/tex]. - Convert this to an improper fraction. The mixed number [tex]\(1 \frac{1}{5}\)[/tex] can be expressed as [tex]\(1 + \frac{1}{5}\)[/tex]. - Convert [tex]\(1\)[/tex] to a fraction with the same denominator as [tex]\(\frac{1}{5}\)[/tex]: [tex]\[
1 = \frac{5}{5}
\][/tex] - Now add the two fractions: [tex]\[
1 \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}
\][/tex]
2. Perform the Division: - Now we need to divide 48 by [tex]\(\frac{6}{5}\)[/tex]. - Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{6}{5}\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
3. Multiply by the Reciprocal: - Multiply 48 by [tex]\(\frac{5}{6}\)[/tex]: [tex]\[
48 \div \frac{6}{5} = 48 \times \frac{5}{6}
\][/tex] - Simplify the multiplication: [tex]\[
48 \times \frac{5}{6} = \frac{48 \times 5}{6} = \frac{240}{6} = 40
\][/tex]
So, the result of [tex]\(48 \div 1 \frac{1}{5}\)[/tex] is [tex]\(40\)[/tex].
