Question

subtract the fractions and reduce to lowest terms. (enter your answer as a simplified mixed number.)
$12\frac{1}{10} - 4\frac{1}{5}$
7 $\frac{9}{10}$

Explanation:

Step1: Convert mixed numbers to improper fractions (or adjust fractions for subtraction)

First, we can handle the mixed numbers. Let's rewrite \(4\frac{1}{5}\) with a denominator of 10 to have the same denominator as the fraction part of \(12\frac{1}{10}\).

\(4\frac{1}{5}=4\frac{1\times2}{5\times2}=4\frac{2}{10}\)

Now, we have \(12\frac{1}{10}-4\frac{2}{10}\). But wait, the numerator of the fraction part of the first mixed number is less than the second. So we can borrow 1 from the whole number part of \(12\frac{1}{10}\).

\(12\frac{1}{10}=11 + 1+\frac{1}{10}=11+\frac{10}{10}+\frac{1}{10}=11\frac{11}{10}\)

Step2: Subtract the mixed numbers

Now subtract the whole numbers and the fractions:

Whole numbers: \(11 - 4 = 7\)

Fractions: \(\frac{11}{10}-\frac{2}{10}=\frac{11 - 2}{10}=\frac{9}{10}\)

Step3: Combine the results

Combine the whole number and the fraction: \(7+\frac{9}{10}=7\frac{9}{10}\)

Answer:

\(7\frac{9}{10}\)