Question

1. use the fraction strips to find the difference.

$3\frac{1}{5} - 2\frac{2}{5}$
image of fraction strips
options:
$\frac{4}{5}$
1
$1\frac{4}{5}$
$5\frac{3}{5}$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(3\frac{1}{5}\) and \(2\frac{2}{5}\) to improper fractions.
For \(3\frac{1}{5}\), we have \(3\frac{1}{5}=\frac{3\times5 + 1}{5}=\frac{16}{5}\).
For \(2\frac{2}{5}\), we have \(2\frac{2}{5}=\frac{2\times5+2}{5}=\frac{12}{5}\).

Step2: Subtract the two improper fractions

Now subtract the two fractions: \(\frac{16}{5}-\frac{12}{5}=\frac{16 - 12}{5}=\frac{4}{5}\).

Alternatively, we can also subtract the whole numbers and the fractions separately.
The whole number part: \(3 - 2=1\).
The fraction part: \(\frac{1}{5}-\frac{2}{5}\). Since \(\frac{1}{5}<\frac{2}{5}\), we need to borrow 1 from the whole number part. So \(3\frac{1}{5}=2 + 1+\frac{1}{5}=2+\frac{5}{5}+\frac{1}{5}=2\frac{6}{5}\).
Now subtract: \(2\frac{6}{5}-2\frac{2}{5}=(2 - 2)+(\frac{6}{5}-\frac{2}{5})=0+\frac{4}{5}=\frac{4}{5}\).

Answer:

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