Question

determine if each expression is less than 1 or greater than 1.
less than 1
$1\frac{2}{5} - \frac{4}{5}$
greater than 1
$1\frac{9}{12} - \frac{5}{12}$

Explanation:

For the expression \( 1\frac{2}{5} - \frac{4}{5} \):

Step 1: Convert mixed number to improper fraction

\( 1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5} \)

Step 2: Subtract the fractions

\( \frac{7}{5}-\frac{4}{5}=\frac{7 - 4}{5}=\frac{3}{5} \)

Step 3: Compare with 1

\( \frac{3}{5}=0.6 \), and \( 0.6<1 \), so \( 1\frac{2}{5}-\frac{4}{5} \) is less than 1.

For the expression \( 1\frac{9}{12} - \frac{5}{12} \):

Step 1: Convert mixed number to improper fraction

\( 1\frac{9}{12}=\frac{1\times12 + 9}{12}=\frac{21}{12} \)

Step 2: Subtract the fractions

\( \frac{21}{12}-\frac{5}{12}=\frac{21 - 5}{12}=\frac{16}{12}=\frac{4}{3}\approx1.33 \)

Step 3: Compare with 1

\( \frac{4}{3}\approx1.33>1 \), so \( 1\frac{9}{12}-\frac{5}{12} \) is greater than 1.

Answer:

• \( 1\frac{2}{5}-\frac{4}{5} \): Less than 1
• \( 1\frac{9}{12}-\frac{5}{12} \): Greater than 1