Question

40 determine if each expression is less than 1 or greater than 1.
40 less than 1
$1\frac{2}{5} - \frac{4}{5}$
40 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

Since \(\frac{3}{5}=0.6\) 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

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

Step 3: Compare with 1

Since \(\frac{4}{3}\approx1.33\) and \(1.33 > 1\), so \(1\frac{9}{12}-\frac{5}{12}\) is greater than 1.

Answer:

• \(1\frac{2}{5}-\frac{4}{5}\) is less than 1.
• \(1\frac{9}{12}-\frac{5}{12}\) is greater than 1.