Evaluate: $1 \frac{2}{5} + 1 \frac{1}{2}$

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alyssa8991 alyssa8991

05-11-2026
Mathematics

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Evaluate: $1 \frac{2}{5} + 1 \frac{1}{2}$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T18:50:25-05:00

Convert the mixed numbers $1 \frac{2}{5}$ and $1 \frac{1}{2}$ to their improper fraction equivalents $\frac{7}{5}$ and $\frac{3}{2}$.
Find the common denominator of 10 to add the two fractions $\frac{14}{10}$ and $\frac{15}{10}$.
Calculate the sum of the fractions to get $\frac{29}{10}$.
Convert the result back to a mixed number: $\boxed{2 \frac{9}{10}}$.

Explanation

Understanding the Problem

The expression given is the sum of two mixed numbers: $1 \frac{2}{5}$ and $1 \frac{1}{2}$. To add these, we can represent each mixed number in its equivalent improper fraction form. A mixed number of the form $a \frac{b}{c}$ can be written as the sum $a + \frac{b}{c}$, which is equal to $\frac{ac + b}{c}$.

Converting to Improper Fractions

First, we convert the mixed numbers to improper fractions:
$1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5}$
$1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$
Now the sum is $\frac{7}{5} + \frac{3}{2}$.

Adding the Fractions

To add the fractions $\frac{7}{5}$ and $\frac{3}{2}$, we find a common denominator, which is the least common multiple of 5 and 2, which is 10.
We adjust the fractions:
$\frac{7}{5} = \frac{7 \times 2}{5 \times 2} = \frac{14}{10}$
$\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}$
Summing these gives:
$\frac{14}{10} + \frac{15}{10} = \frac{14 + 15}{10} = \frac{29}{10}$

Final Calculation and Result

Finally, we can convert the improper fraction $\frac{29}{10}$ back to a mixed number. Dividing 29 by 10, we get 2 with a remainder of 9.
Thus, $\frac{29}{10} = 2 \frac{9}{10}$, which is also equal to $2.9$. The final answer is $\boxed{2 \frac{9}{10}}$.

Examples

In daily life, converting mixed numbers is essential for cooking or construction. For instance, if you have a recipe that requires $1 \frac{2}{5}$ cups of sugar and you decide to add $1 \frac{1}{2}$ cups more, calculating the total helps you prepare the correct measurement. Converting these to improper fractions, $\frac{7}{5}$ and $\frac{3}{2}$, allows you to find the total sum of $2.9$ cups or $2 \frac{9}{10}$ cups accurately, ensuring your baking comes out perfectly.