$\frac{3}{5}+\frac{2}{7}=$

Question

31-10-2026
Mathematics

Answered

$\frac{3}{5}+\frac{2}{7}=$

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-10-31T13:58:11-04:00

Identify the least common multiple of the denominators 5 and 7, which is 35.
Convert each fraction to have this common denominator: $\frac{3}{5} = \frac{21}{35}$ and $\frac{2}{7} = \frac{10}{35}$.
Add the numerators of the converted fractions to obtain the sum.
The final result is $\boxed{\frac{31}{35}}$.

Explanation

Problem Analysis and Finding a Common Denominator

To find the sum of $\frac{3}{5}$ and $\frac{2}{7}$, we must add two fractions with different denominators. To perform this addition, we need to express them with a common denominator. The most straightforward common denominator is the least common multiple of the two denominators, 5 and 7. Since 5 and 7 are both prime numbers, their least common multiple is $5 \times 7 = 35$.

Converting Fractions to a Common Denominator

Now, we convert each fraction to have a denominator of 35.
For the first fraction, $\frac{3}{5}$, we multiply both the numerator and the denominator by 7:
\[\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}\]
For the second fraction, $\frac{2}{7}$, we multiply both the numerator and the denominator by 5:
\[\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}\]

Adding the Fractions

Now that both fractions share the same denominator of 35, we can easily add them by summing their numerators:
\[\frac{21}{35} + \frac{10}{35} = \frac{21 + 10}{35} = \frac{31}{35}\]
Since 31 and 35 have no common factors other than 1, the fraction $\frac{31}{35}$ is already in its simplest form.

Examples

Imagine you are baking cookies and a recipe calls for $\frac{3}{5}$ of a cup of sugar for the dough and $\frac{2}{7}$ of a cup of sugar for the topping. To find the total amount of sugar needed, you perform the addition $\frac{3}{5} + \frac{2}{7}$. By finding a common denominator, you realize you need $\frac{31}{35}$ of a cup of sugar in total, helping you measure your ingredients accurately.