Identify LCD: Identify the least common denominator (LCD) for the fractions 2/5 and 4/10. The denominators are 5 and 10, so the LCD is 10 because 10 is the smallest number that both 5 and 10 can divide into without leaving a remainder. Convert fractions: Convert the fractions to have the same denominator. The first fraction, 2/5, needs to be multiplied by 2/2 to have a denominator of 10. So, 2/5 becomes 4/10. The second fraction, 4/10, already has a denominator of 10, so it remains the same. Add numerators: Add the numerators of the converted fractions. Now that both fractions have the same denominator, we can add them directly: 4/10 + 4/10. Perform addition: Perform the addition. Adding the numerators gives us 4 + 4 = 8, so the sum of the fractions is 8/10. Simplify fraction: Simplify the resulting fraction if possible. The fraction 8/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, 8 ÷ 2 = 4 and 10 ÷ 2 = 5. The simplified fraction is 4/5.

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$\frac{2}{5} + \frac{4}{10} =$

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Grade 7

Add and subtract fractions

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\frac{2}{5} + \frac{4}{10} =

Identify LCD: Identify the least common denominator (LCD) for the fractions $\frac{2}{5}$ and $\frac{4}{10}$ . The denominators are $5$ and $10$ , so the LCD is $10$ because $10$ is the smallest number that both $5$ and $10$ can divide into without leaving a remainder.
Convert fractions: Convert the fractions to have the same denominator. The first fraction, $\frac{2}{5}$ , needs to be multiplied by $\frac{2}{2}$ to have a denominator of $10$ . So, $\frac{2}{5}$ becomes $\frac{4}{10}$ . The second fraction, $\frac{4}{10}$ , already has a denominator of $10$ , so it remains the same.
Add numerators: Add the numerators of the converted fractions. Now that both fractions have the same denominator, we can add them directly: $\frac{4}{10} + \frac{4}{10}$ .
Perform addition: Perform the addition. Adding the numerators gives us $4 + 4 = 8$ , so the sum of the fractions is $\frac{8}{10}$ .
Simplify fraction: Simplify the resulting fraction if possible. The fraction $\frac{8}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . So, $8 \div 2 = 4$ and $10 \div 2 = 5$ . The simplified fraction is $\frac{4}{5}$ .