Solve: Adding Fractions 2/5 + 5/10 Step-by-Step

Q: Why can't I just add the numerators and denominators separately?

Because fractions represent parts of a whole! Adding $ \frac{2}{5} + \frac{5}{10} $ means combining 2 fifths with 5 tenths. You need the same-sized pieces (common denominator) to add them properly.

Q: How do I know which denominator to use as the common denominator?

Look for the Least Common Multiple (LCM) of the denominators. For 5 and 10, the LCM is 10 because 10 is divisible by both 5 and 10.

Q: What if my answer needs to be simplified?

Always check if your answer can be reduced! Look for common factors in the numerator and denominator. In this case, $ \frac{9}{10} $ is already in lowest terms since 9 and 10 share no common factors.

Q: Can I convert both fractions to decimals instead?

Yes! $ \frac{2}{5} = 0.4 $ and $ \frac{5}{10} = 0.5 $, so 0.4 + 0.5 = 0.9 = $ \frac{9}{10} $. Both methods work, but fractions often give exact answers.

Fraction Addition with Common Denominators

Solve the following exercise:

$\frac{2}{5}+\frac{5}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem step by step.

00:09 First, multiply the fraction by 2 to find a common denominator.

00:14 Remember, multiply both the top and bottom numbers of the fraction.

00:25 Now, let's calculate these multiplications carefully.

00:31 Add the results together under the common denominator.

00:35 Next, compute the numerator to get the final result.

00:39 Great job! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{2}{5}+\frac{5}{10}=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the fractions to have the same denominator.
Step 2: Add the fractions.
Step 3: Simplify the resulting fraction.

Let's proceed with solving the problem:

Step 1: Convert $\frac{2}{5}$ to a fraction with a denominator of 10. The equivalent fraction is found by multiplying the numerator and the denominator by 2:

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

Step 2: Add the fractions $\frac{4}{10}$ and $\frac{5}{10}$ :

$\frac{4}{10} + \frac{5}{10} = \frac{4 + 5}{10} = \frac{9}{10}$

Step 3: Simplify the resulting fraction. Since $\frac{9}{10}$ is already in its simplest form, we conclude:

Therefore, the solution to the problem is $\frac{9}{10}$ .

Final Answer

$\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding numerators together
Technique: Convert $\frac{2}{5}$ to $\frac{4}{10}$ by multiplying by 2
Check: Verify $\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$ makes sense ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 2+5 = 7 and 5+10 = 15 to get $\frac{7}{15}$ ! This treats fractions like two separate numbers instead of one value. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators separately?

Because fractions represent parts of a whole! Adding $\frac{2}{5} + \frac{5}{10}$ means combining 2 fifths with 5 tenths. You need the same-sized pieces (common denominator) to add them properly.

How do I know which denominator to use as the common denominator?

Look for the Least Common Multiple (LCM) of the denominators. For 5 and 10, the LCM is 10 because 10 is divisible by both 5 and 10.

What if my answer needs to be simplified?

Always check if your answer can be reduced! Look for common factors in the numerator and denominator. In this case, $\frac{9}{10}$ is already in lowest terms since 9 and 10 share no common factors.

Can I convert both fractions to decimals instead?

Yes! $\frac{2}{5} = 0.4$ and $\frac{5}{10} = 0.5$ , so 0.4 + 0.5 = 0.9 = $\frac{9}{10}$ . Both methods work, but fractions often give exact answers.

What if the denominators are much bigger numbers?

The same process works! Find the LCM of the denominators, convert each fraction, then add. It might take more steps, but the method stays the same.

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