Solve the Fraction Addition: 3/10 + 1/5 + 4/10 Step-by-Step

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

Because fractions represent parts of a whole! Adding $ \frac{1}{5} $ and $ \frac{3}{10} $ means combining different-sized pieces. You need to make them the same size first by finding a common denominator.

Q: How do I find the common denominator of 10 and 5?

Look for the smallest number that both denominators divide into evenly. Since 10 ÷ 5 = 2, the number 10 works perfectly! So 10 is our LCD (Least Common Denominator).

Q: What do I multiply 1/5 by to get tenths?

Multiply both the numerator and denominator by 2: $ \frac{1 \times 2}{5 \times 2} = \frac{2}{10} $. This doesn't change the value of the fraction, just makes it easier to add!

Q: Can I simplify 9/10 further?

No, $ \frac{9}{10} $ is already in its simplest form! Since 9 and 10 don't share any common factors except 1, this fraction cannot be reduced.

Q: What if I have more than three fractions to add?

The same process works! Find the LCD of all denominators, convert each fraction, then add all the numerators. Just take it one step at a time.

Fraction Addition with Mixed Denominators

Solve the following exercise:

$\frac{3}{10}+\frac{1}{5}+\frac{4}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 We want to find the least common denominator

00:06 Therefore multiply by 2 to get common denominator 10

00:10 Remember to multiply both numerator and denominator

00:19 Calculate the multiplications

00:26 Add under common denominator

00:34 Calculate the numerator

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{3}{10}+\frac{1}{5}+\frac{4}{10}=\text{?}$

Step-by-step solution

When we have a fraction addition exercise with more than one fraction, we make sure all the denominators of the fractions are identical.

Let's find the common denominator of the fractions' denominators: $10$ and $5$

The common denominator is $10$ .

Now we'll multiply both numerator and denominator of the fraction $\frac{1}{5}$ by $2$ and create a fraction addition exercise where all denominators are $10$ :

$\frac{3}{10}+\frac{1\times2}{5\times2}+\frac{4}{10}=\frac{3}{10}+\frac{2}{10}+\frac{4}{10}$

Finally, we'll add all the numerators of the fractions:

$\frac{3}{10}+\frac{2}{10}+\frac{4}{10}=\frac{3+2+4}{10}=\frac{9}{10}$

Final Answer

$\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCD of all denominators before adding fractions
Technique: Convert $\frac{1}{5}$ to $\frac{2}{10}$ by multiplying by 2/2
Check: Add numerators only: 3 + 2 + 4 = 9, keep denominator 10 ✓

Common Mistakes

Avoid these frequent errors

Adding denominators along with numerators
Don't add 3/10 + 1/5 + 4/10 = 8/25! This creates a completely wrong fraction. The denominators stay the same when you add fractions - only numerators get added. Always find common denominators first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

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 $\frac{1}{5}$ and $\frac{3}{10}$ means combining different-sized pieces. You need to make them the same size first by finding a common denominator.

How do I find the common denominator of 10 and 5?

Look for the smallest number that both denominators divide into evenly. Since 10 ÷ 5 = 2, the number 10 works perfectly! So 10 is our LCD (Least Common Denominator).

What do I multiply 1/5 by to get tenths?

Multiply both the numerator and denominator by 2: $\frac{1 \times 2}{5 \times 2} = \frac{2}{10}$ . This doesn't change the value of the fraction, just makes it easier to add!

Can I simplify 9/10 further?

No, $\frac{9}{10}$ is already in its simplest form! Since 9 and 10 don't share any common factors except 1, this fraction cannot be reduced.

What if I have more than three fractions to add?

The same process works! Find the LCD of all denominators, convert each fraction, then add all the numerators. Just take it one step at a time.

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