Solve the Fraction Addition: 2/10 + 1/3 Step by Step

Q: How do I find the least common denominator of 10 and 3?

List multiples of each number: 10: 10, 20, 30, 40... and 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... The first number that appears in both lists is 30, so that's your LCD!

Q: Why can't I just add the fractions as they are?

Fractions need the same denominator to be added, just like you can't add 2 apples + 1 orange directly. You need a common 'unit' (denominator) first!

Q: What numbers do I multiply each fraction by?

Divide the LCD by each original denominator: 30 ÷ 10 = 3 and 30 ÷ 3 = 10. So multiply the first fraction by $ \frac{3}{3} $ and the second by $ \frac{10}{10} $.

Q: Do I need to simplify my final answer?

Always check if you can simplify! $ \frac{16}{30} $ can be reduced by dividing both numerator and denominator by their greatest common factor, which is 2, giving $ \frac{8}{15} $.

Q: What if one denominator divides evenly into the other?

Great! That makes it easier. If you had $ \frac{1}{5} + \frac{2}{10} $, since 10 ÷ 5 = 2, you'd just convert $ \frac{1}{5} $ to $ \frac{2}{10} $ and add normally.

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{2}{10}+\frac{1}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together.

00:09 First, multiply each fraction by the second fraction's denominator to get a common denominator.

00:16 Remember, multiply both the top number, the numerator, and the bottom number, the denominator.

00:24 Now, do the multiplications carefully.

00:30 Add the fractions using your common denominator.

00:37 Finally, calculate the numerator.

00:41 Great job! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{2}{10}+\frac{1}{3}=$

Step-by-step solution

Let's try to find the least common denominator between 10 and 3

To find the least common denominator, we need to find a number that is divisible by both 10 and 3

In this case, the common denominator is 30

Now we'll multiply each fraction by the appropriate number to reach the denominator 30

We'll multiply the first fraction by 3

We'll multiply the second fraction by 10

$\frac{2\times3}{10\times3}+\frac{1\times10}{3\times10}=\frac{6}{30}+\frac{10}{30}$

Now we'll combine and get:

$\frac{6+10}{30}=\frac{16}{30}$

Final Answer

$\frac{16}{30}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find least common denominator to add fractions properly
Technique: Convert $\frac{2}{10}$ to $\frac{6}{30}$ and $\frac{1}{3}$ to $\frac{10}{30}$
Check: Add numerators only: $\frac{6+10}{30} = \frac{16}{30}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators together instead of finding LCD
Don't add $\frac{2}{10} + \frac{1}{3} = \frac{3}{13}$ ! This completely ignores fraction rules and gives meaningless results. Always find the least common denominator first, then convert both fractions before adding numerators only.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the least common denominator of 10 and 3?

List multiples of each number: 10: 10, 20, 30, 40... and 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... The first number that appears in both lists is 30, so that's your LCD!

Why can't I just add the fractions as they are?

Fractions need the same denominator to be added, just like you can't add 2 apples + 1 orange directly. You need a common 'unit' (denominator) first!

What numbers do I multiply each fraction by?

Divide the LCD by each original denominator: 30 ÷ 10 = 3 and 30 ÷ 3 = 10. So multiply the first fraction by $\frac{3}{3}$ and the second by $\frac{10}{10}$ .

Do I need to simplify my final answer?

Always check if you can simplify! $\frac{16}{30}$ can be reduced by dividing both numerator and denominator by their greatest common factor, which is 2, giving $\frac{8}{15}$ .

What if one denominator divides evenly into the other?

Great! That makes it easier. If you had $\frac{1}{5} + \frac{2}{10}$ , since 10 ÷ 5 = 2, you'd just convert $\frac{1}{5}$ to $\frac{2}{10}$ and add normally.

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Solve the Fraction Addition: 2/10 + 1/3 Step by Step

Fraction Addition with Different Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I find the least common denominator of 10 and 3?

Why can't I just add the fractions as they are?

What numbers do I multiply each fraction by?

Do I need to simplify my final answer?

What if one denominator divides evenly into the other?

🌟 Unlock Your Math Potential

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