Solve: 1/2 + 3/10 - Adding Fractions with Unlike Denominators

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

Look for the Least Common Multiple (LCM) of the denominators. Since 10 is already a multiple of 2, we use 10. This makes the math easier than using a larger number like 20!

Q: Do I always need to simplify my final answer?

It depends on what the question asks! $ \frac{8}{10} $ simplifies to $ \frac{4}{5} $, but both are correct. Check if the problem or answer choices specify which form to use.

Fraction Addition with Common Denominator Finding

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply the fraction by 5 to get a common denominator

00:09 Remember to multiply both numerator and denominator

00:16 Calculate the multiplications

00:23 Add under common denominator

00:29 Calculate the numerator

00:33 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:

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

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Recognize the denominators $2$ and $10$ and note that $10$ is a common multiple.
Step 2: Convert $\frac{1}{2}$ to a fraction with a denominator of 10. Since $2 \times 5 = 10$ , multiply both the numerator and denominator of $\frac{1}{2}$ by 5 to get $\frac{5}{10}$ .
Step 3: The second fraction, $\frac{3}{10}$ , already has a denominator of 10, so no conversion is needed.
Step 4: Add the two fractions: $\frac{5}{10} + \frac{3}{10}$ .
Step 5: As the denominators are the same, add the numerators: $5 + 3 = 8$ .
Step 6: Write the result with the common denominator: $\frac{8}{10}$ .
Step 7: Check if the fraction can be simplified further. Since 8 and 10 have a common factor of 2, divide by 2 to simplify: $\frac{8}{10} = \frac{4}{5}$ .

The problem's correct answer without simplification matches choice 1.

Therefore, the solution to the problem is $\frac{8}{10}$ .

Final Answer

$\frac{8}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions with different denominators
Technique: Convert $\frac{1}{2}$ to $\frac{5}{10}$ by multiplying by $\frac{5}{5}$
Check: Verify $\frac{5}{10} + \frac{3}{10} = \frac{8}{10}$ by adding numerators only ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{2} + \frac{3}{10}$ as $\frac{1+3}{2+10} = \frac{4}{12}$ ! This creates a completely wrong fraction. Always find a common denominator 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 1+3 and 2+10 to get 4/12?

That's not how fraction addition works! You can only add fractions when they have the same denominator. Think of it like pizza slices - you can't add half a pizza to three-tenths of a pizza without making the pieces the same size first.

How do I know which common denominator to use?

Look for the Least Common Multiple (LCM) of the denominators. Since 10 is already a multiple of 2, we use 10. This makes the math easier than using a larger number like 20!

Do I always need to simplify my final answer?

It depends on what the question asks! $\frac{8}{10}$ simplifies to $\frac{4}{5}$ , but both are correct. Check if the problem or answer choices specify which form to use.

What if the denominators don't have an obvious common multiple?

You can always multiply the denominators together as a last resort. For example, with $\frac{1}{3} + \frac{1}{7}$ , use 21 as the common denominator (3 × 7 = 21).

Why does 1/2 become 5/10 and not something else?

Because we multiply both numerator and denominator by the same number to keep the fraction equivalent. Since $2 \times 5 = 10$ , we also do $1 \times 5 = 5$ to get $\frac{5}{10}$ .

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