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

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

Because fractions represent parts of a whole. $ \frac{1}{5} $ means 1 part out of 5, while $ \frac{3}{10} $ means 3 parts out of 10. You need the same-sized parts (same denominator) to add them correctly!

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

Since 10 is already a multiple of 5 (5 × 2 = 10), the LCD is simply 10. For other cases, list multiples of each number until you find the smallest one they share.

Q: What if the denominators don't have an obvious relationship?

Use the multiplication method: multiply both denominators together, then simplify if possible. For example, if adding $ \frac{1}{3} + \frac{1}{4} $, use 12 as the common denominator (3 × 4 = 12).

Q: How can I check if my fraction conversion is correct?

Cross-multiply to verify! For $ \frac{1}{5} = \frac{2}{10} $, check: 1 × 10 = 10 and 5 × 2 = 10. Since both equal 10, the fractions are equivalent!

Fraction Addition with Mixed Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Alright, let's solve the problem together.

00:08 We need to find the smallest common denominator.

00:12 So, we'll multiply by 2, to make 10 the common denominator.

00:17 Remember, we multiply both the top and bottom numbers.

00:21 Let's do these multiplications step by step.

00:26 Now, let's add with the common denominator.

00:32 Let's calculate what's on top, the numerator.

00:36 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

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

Step-by-step solution

To solve this problem, let's break it down into clear, manageable steps:

Step 1: Identify the common denominator. Here, the denominators are 5 and 10. The least common denominator (LCD) is 10.
Step 2: Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 10. This means multiplying both the numerator and denominator by 2. Thus, $\frac{1}{5} = \frac{2}{10}$ .
Step 3: We already have $\frac{3}{10}$ with a denominator of 10, so no conversion is necessary.
Step 4: Add the two fractions: $\frac{2}{10} + \frac{3}{10} = \frac{2 + 3}{10} = \frac{5}{10}$ .
Step 5: Verify if the fraction can be simplified. Here, $\frac{5}{10}$ is already in its simplest form equivalent to $\frac{1}{2}$ , but, as part of the answer choices, it appears as $\frac{5}{10}$ .

Therefore, the correct answer is $\frac{5}{10}$ .

Final Answer

$\frac{5}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find least common denominator to add fractions properly
Technique: Convert $\frac{1}{5}$ to $\frac{2}{10}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{2}{10} + \frac{3}{10} = \frac{5}{10}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{5} + \frac{3}{10}$ as $\frac{1+3}{5+10} = \frac{4}{15}$ ! This breaks fraction addition rules and gives completely wrong results. 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. $\frac{1}{5}$ means 1 part out of 5, while $\frac{3}{10}$ means 3 parts out of 10. You need the same-sized parts (same denominator) to add them correctly!

How do I find the least common denominator between 5 and 10?

Since 10 is already a multiple of 5 (5 × 2 = 10), the LCD is simply 10. For other cases, list multiples of each number until you find the smallest one they share.

Do I always need to simplify my final answer?

It's good practice, but check what the question asks for! Here, $\frac{5}{10}$ could be simplified to $\frac{1}{2}$ , but the answer choices show $\frac{5}{10}$ , so that's what they want.

What if the denominators don't have an obvious relationship?

Use the multiplication method: multiply both denominators together, then simplify if possible. For example, if adding $\frac{1}{3} + \frac{1}{4}$ , use 12 as the common denominator (3 × 4 = 12).

How can I check if my fraction conversion is correct?

Cross-multiply to verify! For $\frac{1}{5} = \frac{2}{10}$ , check: 1 × 10 = 10 and 5 × 2 = 10. Since both equal 10, the fractions are equivalent!

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