Solve the Fraction Addition: 1/2 + 1/5 Step-by-Step

Q: How do I find the least common denominator of 2 and 5?

Look for the smallest number that both denominators divide into evenly. Since 2 and 5 are both prime numbers, their LCD is simply 2 × 5 = 10.

Q: Why can't I just add 1 + 1 = 2 and 2 + 5 = 7?

Because $ \frac{1}{2} $ and $ \frac{1}{5} $ represent different-sized pieces! You can't add half of a pizza to one-fifth of a pizza without first cutting them into same-sized pieces.

Q: What if the denominators have a common factor?

Find the LCD by using the smallest multiple both denominators share. For example, with 4 and 6, the LCD is 12 (not 24), because 12 is the smallest number both 4 and 6 divide into.

Q: Do I need to simplify my final answer?

Always check if you can simplify! In this case, $ \frac{7}{10} $ is already in lowest terms because 7 and 10 share no common factors other than 1.

Q: Can I use cross-multiplication for adding fractions?

No, cross-multiplication is for equations! When adding fractions like $ \frac{1}{2}+\frac{1}{5} $, you must use a common denominator method instead.

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{1}{2}+\frac{1}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each fraction by the second denominator to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:15 Calculate the products

00:22 Add with the common denominator

00:26 Calculate the numerator

00:31 Add with the common denominator

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{2}+\frac{1}{5}=$

Step-by-step solution

Let's try to find the lowest common denominator between 2 and 5

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 5

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 2

$\frac{1\times5}{2\times5}+\frac{1\times2}{5\times2}=\frac{5}{10}+\frac{2}{10}$

Now we'll combine and get:

$\frac{5+2}{10}=\frac{7}{10}$

Final Answer

$\frac{7}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator before adding fractions
Technique: Convert $\frac{1}{2}$ to $\frac{5}{10}$ and $\frac{1}{5}$ to $\frac{2}{10}$
Check: Verify $\frac{7}{10}$ equals 0.7 on calculator ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators directly
Don't add $\frac{1}{2}+\frac{1}{5}=\frac{2}{7}$ ! This ignores that fractions represent parts of different-sized wholes. Always find a common denominator first, then add only the numerators.

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 2 and 5?

Look for the smallest number that both denominators divide into evenly. Since 2 and 5 are both prime numbers, their LCD is simply 2 × 5 = 10.

Why can't I just add 1 + 1 = 2 and 2 + 5 = 7?

Because $\frac{1}{2}$ and $\frac{1}{5}$ represent different-sized pieces! You can't add half of a pizza to one-fifth of a pizza without first cutting them into same-sized pieces.

What if the denominators have a common factor?

Find the LCD by using the smallest multiple both denominators share. For example, with 4 and 6, the LCD is 12 (not 24), because 12 is the smallest number both 4 and 6 divide into.

Do I need to simplify my final answer?

Always check if you can simplify! In this case, $\frac{7}{10}$ is already in lowest terms because 7 and 10 share no common factors other than 1.

Can I use cross-multiplication for adding fractions?

No, cross-multiplication is for equations! When adding fractions like $\frac{1}{2}+\frac{1}{5}$ , you must use a common denominator method instead.

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