Solve Fraction Addition: 1/15 + 2/5 Step-by-Step

Q: How do I find the LCD of 15 and 5?

Since 15 is a multiple of 5 (15 = 5 × 3), the LCD is simply 15! When one denominator divides evenly into the other, the larger number is always the LCD.

Q: Why can't I just add 1/15 + 2/5 directly?

Fractions represent parts of different sized wholes. Adding $ \frac{1}{15} $ (fifteenths) and $ \frac{2}{5} $ (fifths) is like adding apples and oranges - you need a common unit first!

Q: How do I convert 2/5 to have denominator 15?

Ask yourself: "What times 5 equals 15?" Since 5 × 3 = 15, multiply both numerator and denominator by 3: $ \frac{2 \times 3}{5 \times 3} = \frac{6}{15} $

Q: Is 7/15 in simplest form?

Yes! Since 7 and 15 share no common factors other than 1 (7 is prime and doesn't divide 15), $ \frac{7}{15} $ is already simplified.

Q: What if I got a different LCD?

You might use a common multiple instead of the least common multiple. For example, 30 works too, but using 15 keeps numbers smaller and makes calculation easier!

Q: Can I check my answer?

Absolutely! Convert your answer to decimals: $ \frac{1}{15} ≈ 0.067 $ and $ \frac{2}{5} = 0.4 $, so $ \frac{7}{15} ≈ 0.467 $ which equals 0.067 + 0.4 ✓

Fraction Addition with Different Denominators

$\frac{1}{15}+\frac{2}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 Therefore we'll multiply by 3, to get the common denominator 15

00:09 Remember to multiply both numerator and denominator

00:18 Let's calculate the multiplications

00:26 Add under the common denominator

00:32 Calculate the numerator

00:36 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

$\frac{1}{15}+\frac{2}{5}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Determine the least common denominator (LCD) of the fractions.
Step 2: Convert each fraction to have the common denominator.
Step 3: Add the numerators and keep the denominator the same.

Now, let's work through each step:

Step 1: The least common denominator of 15 and 5 is 15.

Step 2: Convert the fraction $\frac{2}{5}$ to have the denominator of 15.
To convert $\frac{2}{5}$ , we need to multiply both the numerator and the denominator by 3, because ${5 \times 3 = 15}$ .
Thus, $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$ .

Step 3: Now, add the fractions $\frac{1}{15}$ and $\frac{6}{15}$ .
When adding these fractions, the equation is $\frac{1}{15} + \frac{6}{15} = \frac{1 + 6}{15} = \frac{7}{15}$ .

Therefore, the solution to the problem is $\frac{7}{15}$ .

Final Answer

$\frac{7}{15}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the LCD before adding fractions with different denominators
Technique: Convert $\frac{2}{5}$ to $\frac{6}{15}$ by multiplying by 3/3
Check: Verify $\frac{1}{15} + \frac{6}{15} = \frac{7}{15}$ is in simplest form ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{15} + \frac{2}{5}$ as $\frac{1+2}{15+5} = \frac{3}{20}$ ! This ignores the fundamental rule that fractions need common denominators. Always find the LCD first and convert both fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

How do I find the LCD of 15 and 5?

Since 15 is a multiple of 5 (15 = 5 × 3), the LCD is simply 15! When one denominator divides evenly into the other, the larger number is always the LCD.

Why can't I just add 1/15 + 2/5 directly?

Fractions represent parts of different sized wholes. Adding $\frac{1}{15}$ (fifteenths) and $\frac{2}{5}$ (fifths) is like adding apples and oranges - you need a common unit first!

How do I convert 2/5 to have denominator 15?

Ask yourself: "What times 5 equals 15?" Since 5 × 3 = 15, multiply both numerator and denominator by 3: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$

Is 7/15 in simplest form?

Yes! Since 7 and 15 share no common factors other than 1 (7 is prime and doesn't divide 15), $\frac{7}{15}$ is already simplified.

What if I got a different LCD?

You might use a common multiple instead of the least common multiple. For example, 30 works too, but using 15 keeps numbers smaller and makes calculation easier!

Can I check my answer?

Absolutely! Convert your answer to decimals: $\frac{1}{15} ≈ 0.067$ and $\frac{2}{5} = 0.4$ , so $\frac{7}{15} ≈ 0.467$ which equals 0.067 + 0.4 ✓

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