Solve Fraction Addition: 4/15 + 2/5 Step by Step

Q: Why can't I just add 4+2 and 15+5?

Because fractions represent parts of a whole! You can't add parts unless they're the same size. Think of it like adding 1/2 pizza + 1/3 pizza - you need equal-sized slices first.

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

Since 5 is a factor of 15, the LCD is simply 15! List multiples: 5 (5, 10, 15...) and 15 (15, 30, 45...). The smallest common multiple is 15.

Q: Do I always need to simplify my answer?

Yes, always simplify! $ \frac{10}{15} $ and $ \frac{2}{3} $ are equal, but $ \frac{2}{3} $ is the simplest form. Divide numerator and denominator by their GCD.

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

Use the multiplication method! For fractions like $ \frac{3}{7} + \frac{2}{9} $, multiply the denominators: 7 × 9 = 63. Then convert both fractions to have denominator 63.

Q: How can I check if my final answer is correct?

Convert your answer back to decimal and check: $ \frac{4}{15} = 0.267 $, $ \frac{2}{5} = 0.4 $, so $ 0.267 + 0.4 = 0.667 $. Also, $ \frac{2}{3} = 0.667 $ ✓

Fraction Addition with Different Denominators

$\frac{4}{15}+\frac{2}{5}=$

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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 multiply by 3, to get the common denominator 15

00:09 Remember to multiply both numerator and denominator

00:16 Calculate the multiplications

00:25 Add under the common denominator

00:30 Calculate the numerator

00:36 Reduce the fraction as much as possible

00:40 Remember to divide both numerator and denominator

00:46 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{4}{15}+\frac{2}{5}=$

Step-by-step solution

To solve the problem of adding $\frac{4}{15} + \frac{2}{5}$ , follow these steps:

Step 1: Identify a common denominator. Since 5 is a factor of 15, we will use 15 as the common denominator.
Step 2: Convert $\frac{2}{5}$ to a fraction with a denominator of 15. To do this, multiply both the numerator and denominator by 3: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$ .
Step 3: Add the fractions: $\frac{4}{15} + \frac{6}{15}$ .
Step 4: Since both fractions now have the same denominator, add the numerators: $\frac{4 + 6}{15} = \frac{10}{15}$ .
Step 5: Simplify $\frac{10}{15}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5: $\frac{10 \div 5}{15 \div 5} = \frac{2}{3}$ .

Therefore, the sum of $\frac{4}{15} + \frac{2}{5}$ is $\frac{2}{3}$ .

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Use LCD to make denominators equal before adding
Technique: Convert $\frac{2}{5}$ to $\frac{6}{15}$ by multiplying by 3
Check: Verify $\frac{10}{15} = \frac{2}{3}$ by dividing both by 5 ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{4}{15} + \frac{2}{5}$ as $\frac{6}{20}$ ! This ignores the fundamental rule that fractions need common denominators. Always find the LCD first, convert both fractions, 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 4+2 and 15+5?

Because fractions represent parts of a whole! You can't add parts unless they're the same size. Think of it like adding 1/2 pizza + 1/3 pizza - you need equal-sized slices first.

How do I find the LCD of 15 and 5?

Since 5 is a factor of 15, the LCD is simply 15! List multiples: 5 (5, 10, 15...) and 15 (15, 30, 45...). The smallest common multiple is 15.

Do I always need to simplify my answer?

Yes, always simplify! $\frac{10}{15}$ and $\frac{2}{3}$ are equal, but $\frac{2}{3}$ is the simplest form. Divide numerator and denominator by their GCD.

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

Use the multiplication method! For fractions like $\frac{3}{7} + \frac{2}{9}$ , multiply the denominators: 7 × 9 = 63. Then convert both fractions to have denominator 63.

How can I check if my final answer is correct?

Convert your answer back to decimal and check: $\frac{4}{15} = 0.267$ , $\frac{2}{5} = 0.4$ , so $0.267 + 0.4 = 0.667$ . Also, $\frac{2}{3} = 0.667$ ✓

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