Solve the Fraction Addition: 2/5 + 1/3 Step by Step

Fraction Addition with Different Denominators

Solve the following exercise:

25+13= \frac{2}{5}+\frac{1}{3}=

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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
00:14 Calculate the multiplications
00:20 Add with the common denominator
00:26 Calculate the numerator
00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

25+13= \frac{2}{5}+\frac{1}{3}=

2

Step-by-step solution

Let's try to find the least common denominator between 5 and 3

To find the least common denominator, we need to find a number that is divisible by both 5 and 3

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 5

2×35×3+1×53×5=615+515 \frac{2\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{6}{15}+\frac{5}{15}

Now we'll combine and get:

6+515=1115 \frac{6+5}{15}=\frac{11}{15}

3

Final Answer

1115 \frac{11}{15}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find least common denominator before adding fractions
  • Technique: Convert 25 \frac{2}{5} to 615 \frac{6}{15} and 13 \frac{1}{3} to 515 \frac{5}{15}
  • Check: Verify LCD is correct: 15 divides by both 5 and 3 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 2+1=3 and 5+3=8 to get 3/8 = wrong answer! This ignores that fractions represent parts of different 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

Why can't I just add 2/5 + 1/3 = 3/8?

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Because you can only add fractions with the same denominator! Think of it like adding apples and oranges - you need to convert them to the same units first. 25 \frac{2}{5} means 2 parts out of 5, while 13 \frac{1}{3} means 1 part out of 3 - completely different sized pieces!

How do I find the least common denominator of 5 and 3?

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Since 5 and 3 are both prime numbers, their LCD is simply their product: 5 × 3 = 15. For other numbers, list multiples of each until you find the smallest one they share.

Do I always multiply the first fraction by the second denominator?

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Not always! You multiply each fraction by whatever number makes its denominator equal to the LCD. Here: 25×33 \frac{2}{5} \times \frac{3}{3} and 13×55 \frac{1}{3} \times \frac{5}{5} both give denominator 15.

What if my answer is an improper fraction?

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That's fine! 1115 \frac{11}{15} is already in simplest form since 11 and 15 share no common factors. You could convert it to a mixed number if needed, but improper fractions are perfectly valid answers.

How do I know if I can simplify my final answer?

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Check if the numerator and denominator have any common factors. For 1115 \frac{11}{15} , since 11 is prime and doesn't divide 15, the fraction is already simplified!

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