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

Fraction Addition with Unlike 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
00:18 Calculate the multiplications
00:24 Add with the common denominator
00:28 Calculate the numerator
00:31 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 lowest common denominator between 5 and 3

To find the lowest 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
  • LCD Rule: Find common denominator before adding fractions together
  • Technique: Multiply 25 \frac{2}{5} by 3 and 13 \frac{1}{3} by 5 for LCD 15
  • Check: Verify 615+515=1115 \frac{6}{15} + \frac{5}{15} = \frac{11}{15} in simplest form ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add straight across like 25+13=38 \frac{2}{5} + \frac{1}{3} = \frac{3}{8} ! This ignores that fractions represent different-sized pieces. Always find the LCD first to make equal-sized pieces before adding.

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+1 and 5+3 directly?

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Because 25 \frac{2}{5} and 13 \frac{1}{3} represent different-sized pieces! It's like trying to add 2 slices of pizza cut into 5 pieces with 1 slice cut into 3 pieces. You need equal-sized pieces first.

How do I find the LCD of 5 and 3?

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Since 5 and 3 are both prime numbers, their LCD is simply 5 × 3 = 15. For other numbers, list multiples or use prime factorization to find the smallest common multiple.

Do I need to simplify my final answer?

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Yes, always check! In this case, 1115 \frac{11}{15} is already in simplest form because 11 and 15 share no common factors other than 1.

What if the denominators have common factors?

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Great question! If denominators like 6 and 9 share factors, find their LCD using prime factorization. For 6 and 9, the LCD is 18 (not 6×9=54), making calculations easier.

Can I convert to decimals instead?

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You could, but fractions often give exact answers while decimals might be rounded. Plus, many math problems require fraction answers, so it's important to master this method!

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