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

Fraction Addition with Different Denominators

Solve the following exercise:

15+13= \frac{1}{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
00:12 Calculate the products
00:19 Add with the common denominator
00:24 Calculate the numerator
00:27 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:

15+13= \frac{1}{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

1×35×3+1×53×5=315+515 \frac{1\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{3}{15}+\frac{5}{15}

Now we'll combine and get:

3+515=815 \frac{3+5}{15}=\frac{8}{15}

3

Final Answer

815 \frac{8}{15}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the LCD before adding fractions with different denominators
  • Technique: Convert 15 \frac{1}{5} to 315 \frac{3}{15} and 13 \frac{1}{3} to 515 \frac{5}{15}
  • Check: Verify 315+515=815 \frac{3}{15} + \frac{5}{15} = \frac{8}{15} and cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 15+13 \frac{1}{5} + \frac{1}{3} as 28 \frac{2}{8} ! This ignores the different denominators and gives a completely wrong answer. Always find the LCD first and convert both fractions before adding 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 1 + 1 = 2 and 5 + 3 = 8 to get 2/8?

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Because fractions represent parts of different wholes! 15 \frac{1}{5} means 1 part of 5, while 13 \frac{1}{3} means 1 part of 3. You need the same denominator to add them properly.

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 5 \times 3 = 15 . For other numbers, list multiples of each until you find the smallest common one.

Do I need to simplify 8/15?

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Check if 8 and 15 share any common factors. Since 8 = 2³ and 15 = 3×5 share no common factors, 815 \frac{8}{15} is already in simplest form!

What if I multiply the fractions wrong?

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Remember: multiply both numerator and denominator by the same number! For 15 \frac{1}{5} , multiply by 33 \frac{3}{3} to get 315 \frac{3}{15} . This keeps the fraction's value unchanged.

Can I use a different common denominator instead of 15?

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Yes, but using the LCD (15) keeps numbers smaller and easier to work with. Using 30 or 45 would work but create unnecessarily large fractions that you'd need to simplify later.

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