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

Fraction Addition with Unlike Denominators

Solve the following exercise:

15+23=? \frac{1}{5}+\frac{2}{3}=\text{?}

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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 a common denominator
00:09 Remember to multiply both numerator and denominator
00:22 Calculate the multiplications
00:33 Add under common denominator
00:37 Calculate the numerator
00:40 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+23=? \frac{1}{5}+\frac{2}{3}=\text{?}

2

Step-by-step solution

To solve the problem of adding two fractions, follow these steps:

  • Step 1: Identify the fractions involved: 15 \frac{1}{5} and 23 \frac{2}{3} .
  • Step 2: Find a common denominator. Multiply the denominators: 5×3=15 5 \times 3 = 15 .
  • Step 3: Convert each fraction to have the common denominator of 15:
    • Convert 15 \frac{1}{5} by multiplying both numerator and denominator by 3: 15×33=315 \frac{1}{5} \times \frac{3}{3} = \frac{3}{15}
    • Convert 23 \frac{2}{3} by multiplying both numerator and denominator by 5: 23×55=1015 \frac{2}{3} \times \frac{5}{5} = \frac{10}{15}
  • Step 4: Add the converted fractions: 315+1015=1315 \frac{3}{15} + \frac{10}{15} = \frac{13}{15}

Therefore, the sum of 15+23 \frac{1}{5} + \frac{2}{3} is 1315 \frac{13}{15} .

3

Final Answer

1315 \frac{13}{15}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator: Find LCD by multiplying different denominators together
  • Technique: Convert 15 \frac{1}{5} to 315 \frac{3}{15} and 23 \frac{2}{3} to 1015 \frac{10}{15}
  • Check: Verify that 315+1015=1315 \frac{3}{15} + \frac{10}{15} = \frac{13}{15} and cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 15+23 \frac{1}{5} + \frac{2}{3} by doing 1+2=3 and 5+3=8 to get 38 \frac{3}{8} ! This ignores that fractions represent parts of different-sized wholes. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

\( \frac{3}{4}:\frac{5}{6}=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators directly?

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Because 15 \frac{1}{5} and 23 \frac{2}{3} represent different sized pieces! Think of pizza slices - you can't add 1 slice from a 5-piece pizza to 2 slices from a 3-piece pizza without first making the pieces the same size.

How do I find the least common denominator?

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For denominators 5 and 3, check if one divides into the other. Since they don't, multiply them together: 5 × 3 = 15. For more complex problems, find the least common multiple of the denominators.

Do I always multiply the denominators together?

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Not always! If one denominator divides evenly into the other (like 4 and 8), use the larger one. Only multiply when the denominators share no common factors, like 5 and 3.

What if my answer can be simplified?

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Always check if your final answer can be reduced! Look for common factors in the numerator and denominator. In this case, 1315 \frac{13}{15} cannot be simplified since 13 and 15 share no common factors.

Can I use a different common denominator besides 15?

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You could use 30, 45, or any multiple of 15, but it makes the problem harder! The least common denominator gives you the smallest numbers to work with, reducing calculation errors.

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