Solve the Fraction Addition: 3/7 + 5/14 + 1/3

Fraction Addition with Mixed Denominators

37+514+13= \frac{3}{7}+\frac{5}{14}+\frac{1}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solution
00:03 We want to find the least common denominator
00:06 Therefore we'll multiply by 3, 6, and 14 respectively to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:32 Let's calculate the multiplications
00:46 Let's add under the common denominator
00:54 Let's calculate the numerator
01:06 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

37+514+13= \frac{3}{7}+\frac{5}{14}+\frac{1}{3}=

2

Step-by-step solution

To solve the problem of adding the fractions 37+514+13 \frac{3}{7} + \frac{5}{14} + \frac{1}{3} , we follow these steps:

  • Step 1: Find the Least Common Denominator (LCD).
    We have denominators 7, 14, and 3. The least common multiple (LCM) of these numbers is 42.
  • Step 2: Convert each fraction to the equivalent fraction with denominator 42.
    • 37 \frac{3}{7} : Multiply both the numerator and the denominator by 6 to get 1842 \frac{18}{42} .
    • 514 \frac{5}{14} : Multiply both the numerator and the denominator by 3 to get 1542 \frac{15}{42} .
    • 13 \frac{1}{3} : Multiply both the numerator and the denominator by 14 to get 1442 \frac{14}{42} .
  • Step 3: Add the fractions.
    Now, we add the numerators of these fractions: 18+15+14=47 18 + 15 + 14 = 47 .
  • Final Result:
    The sum of the fractions is 4742 \frac{47}{42} .

Therefore, the final answer is 4742 \frac{47}{42} .

3

Final Answer

4742 \frac{47}{42}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find least common multiple of all denominators first
  • Convert Method: Transform 37 \frac{3}{7} to 1842 \frac{18}{42} by multiplying by 6
  • Verify Sum: Check that 18 + 15 + 14 = 47 in numerator ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators together
    Don't add fractions like 37+514=821 \frac{3}{7} + \frac{5}{14} = \frac{8}{21} ! Adding denominators creates meaningless results. Always find the LCD first, convert all fractions to equivalent forms with that denominator, 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

How do I find the LCD of 7, 14, and 3?

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List the multiples of each number: 7 (7, 14, 21, 28, 35, 42), 14 (14, 28, 42), 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42). The first number that appears in all lists is 42!

Why do I multiply 37 \frac{3}{7} by 6?

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Because 7 × 6 = 42, which is our LCD. To keep fractions equivalent, you must multiply both top and bottom by the same number: 3×67×6=1842 \frac{3 × 6}{7 × 6} = \frac{18}{42}

Can I simplify 4742 \frac{47}{42} ?

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Since 47 is prime and doesn't share any common factors with 42, this fraction is already in lowest terms. You could convert it to a mixed number: 1542 1\frac{5}{42}

What if the denominators were bigger numbers?

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The same method works! Just find the LCD of all denominators first. You might need to use prime factorization for larger numbers to find the LCM more easily.

How can I check my answer is correct?

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  • Convert each original fraction to decimal and add: 0.429 + 0.357 + 0.333 ≈ 1.119
  • Convert your answer: 4742 \frac{47}{42} ≈ 1.119 ✓

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