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

Fraction Addition with Unlike Denominators

Solve the following exercise:

35+13=? \frac{3}{5}+\frac{1}{3}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem together.
00:09 First, multiply each fraction by the second denominator to find a common one.
00:19 Remember, multiply both the top number, the numerator, and the bottom number, the denominator.
00:32 Now, calculate these multiplications carefully.
00:45 Next, add the fractions using the common denominator you found.
00:52 Work out the new numerator by adding the top numbers.
00:56 And there you have it! That's 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:

35+13=? \frac{3}{5}+\frac{1}{3}=\text{?}

2

Step-by-step solution

To solve the problem of adding 35 \frac{3}{5} and 13 \frac{1}{3} , the solution steps are as follows:

  • Step 1: Identify a common denominator. Multiply the denominators: 5×3=15 5 \times 3 = 15 .
  • Step 2: Convert each fraction to have this common denominator.
    • Convert 35 \frac{3}{5} : Multiply both numerator and denominator by 3: 3×35×3=915 \frac{3 \times 3}{5 \times 3} = \frac{9}{15} .
    • Convert 13 \frac{1}{3} : Multiply both numerator and denominator by 5: 1×53×5=515 \frac{1 \times 5}{3 \times 5} = \frac{5}{15} .
  • Step 3: Add the two fractions now that they have the same denominator: 915+515=9+515=1415 \frac{9}{15} + \frac{5}{15} = \frac{9+5}{15} = \frac{14}{15} .
  • Step 4: Simplify if possible. In this case, 1415 \frac{14}{15} is already in its simplest form.

Thus, the result of adding 35 \frac{3}{5} and 13 \frac{1}{3} is 1415 \frac{14}{15} , which corresponds to choice id "3" in the provided multiple-choice options.

3

Final Answer

1415 \frac{14}{15}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator Rule: Find LCD before adding fractions with different denominators
  • Conversion Technique: 35=915 \frac{3}{5} = \frac{9}{15} and 13=515 \frac{1}{3} = \frac{5}{15} using LCD 15
  • Verification Check: Ensure 915+515=1415 \frac{9}{15} + \frac{5}{15} = \frac{14}{15} cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators directly
    Don't add 35+13=48 \frac{3}{5} + \frac{1}{3} = \frac{4}{8} ! This breaks fraction addition rules and gives completely wrong results. 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 separately?

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Because fractions represent parts of different wholes! Adding 35+13 \frac{3}{5} + \frac{1}{3} as 48 \frac{4}{8} is like adding 3 fifths to 1 third directly - it doesn't make mathematical sense.

How do I find the common denominator quickly?

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For simple fractions, multiply the denominators together. Here: 5×3=15 5 \times 3 = 15 . For more complex problems, find the LCM (Least Common Multiple) to keep numbers smaller.

Do I always multiply both parts of each fraction?

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Yes, always! When converting 35 \frac{3}{5} to fifteenths, multiply both numerator and denominator by 3: 3×35×3=915 \frac{3 \times 3}{5 \times 3} = \frac{9}{15} .

How do I know if my answer needs to be simplified?

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Check if the numerator and denominator share any common factors. Since 14 and 15 share no common factors other than 1, 1415 \frac{14}{15} is already in simplest form.

What if I get a whole number or mixed number?

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That's great! If your numerator equals or exceeds the denominator, convert to a mixed number. For example, 1715=1215 \frac{17}{15} = 1\frac{2}{15} .

Can I use a different common denominator?

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Yes, but using the smallest common denominator (LCD) makes calculations easier. You could use 30 or 45, but 15 keeps the numbers simpler!

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