Solve the Fraction Addition: 4/15 + 1/2 Step-by-Step

Fraction Addition with Different Denominators

415+12= \frac{4}{15}+\frac{1}{2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to find the lowest common denominator
00:06 Multiply each fraction by the other denominator to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:18 Calculate the multiplications
00:32 Add under the common denominator
00:38 Calculate the numerator
00:42 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

415+12= \frac{4}{15}+\frac{1}{2}=

2

Step-by-step solution

To solve the problem of adding 415 \frac{4}{15} and 12 \frac{1}{2} , follow these steps:

  • Step 1: Identify the denominators of the given fractions, which are 15 15 and 2 2 .

  • Step 2: Find the common denominator by multiplying the denominators: 15×2=30 15 \times 2 = 30 .

  • Step 3: Adjust each fraction to have the common denominator:

    • Convert 415 \frac{4}{15} to 4×215×2=830 \frac{4 \times 2}{15 \times 2} = \frac{8}{30} .

    • Convert 12 \frac{1}{2} to 1×152×15=1530 \frac{1 \times 15}{2 \times 15} = \frac{15}{30} .

  • Step 4: Add the adjusted fractions:
    830+1530=8+1530=2330 \frac{8}{30} + \frac{15}{30} = \frac{8 + 15}{30} = \frac{23}{30} .

  • Step 5: Simplify the final expression. In this case, 2330 \frac{23}{30} is already in simplest form.

The solution to the problem is 2330 \frac{23}{30} , which corresponds with choice 1 in the provided answer choices.

3

Final Answer

2330 \frac{23}{30}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding fractions with different denominators
  • Technique: Multiply denominators: 15 × 2 = 30, then convert fractions
  • Check: Verify 830+1530=2330 \frac{8}{30} + \frac{15}{30} = \frac{23}{30} is simplified ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators directly
    Don't add 415+12 \frac{4}{15} + \frac{1}{2} as 517 \frac{5}{17} ! You can't add fractions with different denominators directly - this 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 4 + 1 and 15 + 2?

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Because fractions represent parts of different wholes! 415 \frac{4}{15} means 4 parts out of 15, while 12 \frac{1}{2} means 1 part out of 2. You need to make the "wholes" the same size first.

How do I find the common denominator?

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The easiest way is to multiply the denominators together: 15 × 2 = 30. This always works! For more advanced problems, you can find the least common multiple to get smaller numbers.

Do I always multiply both numerator and denominator?

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Yes, always! When converting 415 \frac{4}{15} to thirtieths, multiply both: 4×215×2=830 \frac{4 \times 2}{15 \times 2} = \frac{8}{30} . This keeps the fraction's value the same.

How do I know if my final answer needs simplifying?

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Check if the numerator and denominator share any common factors. Since 23 is prime and doesn't divide 30, 2330 \frac{23}{30} is already in simplest form!

What if I get a different common denominator?

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Any common denominator works! You could use 30, 60, 90, etc. But using the smallest one (like 30) makes the arithmetic easier and gives you the simplest form faster.

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