Solve the Fraction Subtraction: 1/3 minus 1/5

Fraction Subtraction with Unlike Denominators

Solve the following exercise:

1315=? \frac{1}{3}-\frac{1}{5}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem step by step.
00:09 First, multiply by the second denominator. This helps us find a common denominator.
00:15 Remember, multiply both the numerator and the denominator. This keeps the fraction balanced.
00:24 Now, let's calculate the products carefully.
00:29 Next, subtract using the common denominator we've found.
00:38 Great! Let's calculate the new numerator.
00:42 And that's how we solve the problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

1315=? \frac{1}{3}-\frac{1}{5}=\text{?}

2

Step-by-step solution

To solve the problem 1315 \frac{1}{3} - \frac{1}{5} , we follow these steps:

First, we need to find a common denominator for the fractions 13\frac{1}{3} and 15\frac{1}{5}. The denominators are 3 and 5, and their least common multiple (LCM) is 15.

We will convert each fraction to an equivalent fraction with the denominator 15:

  • To convert 13\frac{1}{3} to a fraction with denominator 15, multiply both the numerator and the denominator by 5: 13=1×53×5=515 \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
  • To convert 15\frac{1}{5} to a fraction with denominator 15, multiply both the numerator and the denominator by 3: 15=1×35×3=315 \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}

Now that both fractions have the same denominator, we can subtract the numerators:

515315=5315=215 \frac{5}{15} - \frac{3}{15} = \frac{5 - 3}{15} = \frac{2}{15}

Therefore, the solution to the problem is 215\frac{2}{15}.

3

Final Answer

215 \frac{2}{15}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator: Find LCM of denominators before subtracting fractions
  • Technique: Convert 13=515 \frac{1}{3} = \frac{5}{15} and 15=315 \frac{1}{5} = \frac{3}{15}
  • Check: Verify 215 \frac{2}{15} cannot simplify further since 2 and 15 share no common factors ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting denominators along with numerators
    Don't subtract 1/3 - 1/5 = (1-1)/(3-5) = 0/-2 = 0! This treats fractions like regular subtraction and ignores fraction rules. Always find a common denominator first, then subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

Why can't I just subtract the numerators and denominators separately?

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Because fractions represent parts of a whole, not separate numbers! You can only subtract fractions when they have the same denominator - like subtracting 5 apples from 3 apples, not 3 apples from 5 oranges.

How do I find the least common multiple of 3 and 5?

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List multiples of each number: 3: 3, 6, 9, 12, 15... 5: 5, 10, 15... The first number that appears in both lists is 15, so LCM(3,5) = 15.

What if the denominators are bigger numbers?

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The same process works! Find the LCM of the denominators, convert both fractions, then subtract. For larger numbers, you can use prime factorization to find the LCM more easily.

Do I always need to simplify my final answer?

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Yes, always check! Look for common factors between the numerator and denominator. In this case, 215 \frac{2}{15} is already in lowest terms since 2 and 15 share no common factors.

What if I get a negative answer?

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That's possible! If you're subtracting a larger fraction from a smaller one, like 1513 \frac{1}{5} - \frac{1}{3} , you'd get 215 -\frac{2}{15} . Just keep the negative sign with the numerator.

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