Solve the Fraction Subtraction: 3/7 minus 1/3

Fraction Subtraction with Different Denominators

Solve the following exercise:

3713=? \frac{3}{7}-\frac{1}{3}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve the math problem.
00:10 First, multiply by the second denominator to get a common denominator.
00:15 Be sure to multiply both the top and bottom numbers.
00:25 Now, let's calculate those multiplications carefully.
00:33 Next, subtract, keeping the common denominator.
00:39 It's time to work out the top number, or numerator.
00:43 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

3713=? \frac{3}{7}-\frac{1}{3}=\text{?}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the fractions and denominators involved.
  • Step 2: Find a common denominator for the two fractions.
  • Step 3: Convert each fraction to an equivalent fraction with the common denominator.
  • Step 4: Subtract the numerators and simplify the result.

Let's perform each of these steps:

Step 1: We have the fractions 37\frac{3}{7} and 13\frac{1}{3}.

Step 2: Find a common denominator. The denominators are 7 and 3, so the common denominator will be 7×3=217 \times 3 = 21.

Step 3: Convert each fraction:

  • For 37\frac{3}{7}, multiply both numerator and denominator by 3 to get 3×37×3=921\frac{3 \times 3}{7 \times 3} = \frac{9}{21}.
  • For 13\frac{1}{3}, multiply both numerator and denominator by 7 to get 1×73×7=721\frac{1 \times 7}{3 \times 7} = \frac{7}{21}.

Step 4: Subtract the numerators:

921721=9721=221\frac{9}{21} - \frac{7}{21} = \frac{9 - 7}{21} = \frac{2}{21}.

Simplify if necessary: Here, 221\frac{2}{21} is already in its simplest form.

Therefore, the solution to the problem is 221 \frac{2}{21} .

3

Final Answer

221 \frac{2}{21}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator: Find LCD by multiplying denominators when they're coprime
  • Convert: Change 37 \frac{3}{7} to 921 \frac{9}{21} and 13 \frac{1}{3} to 721 \frac{7}{21}
  • Verify: Check that 921721=221 \frac{9}{21} - \frac{7}{21} = \frac{2}{21} cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting denominators along with numerators
    Don't subtract 3-1 = 2 and 7-3 = 4 to get 24 \frac{2}{4} ! This completely ignores how fractions work and gives a wrong answer. 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, and you can only subtract parts when they're the same size! Think of it like subtracting 3 slices of a 7-piece pizza minus 1 slice of a 3-piece pizza - the slices are different sizes!

How do I know when 7 × 3 = 21 is the right common denominator?

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When the denominators don't share any common factors (like 7 and 3), multiply them together to get the LCD. For 7 and 3, since both are prime numbers, 21 is the smallest common multiple.

Do I always need to simplify my final answer?

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Yes, always check! Look for common factors between numerator and denominator. Since 2 and 21 share no common factors, 221 \frac{2}{21} is already fully simplified.

What if I get confused about which number to multiply by?

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Use this rule: To convert 37 \frac{3}{7} to denominator 21, ask "7 times what equals 21?" The answer is 3, so multiply both top and bottom by 3!

Can this method work for adding fractions too?

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Absolutely! Finding a common denominator works for both addition and subtraction of fractions. The only difference is you add the numerators instead of subtracting them.

What happens if my answer comes out negative?

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That's totally fine! If the second fraction is larger than the first, your answer will be negative. Just follow the same steps and include the negative sign in your final answer.

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