Solve: 5 minus 2⅓ - Mixed Number Subtraction Problem

Subtracting Mixed Numbers from Whole Numbers

5213= 5-2\frac{1}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Break down each mixed fraction into whole number and remainder
00:14 Subtract between the whole numbers
00:22 Break down 3 into 2 plus 1
00:28 Convert from whole number to the corresponding proper fraction
00:37 Subtract with common denominator
00:44 Add to mixed fraction
00:47 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

5213= 5-2\frac{1}{3}=

2

Step-by-step solution

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

  • Step 1: Convert the mixed number 2132\frac{1}{3} to an improper fraction.
  • Step 2: Subtract the improper fraction from the whole number 5.
  • Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed number to an improper fraction. For 2132\frac{1}{3}, multiply the whole number 2 by the denominator 3 and add the numerator 1: (2×3)+1=7(2 \times 3) + 1 = 7. Thus, 2132\frac{1}{3} is 73\frac{7}{3}.

Step 2: Subtract 73\frac{7}{3} from 5. First, convert 5 to a fraction with the same denominator: 5=1535 = \frac{15}{3}. Subtract: 15373=83\frac{15}{3} - \frac{7}{3} = \frac{8}{3}.

Step 3: Convert 83\frac{8}{3} back to a mixed number. Divide 8 by 3: 8 divided by 3 is 2 with a remainder of 2, so 83=223\frac{8}{3} = 2\frac{2}{3}.

Therefore, the solution to the problem is 2232\frac{2}{3}.

3

Final Answer

223 2\frac{2}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert mixed numbers to improper fractions before subtracting
  • Technique: Change 5 to 153 \frac{15}{3} , then subtract 73 \frac{7}{3}
  • Check: 223+213=5 2\frac{2}{3} + 2\frac{1}{3} = 5 confirms our answer ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting whole number and fraction parts separately
    Don't subtract 5 - 2 = 3, then 0 - 1/3 = wrong answer! This ignores proper borrowing and gives incorrect results. Always convert both numbers to the same format (improper fractions) before subtracting.

Practice Quiz

Test your knowledge with interactive questions

\( 2\frac{2}{5}+2\frac{2}{5}= \)

FAQ

Everything you need to know about this question

Why can't I just subtract the whole numbers first?

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When subtracting mixed numbers from whole numbers, you need to borrow from the whole number if you subtract parts separately. Converting to improper fractions avoids this complexity and prevents errors!

How do I convert a whole number to a fraction?

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Multiply the whole number by the denominator of the fraction you're working with. For example: 5=5×33=153 5 = \frac{5 \times 3}{3} = \frac{15}{3}

What if I get an improper fraction as my answer?

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Always convert improper fractions back to mixed numbers! Divide the numerator by denominator: 83=8÷3=2 \frac{8}{3} = 8 ÷ 3 = 2 remainder 2 2 , so 223 2\frac{2}{3}

Can I use a different method to solve this?

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Yes! You could also borrow from the whole number: Think of 5 as 433 4\frac{3}{3} , then subtract 213 2\frac{1}{3} to get 223 2\frac{2}{3} . Both methods work!

How do I check if my mixed number answer is correct?

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Add your answer back to what you subtracted: 223+213 2\frac{2}{3} + 2\frac{1}{3} should equal the original number (5). If it does, you're right!

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