Solve the Expression: 2 - 1/2 in Basic Arithmetic

Fraction Subtraction with Mixed Number Results

212= 2-\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 Break down 2 into 1 plus 1
00:09 Convert from whole number to its proper fraction
00:19 Subtract with common denominator
00:26 Add to get a mixed fraction
00:34 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

212= 2-\frac{1}{2}=

2

Step-by-step solution

To solve the problem of subtracting 12\frac{1}{2} from the whole number 22, we proceed as follows:

First, understand that the whole number 22 can be considered as a fraction with a denominator of 2. This means that 22 is equivalent to 42\frac{4}{2}. This step is crucial to ensure both numbers have a common denominator, facilitating the subtraction of fractions.

Now, subtract the fraction 12\frac{1}{2} from 42\frac{4}{2}:

4212=412=32 \frac{4}{2} - \frac{1}{2} = \frac{4-1}{2} = \frac{3}{2}

The fraction 32\frac{3}{2} is improper because the numerator is larger than the denominator. Thus, we convert this into a mixed number, which is a combination of a whole number and a proper fraction. The mixed number form of 32\frac{3}{2} is 1121\frac{1}{2} because 22 fits into 33 once with a remainder of 11.

Therefore, the result of 212 2-\frac{1}{2} is 112\mathbf{1\frac{1}{2}}.

3

Final Answer

112 1\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert whole numbers to fractions with common denominators
  • Technique: Change 2 to 42 \frac{4}{2} , then subtract: 4212=32 \frac{4}{2} - \frac{1}{2} = \frac{3}{2}
  • Check: Convert 32 \frac{3}{2} to mixed number: 112 1\frac{1}{2} because 3÷2 = 1 remainder 1 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting denominators along with numerators
    Don't subtract 2 - 1/2 = 1/1 = 1! This treats the whole number and fraction as separate parts instead of performing proper fraction subtraction. Always convert the whole number to a fraction with the same denominator first.

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 2 - 1 = 1?

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Because you're subtracting one-half, not one whole! The fraction 12 \frac{1}{2} means you're taking away half of something, so you need to work with fractions.

How do I convert 2 into a fraction?

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Think of 2 as 2 wholes. Since we're working with halves, 2 = 42 \frac{4}{2} because 4 halves make 2 wholes. Always match the denominator!

What's the difference between 3/2 and 1 1/2?

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They're the same value! 32 \frac{3}{2} is an improper fraction and 112 1\frac{1}{2} is a mixed number. Mixed numbers are often easier to understand.

How do I convert 3/2 to a mixed number?

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Divide the numerator by the denominator: 3 ÷ 2 = 1 with remainder 1. So 32=112 \frac{3}{2} = 1\frac{1}{2} .

Can I check my answer?

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Yes! Add your answer back: 112+12=32+12=42=2 1\frac{1}{2} + \frac{1}{2} = \frac{3}{2} + \frac{1}{2} = \frac{4}{2} = 2

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