Solve the Fraction Addition: 1/2 + 0 + 1/2 Step by Step

Fraction Addition with Identity Elements

12+0+12= \frac{1}{2}+0+\frac{1}{2}= ?

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00:00 Solve
00:07 Let's reduce the 0, and continue solving
00:14 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

12+0+12= \frac{1}{2}+0+\frac{1}{2}= ?

2

Step-by-step solution

According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right:

12+0=12 \frac{1}{2}+0=\frac{1}{2}

12+12=11=1 \frac{1}{2}+\frac{1}{2}=\frac{1}{1}=1

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Identity Element: Adding zero to any number leaves it unchanged
  • Same Denominators: Add numerators: 12+12=22=1 \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1
  • Check: Verify 12+0+12=1 \frac{1}{2} + 0 + \frac{1}{2} = 1 by simplifying step-by-step ✓

Common Mistakes

Avoid these frequent errors
  • Treating zero as having a denominator
    Don't write 0 as 02 \frac{0}{2} and then add 12+02+12=22 \frac{1}{2} + \frac{0}{2} + \frac{1}{2} = \frac{2}{2} ! While this gives the right answer, it's unnecessary work. Always remember that adding zero to anything leaves it unchanged.

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FAQ

Everything you need to know about this question

Why doesn't adding zero change the result?

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Zero is called the additive identity because adding it to any number leaves that number unchanged. Think of it like this: if you have half a pizza and add zero more pieces, you still have half a pizza!

Do I need to find a common denominator when one number is zero?

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No! Zero doesn't have a denominator, so you can simply ignore it in fraction addition problems. Focus on adding the actual fractions together.

What's the easiest way to add fractions with the same denominator?

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When denominators are the same, just add the numerators and keep the same denominator: 12+12=1+12=22=1 \frac{1}{2} + \frac{1}{2} = \frac{1+1}{2} = \frac{2}{2} = 1

Should I work from left to right or can I rearrange?

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With addition, you can work in any order because addition is commutative. However, working left to right is often clearest and follows the standard order of operations.

How do I know when to simplify my fraction answer?

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Always simplify! If your numerator and denominator have common factors, divide both by their greatest common factor. Here, 22=1 \frac{2}{2} = 1 because 2 ÷ 2 = 1.

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