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.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( 12+3\cdot0= \)

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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