Solve the Fraction Addition: 2/4 + 1/2 Step by Step

Fraction Addition with Common Denominators

Solve the following equation:

24+12= \frac{2}{4}+\frac{1}{2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem together.
00:10 First, multiply the fraction by two. This helps us find a common denominator.
00:16 Remember, multiply both the top number, called the numerator, and the bottom number, called the denominator.
00:24 Now, calculate these multiplications carefully.
00:27 Next, add them using the common denominator.
00:33 Keep in mind, any number divided by itself is always one.
00:38 And that's how we find the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

24+12= \frac{2}{4}+\frac{1}{2}=

2

Step-by-step solution

Let's first identify the lowest common denominator between 4 and 2.

In order to identify the lowest common denominator, we need to find a number that is divisible by both 4 and 2.

In this case, the common denominator is 4

We will then proceed to multiply each fraction by the appropriate number in order to reach the denominator 4

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

2×14×1+1×22×2=24+24 \frac{2\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{2}{4}+\frac{2}{4}

Finally we will combine and obtain the following:

2+24=44=1 \frac{2+2}{4}=\frac{4}{4}=1

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding fractions
  • Technique: Convert 12 \frac{1}{2} to 24 \frac{2}{4} by multiplying by 22 \frac{2}{2}
  • Check: Final answer simplifies: 44=1 \frac{4}{4} = 1

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 24+12 \frac{2}{4} + \frac{1}{2} as 36 \frac{3}{6} ! This treats fractions like separate whole numbers and gives completely wrong results. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators directly?

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Fractions represent parts of a whole. You can only add parts that are the same size! 24 \frac{2}{4} uses fourths while 12 \frac{1}{2} uses halves - they're different sized pieces.

How do I find the common denominator between 4 and 2?

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Look for the smallest number both denominators divide into evenly. Since 4 ÷ 2 = 2 exactly, the number 4 works perfectly as our common denominator.

Why does the first fraction stay the same?

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24 \frac{2}{4} already has denominator 4, so we multiply by 11 \frac{1}{1} (which equals 1). This doesn't change the value: 2×14×1=24 \frac{2 \times 1}{4 \times 1} = \frac{2}{4}

Can I simplify before adding the fractions?

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Yes! You could simplify 24=12 \frac{2}{4} = \frac{1}{2} first, then add 12+12=22=1 \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1 . Both methods work perfectly!

What if my final answer is an improper fraction?

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That's fine! But always check if you can convert to a mixed number or whole number. Here, 44=1 \frac{4}{4} = 1 whole, which looks much cleaner.

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