Solve the Fraction Equation: Finding the Missing Number in ?+2/8=3/4

Fraction Equations with Missing Addends

?+28=34 ?+\frac{2}{8}=\frac{3}{4}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's find the unknown value in our problem.
00:12 First, reduce the fraction to its simplest form.
00:16 Remember to divide, both the top and bottom numbers.
00:21 Here's our reduced fraction. Now, let's substitute it back in.
00:38 The solution has the same bottom number, so the unknown shares it too.
00:43 Let's figure out the unknown by just looking at the top numbers.
00:47 And there you have it! That's the answer to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

?+28=34 ?+\frac{2}{8}=\frac{3}{4}

2

Step-by-step solution

To find the missing number in the equation ?+28=34 ? + \frac{2}{8} = \frac{3}{4} , we will follow these steps:

  • Step 1: Simplify the fraction 28\frac{2}{8} to 14\frac{1}{4}.
  • Step 2: Recognize that we need to find a fraction that, when added to 14\frac{1}{4}, results in 34\frac{3}{4}.
  • Step 3: Set up the equation ?+14=34 ? + \frac{1}{4} = \frac{3}{4} .
  • Step 4: Solve for the missing fraction by subtracting 14\frac{1}{4} from 34\frac{3}{4}:
    ?=3414=24 ? = \frac{3}{4} - \frac{1}{4} = \frac{2}{4} .
  • Step 5: Simplify the resulting fraction: 24=12\frac{2}{4} = \frac{1}{2}.

Therefore, the missing number in the equation is 24\frac{2}{4}.

3

Final Answer

24 \frac{2}{4}

Key Points to Remember

Essential concepts to master this topic
  • Simplify first: Always reduce fractions to lowest terms before solving
  • Subtraction method: 3414=24 \frac{3}{4} - \frac{1}{4} = \frac{2}{4} to find missing value
  • Verify answer: Check that 24+14=34 \frac{2}{4} + \frac{1}{4} = \frac{3}{4}

Common Mistakes

Avoid these frequent errors
  • Not simplifying fractions before solving
    Don't work with 28 \frac{2}{8} in its original form = more complex calculations! This makes the problem harder and increases chances of errors. Always simplify 28 \frac{2}{8} to 14 \frac{1}{4} first.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{3}{9}+\frac{1}{9}=\text{?} \)

FAQ

Everything you need to know about this question

Why do I need to simplify 28 \frac{2}{8} first?

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Simplifying 28 \frac{2}{8} to 14 \frac{1}{4} makes the problem much easier! Both fractions will have the same denominator (4), so you can work with the numerators directly.

How do I know what to subtract?

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Think of it like this: "What plus 14 \frac{1}{4} equals 34 \frac{3}{4} ?" To find the missing piece, subtract the known part from the total: 3414 \frac{3}{4} - \frac{1}{4} .

Should my final answer be 24 \frac{2}{4} or 12 \frac{1}{2} ?

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Both are mathematically correct since 24=12 \frac{2}{4} = \frac{1}{2} ! However, check the answer choices - if 24 \frac{2}{4} is listed, choose that one even though 12 \frac{1}{2} is simplified.

Can I solve this without simplifying first?

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Yes, but it's harder! You'd need to convert 34 \frac{3}{4} to eighths: 6828=48=12 \frac{6}{8} - \frac{2}{8} = \frac{4}{8} = \frac{1}{2} . Simplifying first keeps the numbers smaller and easier to work with.

How do I check if my answer is correct?

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Substitute your answer back into the original equation. If you got 24 \frac{2}{4} , check: 24+28=24+14=34 \frac{2}{4} + \frac{2}{8} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}

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