Solve the Fraction Equation: Finding the Missing Term in 2/5 - ? = 1/5

Fraction Subtraction with Missing Subtrahend

Complete the missing fraction
25——=15 \frac{2}{5}-_{——}=\frac{1}{5}

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's find the missing number.
00:09 Notice, the result shares the same denominator.
00:13 So, our missing number needs that same denominator.
00:17 Now, let's focus on the numerators.
00:20 We'll discover the missing number and add it to the numerator.
00:24 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the missing fraction
25——=15 \frac{2}{5}-_{——}=\frac{1}{5}

What is the missing fraction?

2

Step-by-step solution

To solve the problem 25_=15 \frac{2}{5} - \_ = \frac{1}{5} , we will use the concept of subtraction of fractions to find the missing fraction.

Let's follow these steps:

  • Step 1: Identify the given fractions.
  • Step 2: Use the subtraction identity to find the missing fraction.
  • Step 3: Solve for the missing fraction.

Step 1: The initial fraction (minuend) is 25 \frac{2}{5} and the result (difference) is 15 \frac{1}{5} .

Step 2: Apply the formula from our analysis: MinuendDifference=Subtrahend \text{Minuend} - \text{Difference} = \text{Subtrahend} . That means 2515=_ \frac{2}{5} - \frac{1}{5} = \_ .

Step 3: Perform the subtraction by subtracting the numerators:

2515=215=15 \frac{2}{5} - \frac{1}{5} = \frac{2 - 1}{5} = \frac{1}{5} .

Therefore, the missing fraction is 15 \frac{1}{5} .

3

Final Answer

15 \frac{1}{5}

Key Points to Remember

Essential concepts to master this topic
  • Formula: When minuend - subtrahend = difference, then subtrahend = minuend - difference
  • Technique: Calculate 2515=215=15 \frac{2}{5} - \frac{1}{5} = \frac{2-1}{5} = \frac{1}{5}
  • Check: Verify 2515=15 \frac{2}{5} - \frac{1}{5} = \frac{1}{5} matches the original equation ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the subtraction identity and solving incorrectly
    Don't think the missing value equals 15+25=35 \frac{1}{5} + \frac{2}{5} = \frac{3}{5} ! This adds instead of finding what was subtracted. Always remember: to find the missing subtrahend, subtract the difference from the minuend.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

Why can't I just add the fractions I see?

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Adding 25+15 \frac{2}{5} + \frac{1}{5} gives you 35 \frac{3}{5} , but that's not what was subtracted. Think of it like this: if you start with 2 cookies and end with 1 cookie, you ate 1 cookie, not 3!

How do I remember which operation to use?

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Use the inverse operation! Since the original problem is subtraction, work backwards by thinking: "What do I subtract from the first number to get the result?"

What if the denominators were different?

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You'd need to find a common denominator first, then subtract the numerators. But since both fractions have the same denominator (5), you can subtract directly!

Can I check my answer a different way?

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Yes! Substitute your answer back: 2515=15 \frac{2}{5} - \frac{1}{5} = \frac{1}{5} . If the left side equals the right side, you're correct!

What does 'missing subtrahend' mean?

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In subtraction, the subtrahend is the number being subtracted (the second number). When it's missing, you need to figure out what was taken away from the first number.

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