Solve the Fraction Subtraction: 4/10 - 1/4 Step-by-Step

Fraction Subtraction with Unlike Denominators

Solve the following equation:

41014= \frac{4}{10}-\frac{1}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:02 We want to find the least common denominator
00:05 Therefore we'll multiply by 2 and 5 respectively to find the common denominator 20
00:08 Remember to multiply both numerator and denominator
00:18 Let's calculate the multiplications
00:30 Subtract under the common denominator
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

41014= \frac{4}{10}-\frac{1}{4}=

2

Step-by-step solution

We must first identify the lowest common denominator between 4 and 10.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 10.

In this case, the common denominator is 20.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 20

We'll multiply the first fraction by 2

We'll multiply the second fraction by 5

4×210×21×54×5=820520 \frac{4\times2}{10\times2}-\frac{1\times5}{4\times5}=\frac{8}{20}-\frac{5}{20}

Finally we'll combine and obtain the following:

8520=320 \frac{8-5}{20}=\frac{3}{20}

3

Final Answer

320 \frac{3}{20}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find lowest common denominator to subtract unlike fractions
  • Technique: Convert 410 \frac{4}{10} to 820 \frac{8}{20} and 14 \frac{1}{4} to 520 \frac{5}{20}
  • Check: Verify 320 \frac{3}{20} cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting denominators along with numerators
    Don't subtract 4-1 = 3 and 10-4 = 6 to get 36 \frac{3}{6} ! This ignores that fractions need common denominators to subtract. Always find the LCD first, convert both fractions, then subtract 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 subtract 4-1 and 10-4 directly?

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You can only subtract fractions when they have the same denominator. Think of it like trying to subtract 4 apples from 1 orange - they're different units! You must convert to common denominators first.

How do I find the LCD of 10 and 4?

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List the multiples of each number: 10: 10, 20, 30... and 4: 4, 8, 12, 16, 20.... The first number that appears in both lists is your LCD - in this case, 20.

Why do I multiply 4/10 by 2/2 and 1/4 by 5/5?

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To get denominator 20: 410×22=820 \frac{4}{10} \times \frac{2}{2} = \frac{8}{20} and 14×55=520 \frac{1}{4} \times \frac{5}{5} = \frac{5}{20} . Multiplying by equivalent forms of 1 doesn't change the value!

Can I simplify 3/20 further?

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No! Since 3 and 20 share no common factors other than 1, 320 \frac{3}{20} is already in lowest terms. This is your final answer.

What if I get a negative answer?

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If the second fraction is larger than the first, you'll get a negative result - that's perfectly correct! Just make sure to keep track of your negative sign throughout the calculation.

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