Solve the Fraction Expression: 4/10 - 1/5 - 1/10 Step by Step

Fraction Subtraction with Mixed Denominators

41015110= \frac{4}{10}-\frac{1}{5}-\frac{1}{10}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to find the least common denominator
00:06 Therefore multiply by 2, to find the common denominator 10
00:09 Remember to multiply both numerator and denominator
00:16 Calculate the multiplications
00:25 Subtract under the common denominator
00:30 Calculate the numerator
00:38 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

41015110= \frac{4}{10}-\frac{1}{5}-\frac{1}{10}=

2

Step-by-step solution

Let's try to find the least common denominator between 10 and 5

To find the least common denominator, we need to find a number that is divisible by both 10 and 5

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

4×110×11×25×21×110×1=410210110 \frac{4\times1}{10\times1}-\frac{1\times2}{5\times2}-\frac{1\times1}{10\times1}=\frac{4}{10}-\frac{2}{10}-\frac{1}{10}

Now we'll subtract and get:

42110=2110=110 \frac{4-2-1}{10}=\frac{2-1}{10}=\frac{1}{10}

3

Final Answer

110 \frac{1}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the least common denominator before adding or subtracting fractions
  • Technique: Convert 15 \frac{1}{5} to 210 \frac{2}{10} by multiplying by 2
  • Check: Verify 410210110=110 \frac{4}{10} - \frac{2}{10} - \frac{1}{10} = \frac{1}{10} by adding back ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions without finding a common denominator
    Don't subtract numerators and denominators separately like 4/10 - 1/5 = 3/5! This ignores that fractions represent parts of different sized wholes. Always convert all fractions to the same denominator first, 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 4-1-1 and 10-5-10?

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You can't subtract numerators and denominators separately because fractions represent parts of a whole. 15 \frac{1}{5} and 110 \frac{1}{10} are different sized pieces - you need the same denominator to compare them!

How do I find the least common denominator between 10 and 5?

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List the multiples of each number: 5 = 5, 10, 15... and 10 = 10, 20, 30... The smallest common multiple is 10, so that's your LCD.

What if I get a negative answer?

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Negative answers are possible! Just follow the same steps: find the LCD, convert fractions, then subtract. If the first numerator is smaller than what you're subtracting, you'll get a negative result.

Do I need to simplify my final answer?

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Always check if your answer can be simplified! For 110 \frac{1}{10} , since 1 and 10 share no common factors other than 1, it's already in lowest terms.

Can I solve this problem in a different order?

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Yes! You could group the terms differently, like 41011015 \frac{4}{10} - \frac{1}{10} - \frac{1}{5} , but you still need the same LCD and will get the same answer.

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