Solve the Fraction Equation: 8/10 - 1/5 - 2/10

Fraction Subtraction with Mixed Denominators

Solve the following equation:

81015210= \frac{8}{10}-\frac{1}{5}-\frac{2}{10}=

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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 multiply by 2, to find the common denominator 10
00:08 Remember to multiply both numerator and denominator
00:15 Subtract under the common denominator
00:22 Calculate the numerator
00:28 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:

81015210= \frac{8}{10}-\frac{1}{5}-\frac{2}{10}=

2

Step-by-step solution

Let's try to identify the lowest common denominator between 10 and 5.

In order to identify the lowest common denominator, we need to find a number that is divisible by both 10 and 5.

In this case, the common denominator is 10.

Let's proceed to multiply each fraction by the appropriate number in order 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

8×110×11×25×22×110×1=810210210 \frac{8\times1}{10\times1}-\frac{1\times2}{5\times2}-\frac{2\times1}{10\times1}=\frac{8}{10}-\frac{2}{10}-\frac{2}{10}

Finally let's subtract as follows:

82210=6210=410 \frac{8-2-2}{10}=\frac{6-2}{10}=\frac{4}{10}

3

Final Answer

410 \frac{4}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding or subtracting fractions
  • Technique: Convert 15 \frac{1}{5} to 210 \frac{2}{10} by multiplying by 2
  • Check: Verify 410=25 \frac{4}{10} = \frac{2}{5} in lowest terms ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting numerators and denominators separately
    Don't subtract 8-1-2 = 5 and 10-5-10 = -5 to get 5/-5! This creates meaningless results because you're not working with equivalent fractions. 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 the numbers directly?

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Fractions represent parts of a whole, so you need the same-sized parts (same denominator) to subtract them. It's like trying to subtract 8 slices of a pizza cut into 10 pieces from 1 slice of a pizza cut into 5 pieces - you need to make the pieces the same size first!

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

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Look for the smallest number that both denominators divide into evenly. Since 10 ÷ 5 = 2 exactly, 10 is already a multiple of 5, making 10 our LCD (Least Common Denominator).

Do I need to simplify my final answer?

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It's always good practice! 410 \frac{4}{10} can be simplified to 25 \frac{2}{5} by dividing both numerator and denominator by 2. Both forms are correct, but simplified fractions are preferred.

What if the denominators were different numbers like 6 and 8?

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Find the LCD by listing multiples: 6: 6, 12, 18, 24... and 8: 8, 16, 24... The first number that appears in both lists is your LCD. In this case, 24 would be the LCD.

Can I convert everything to decimals instead?

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Yes, but be careful with repeating decimals! 15=0.2 \frac{1}{5} = 0.2 works nicely, but fractions like 13 \frac{1}{3} become 0.333... which can lead to rounding errors.

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