Solve the Fraction Equation: 4/5 - 2/10 - 1/5

Q: Why can't I just subtract the numerators and denominators separately?

Fractions represent parts of a whole. You can only combine fractions when they're divided into the same-sized pieces! Just like you can't subtract 2 apples from 4 oranges directly.

Q: How do I find the least common denominator quickly?

Look for the smallest number that both denominators divide into evenly. For 5 and 10, since 10 ÷ 5 = 2, the LCD is 10!

Q: What if I get confused with all the negative signs?

Work step by step! First convert to common denominators, then carefully subtract from left to right: $ \frac{8}{10} - \frac{2}{10} - \frac{2}{10} $

Q: Do I need to simplify my final answer?

Yes! Always check if your answer can be simplified. $ \frac{4}{10} $ can be reduced to $ \frac{2}{5} $ by dividing both parts by 2.

Q: What's the difference between LCD and LCM?

They're the same thing! LCD (Least Common Denominator) is just the LCM (Least Common Multiple) used specifically for fractions.

Fraction Operations with Common Denominators

Solve the following equation:

$\frac{4}{5}-\frac{2}{10}-\frac{1}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's solve this math problem together.

00:13 We need to multiply each fraction by two to find a common denominator.

00:18 Remember, multiply both the top number and the bottom number.

00:26 Now, let's work out these multiplications.

00:39 Next, subtract the fractions using this common denominator.

00:45 Calculate the new numerator by subtracting the top numbers.

00:51 And there you go! That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{4}{5}-\frac{2}{10}-\frac{1}{5}=$

Step-by-step solution

We must first identify the lowest common denominator between 5 and 10.

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

In this case, the common denominator is 10.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{4\times2}{5\times2}-\frac{2\times1}{10\times1}-\frac{1\times2}{5\times2}=\frac{8}{10}-\frac{2}{10}-\frac{2}{10}$

Finally we'll combine and obtain the following:

$\frac{8-2-2}{10}=\frac{6-2}{10}=\frac{4}{10}$

Final Answer

$\frac{4}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator before adding or subtracting fractions
Technique: Convert $\frac{4}{5}$ to $\frac{8}{10}$ by multiplying by 2
Check: Verify $\frac{8}{10} - \frac{2}{10} - \frac{2}{10} = \frac{4}{10}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting fractions without finding common denominators first
Don't subtract numerators and denominators separately like $\frac{4}{5} - \frac{1}{5} = \frac{3}{0}$ ! This gives meaningless results because you're not working with the same units. Always convert all fractions to have the same denominator before performing operations.

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 numerators and denominators separately?

Fractions represent parts of a whole. You can only combine fractions when they're divided into the same-sized pieces! Just like you can't subtract 2 apples from 4 oranges directly.

How do I find the least common denominator quickly?

Look for the smallest number that both denominators divide into evenly. For 5 and 10, since 10 ÷ 5 = 2, the LCD is 10!

What if I get confused with all the negative signs?

Work step by step! First convert to common denominators, then carefully subtract from left to right: $\frac{8}{10} - \frac{2}{10} - \frac{2}{10}$

Do I need to simplify my final answer?

Yes! Always check if your answer can be simplified. $\frac{4}{10}$ can be reduced to $\frac{2}{5}$ by dividing both parts by 2.

What's the difference between LCD and LCM?

They're the same thing! LCD (Least Common Denominator) is just the LCM (Least Common Multiple) used specifically for fractions.

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