Solve the Fraction Expression: 3/5 - 1/10 - 1/5 Step by Step

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

Fractions represent parts of a whole, not separate numbers! You need equal-sized pieces (same denominator) before you can combine them. Think of it like pizza slices - you can't subtract eighths from fourths until you cut them the same size.

Q: How do I find the LCD between 5 and 10?

List the multiples: 5 has multiples 5, 10, 15, 20... and 10 has multiples 10, 20, 30... The smallest number that appears in both lists is 10, so LCD = 10.

Q: Do I always multiply fractions to get the LCD?

You multiply each fraction by whatever makes the denominator equal to the LCD. For $ \frac{3}{5} $, multiply by $ \frac{2}{2} $ to get $ \frac{6}{10} $. For $ \frac{1}{10} $, multiply by $ \frac{1}{1} $ (no change needed).

Q: Can I simplify my answer further?

Always check if your final answer can be simplified! For $ \frac{3}{10} $, since 3 and 10 share no common factors other than 1, it's already in lowest terms.

Q: What if I get confused with the order of subtraction?

Work from left to right just like regular subtraction: $ \frac{6}{10} - \frac{1}{10} = \frac{5}{10} $, then $ \frac{5}{10} - \frac{2}{10} = \frac{3}{10} $. You can also think of it as $ \frac{6-1-2}{10} $.

Fraction Subtraction with Different Denominators

$\frac{3}{5}-\frac{1}{10}-\frac{1}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each fraction by 2 and 2 respectively to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:21 Calculate the multiplications

00:30 Subtract with the common denominator

00:36 Calculate the numerator

00:42 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{3}{5}-\frac{1}{10}-\frac{1}{5}=$

Step-by-step solution

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

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

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 2

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{3\times2}{5\times2}-\frac{1\times1}{10\times1}-\frac{1\times2}{5\times2}=\frac{6}{10}-\frac{1}{10}-\frac{2}{10}$

Now let's subtract:

$\frac{6-1-2}{10}=\frac{5-2}{10}=\frac{3}{10}$

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find least common denominator before adding or subtracting fractions
Technique: Convert $\frac{3}{5}$ to $\frac{6}{10}$ and $\frac{1}{5}$ to $\frac{2}{10}$
Check: Verify $\frac{6}{10} - \frac{1}{10} - \frac{2}{10} = \frac{3}{10}$ by counting tenths ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract $\frac{3}{5} - \frac{1}{10}$ as $\frac{3-1}{5-10} = \frac{2}{-5}$ ! This treats fractions like regular subtraction and gives meaningless results. Always find the LCD first, then subtract only the numerators while keeping the common denominator.

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, not separate numbers! You need equal-sized pieces (same denominator) before you can combine them. Think of it like pizza slices - you can't subtract eighths from fourths until you cut them the same size.

How do I find the LCD between 5 and 10?

List the multiples: 5 has multiples 5, 10, 15, 20... and 10 has multiples 10, 20, 30... The smallest number that appears in both lists is 10, so LCD = 10.

Do I always multiply fractions to get the LCD?

You multiply each fraction by whatever makes the denominator equal to the LCD. For $\frac{3}{5}$ , multiply by $\frac{2}{2}$ to get $\frac{6}{10}$ . For $\frac{1}{10}$ , multiply by $\frac{1}{1}$ (no change needed).

Can I simplify my answer further?

Always check if your final answer can be simplified! For $\frac{3}{10}$ , since 3 and 10 share no common factors other than 1, it's already in lowest terms.

What if I get confused with the order of subtraction?

Work from left to right just like regular subtraction: $\frac{6}{10} - \frac{1}{10} = \frac{5}{10}$ , then $\frac{5}{10} - \frac{2}{10} = \frac{3}{10}$ . You can also think of it as $\frac{6-1-2}{10}$ .

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