Solve: 10/12 - 1/3 - 2/6 Fraction Subtraction Problem

Q: Why can't I just subtract the numerators 10 - 1 - 2?

Because different denominators represent different-sized pieces! You can't subtract 10 twelfths, 1 third, and 2 sixths directly - it's like subtracting apples, oranges, and bananas. Find the LCD first!

Q: Do I always need to simplify my final answer?

Yes, always simplify! $ \frac{2}{12} $ and $ \frac{1}{6} $ are equal, but $ \frac{1}{6} $ is in lowest terms and looks cleaner.

Q: What if I get confused with all the fraction conversions?

Write each step clearly! Show: $ \frac{10}{12} - \frac{1 \times 4}{3 \times 4} - \frac{2 \times 2}{6 \times 2} $. Taking your time prevents errors and makes checking easier.

Q: Can I use a calculator for this type of problem?

While calculators help with arithmetic, learning the manual method helps you understand fractions better. Plus, showing your work step-by-step is usually required on tests!

Fraction Subtraction with Common Denominators

$\frac{10}{12}-\frac{1}{3}-\frac{2}{6}=$

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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 4 and 2 respectively to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:19 Calculate the multiplications

00:41 Divide by the common denominator

00:47 Calculate the numerator

00:53 Reduce the fraction as much as possible

00:57 Make sure to divide both numerator and denominator

01:00 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

$\frac{10}{12}-\frac{1}{3}-\frac{2}{6}=$

Step-by-step solution

Let's try to find the lowest common denominator between 6, 3, and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 3, and 12

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 1

We'll multiply the second fraction by 4

We'll multiply the third fraction by 2

$\frac{10\times1}{12\times1}-\frac{1\times4}{3\times4}-\frac{2\times2}{6\times2}=\frac{10}{12}-\frac{4}{12}-\frac{4}{12}$

Now let's subtract:

$\frac{10-4-4}{12}=\frac{6-4}{12}=\frac{2}{12}$

Let's divide both numerator and denominator by 2 and we get:

$\frac{2:2}{12:2}=\frac{1}{6}$

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the LCD to create equivalent fractions first
Technique: Convert $\frac{1}{3}$ to $\frac{4}{12}$ when LCD is 12
Check: Simplify final answer: $\frac{2}{12} = \frac{1}{6}$ by dividing by 2 ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators without finding common denominator
Don't subtract 10 - 1 - 2 = 7 over different denominators! This ignores that fractions represent different-sized parts. Always find the LCD first, then convert all fractions before subtracting 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 numerators 10 - 1 - 2?

Because different denominators represent different-sized pieces! You can't subtract 10 twelfths, 1 third, and 2 sixths directly - it's like subtracting apples, oranges, and bananas. Find the LCD first!

How do I find the LCD of 12, 3, and 6?

List the multiples of the largest number (12): 12, 24, 36... Check if smaller denominators divide evenly into these. Since both 3 and 6 divide into 12, the LCD is 12.

Do I always need to simplify my final answer?

Yes, always simplify! $\frac{2}{12}$ and $\frac{1}{6}$ are equal, but $\frac{1}{6}$ is in lowest terms and looks cleaner.

What if I get confused with all the fraction conversions?

Write each step clearly! Show: $\frac{10}{12} - \frac{1 \times 4}{3 \times 4} - \frac{2 \times 2}{6 \times 2}$ . Taking your time prevents errors and makes checking easier.

Can I use a calculator for this type of problem?

While calculators help with arithmetic, learning the manual method helps you understand fractions better. Plus, showing your work step-by-step is usually required on tests!

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