Solve the Fraction Subtraction: 7/10 - 2/6 Step-by-Step

Q: Why can't I just subtract 7-2 and 10-6?

Because fractions represent parts of different wholes! $ \frac{7}{10} $ means 7 parts out of 10, while $ \frac{2}{6} $ means 2 parts out of 6. You need to make the parts the same size first.

Q: How do I find the LCD of 10 and 6?

List the multiples of each number: 10: 10, 20, 30, 40... and 6: 6, 12, 18, 24, 30... The first number that appears in both lists is your LCD. Here, it's 30!

Q: What if my LCD seems too big?

Don't worry! The LCD might look complicated, but it's the smallest number that works. Using 60 or 90 would also work, but 30 keeps your numbers smaller and easier to work with.

Q: Do I need to simplify my final answer?

Always check if you can simplify! For $ \frac{11}{30} $, since 11 is prime and doesn't divide 30, it's already in lowest terms. You're done!

Q: What if I get a different LCD?

If you used a common multiple that's not the LCD (like 60 instead of 30), you'll still get the right answer, but your fractions will be bigger. Just make sure to simplify at the end!

Q: Can I convert to decimals instead?

You could, but $ \frac{7}{10} = 0.7 $ and $ \frac{2}{6} = 0.333... $ The repeating decimal makes it messier. Stick with fractions for exact answers!

Fraction Subtraction with Unlike Denominators

Solve the following exercise:

$\frac{7}{10}-\frac{2}{6}=\text{?}$

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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 We'll multiply by 3 and 5 respectively to find the common denominator

00:09 We'll make sure to multiply both numerator and denominator

00:20 Let's calculate the products

00:28 Let's subtract with the common denominator

00:33 Let's calculate the numerator

00:37 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

Solve the following exercise:

$\frac{7}{10}-\frac{2}{6}=\text{?}$

Step-by-step solution

To solve the problem $\frac{7}{10} - \frac{2}{6}$ , we need to follow these steps:

Find the Least Common Denominator (LCD) for the denominators 10 and 6. The LCD of 10 and 6 is 30.
Convert each fraction to have the common denominator of 30:

$\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}$
$\frac{2}{6} = \frac{2 \times 5}{6 \times 5} = \frac{10}{30}$

Subtract the two fractions:

$\frac{21}{30} - \frac{10}{30} = \frac{21 - 10}{30} = \frac{11}{30}$

Therefore, the solution to the problem is $\frac{11}{30}$ .

Final Answer

$\frac{11}{30}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before subtracting fractions with different denominators
Technique: Convert $\frac{7}{10}$ to $\frac{21}{30}$ and $\frac{2}{6}$ to $\frac{10}{30}$
Check: Verify LCD is correct: 30 ÷ 10 = 3 and 30 ÷ 6 = 5 ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators and denominators separately
Don't subtract $\frac{7}{10} - \frac{2}{6}$ as $\frac{7-2}{10-6} = \frac{5}{4}$ ! This ignores the fundamental rule that fractions need common denominators. Always find the LCD first and convert both fractions before subtracting.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{2}-\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just subtract 7-2 and 10-6?

Because fractions represent parts of different wholes! $\frac{7}{10}$ means 7 parts out of 10, while $\frac{2}{6}$ means 2 parts out of 6. You need to make the parts the same size first.

How do I find the LCD of 10 and 6?

List the multiples of each number: 10: 10, 20, 30, 40... and 6: 6, 12, 18, 24, 30... The first number that appears in both lists is your LCD. Here, it's 30!

What if my LCD seems too big?

Don't worry! The LCD might look complicated, but it's the smallest number that works. Using 60 or 90 would also work, but 30 keeps your numbers smaller and easier to work with.

Do I need to simplify my final answer?

Always check if you can simplify! For $\frac{11}{30}$ , since 11 is prime and doesn't divide 30, it's already in lowest terms. You're done!

What if I get a different LCD?

If you used a common multiple that's not the LCD (like 60 instead of 30), you'll still get the right answer, but your fractions will be bigger. Just make sure to simplify at the end!

Can I convert to decimals instead?

You could, but $\frac{7}{10} = 0.7$ and $\frac{2}{6} = 0.333...$ The repeating decimal makes it messier. Stick with fractions for exact answers!

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