Solve the Fraction Equation: 4/2 - 6/8 - 1/4

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

Fractions represent parts of a whole, and you can only combine parts of the same size! You wouldn't subtract 3 apples from 2 oranges directly - you need a common unit first.

Q: How do I find the LCM of 2, 8, and 4 quickly?

Look for the largest denominator first (8). Check if it's divisible by the others: 8÷2=4 ✓ and 8÷4=2 ✓. Since 8 works for all, it's your LCM!

Q: What if I get a different LCM than 8?

Any common multiple works, but using the least one keeps numbers smaller and easier to work with. You could use 16 or 24, but 8 is most efficient.

Q: Why does 4/2 become 16/8 instead of staying as 2?

While $ \frac{4}{2} = 2 $, keeping it as a fraction with denominator 8 lets you combine all terms easily: $ \frac{16}{8} - \frac{6}{8} - \frac{2}{8} $.

Q: Can I simplify fractions before finding the common denominator?

Yes! $ \frac{6}{8} = \frac{3}{4} $ first makes the problem $ 2 - \frac{3}{4} - \frac{1}{4} $, which is easier to work with.

Fraction Operations with Mixed Denominators

Solve the following equation:

$\frac{4}{2}-\frac{6}{8}-\frac{1}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem together!

00:12 First, multiply each fraction by four and two, to get a common denominator.

00:18 Remember, multiply both the numerator and the denominator. This is important.

00:25 Next, let's calculate the multiplications.

00:37 Now, subtract using the common denominator we found.

00:43 Work out the numerator. You're doing great!

00:47 Remember, any number divided by itself is always one.

00:52 And that is how we solve the question. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{4}{2}-\frac{6}{8}-\frac{1}{4}=$

Step-by-step solution

Let's try to find the least common multiple (LCM) between 2, 8, and 4

To find the least common multiple, we need to find a number that is divisible by 2, 8, and 4

In this case, the least common multiple is 8

Now we'll multiply each fraction by the appropriate number to reach a denominator of 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{4\times4}{2\times4}-\frac{6\times1}{8\times1}-\frac{1\times2}{4\times2}=\frac{16}{8}-\frac{6}{8}-\frac{2}{4}$

Now let's subtract:

$\frac{16-6-2}{8}=\frac{10-2}{8}=\frac{8}{8}$

We'll solve the fraction in the following way:

$\frac{8}{8}=\frac{1}{1}=1$

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCM of all denominators before operating
Conversion: Change $\frac{4}{2}$ to $\frac{16}{8}$ and $\frac{1}{4}$ to $\frac{2}{8}$
Verification: Substitute back: $2 - \frac{3}{4} - \frac{1}{4} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding/subtracting fractions without common denominators
Don't try to subtract $\frac{4}{2} - \frac{6}{8} - \frac{1}{4}$ directly = wrong answer like $\frac{-3}{14}$ ! You can't combine fractions with different denominators. Always convert all fractions to the same denominator first using the LCM.

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, and you can only combine parts of the same size! You wouldn't subtract 3 apples from 2 oranges directly - you need a common unit first.

How do I find the LCM of 2, 8, and 4 quickly?

Look for the largest denominator first (8). Check if it's divisible by the others: 8÷2=4 ✓ and 8÷4=2 ✓. Since 8 works for all, it's your LCM!

What if I get a different LCM than 8?

Any common multiple works, but using the least one keeps numbers smaller and easier to work with. You could use 16 or 24, but 8 is most efficient.

Why does 4/2 become 16/8 instead of staying as 2?

While $\frac{4}{2} = 2$ , keeping it as a fraction with denominator 8 lets you combine all terms easily: $\frac{16}{8} - \frac{6}{8} - \frac{2}{8}$ .

Can I simplify fractions before finding the common denominator?

Yes! $\frac{6}{8} = \frac{3}{4}$ first makes the problem $2 - \frac{3}{4} - \frac{1}{4}$ , which is easier to work with.

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