Convert Mixed Number 6¾ to an Improper Fraction

Q: Why do I divide 3 by 4 instead of 4 by 3?

In the fraction $ \frac{3}{4} $, the numerator (3) goes on top and gets divided by the denominator (4) on bottom. Think of it as "3 parts out of 4 total parts."

Q: What if the fraction doesn't divide evenly?

That's okay! Many fractions create repeating decimals. For example, $ \frac{1}{3} = 0.333... $ You can round to a reasonable number of decimal places or leave it as a fraction.

Q: Can I convert to an improper fraction instead?

Yes! To convert $ 6\frac{3}{4} $ to improper: multiply whole number by denominator, then add numerator: $ \frac{(6 \times 4) + 3}{4} = \frac{27}{4} $

Q: Is there a shortcut for common fractions?

Memorize these! $ \frac{1}{4} = 0.25 $, $ \frac{1}{2} = 0.5 $, $ \frac{3}{4} = 0.75 $. This makes converting mixed numbers much faster!

Mixed Numbers with Decimal Conversion

$6\frac{3}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's change this to a decimal fraction.

00:07 First, split the number into a whole part and a fraction.

00:13 We need the denominator to be a multiple of ten.

00:17 Multiply both the top and bottom numbers by the same fac tor.

00:27 Now it's a decimal fraction.

00:40 Next, add them up carefully.

00:53 And that's the answer to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$6\frac{3}{4}=$

Step-by-step solution

To solve this problem, we'll convert the mixed number $6\frac{3}{4}$ into a decimal by following these steps:

Step 1: Convert the fractional part $\frac{3}{4}$ into a decimal.
To do this, compute $\frac{3}{4} = 3 \div 4 = 0.75$ .
Step 2: Add the decimal result to the whole number.
The whole number given is 6, so we add: $6 + 0.75 = 6.75$ .

Therefore, the correct decimal representation of $6\frac{3}{4}$ is $6.75$ .

Final Answer

$6.75$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fraction part first, then add to whole number
Technique: Divide numerator by denominator: 3 ÷ 4 = 0.75
Check: Verify that 6 + 0.75 = 6.75 matches original mixed number ✓

Common Mistakes

Avoid these frequent errors

Adding numerator and denominator incorrectly
Don't add 6 + 3 + 4 = 13 or treat it like 6.34! This ignores the fraction's true value. Always divide the numerator by denominator first (3 ÷ 4 = 0.75), then add to the whole number.

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

Why do I divide 3 by 4 instead of 4 by 3?

In the fraction $\frac{3}{4}$ , the numerator (3) goes on top and gets divided by the denominator (4) on bottom. Think of it as "3 parts out of 4 total parts."

What if the fraction doesn't divide evenly?

That's okay! Many fractions create repeating decimals. For example, $\frac{1}{3} = 0.333...$ You can round to a reasonable number of decimal places or leave it as a fraction.

Can I convert to an improper fraction instead?

Yes! To convert $6\frac{3}{4}$ to improper: multiply whole number by denominator, then add numerator: $\frac{(6 \times 4) + 3}{4} = \frac{27}{4}$

How do I check if 6.75 is correct?

Convert back to a mixed number: 6.75 = 6 + 0.75, and 0.75 = $\frac{3}{4}$ (since 3 ÷ 4 = 0.75). So you get $6\frac{3}{4}$ ✓

Is there a shortcut for common fractions?

Memorize these! $\frac{1}{4} = 0.25$ , $\frac{1}{2} = 0.5$ , $\frac{3}{4} = 0.75$ . This makes converting mixed numbers much faster!

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