Solve the Fraction Subtraction: 2/3 - 1/9 Step by Step

Q: How do I know what common denominator to use?

Look for the smallest number that both denominators divide into. Since 9 is already a multiple of 3, use 9 as your common denominator. This saves time compared to using larger multiples like 18 or 27.

Q: Why can't I just subtract 2-1 and 3-9?

Fractions represent parts of a whole. You can only subtract parts when they're the same size (same denominator). It's like trying to subtract 2 apples from 1 orange - you need the same units first!

Q: Is there a faster way to do this?

Once you practice, you'll quickly recognize that $ \frac{2}{3} = \frac{6}{9} $. The pattern is: multiply top and bottom by the same number to get equivalent fractions. This becomes automatic with practice!

Q: How do I check if my answer is right?

Add your answer back to the second fraction: $ \frac{5}{9} + \frac{1}{9} = \frac{6}{9} = \frac{2}{3} $. If you get the original first fraction, you're correct!

Fraction Subtraction with Different Denominators

Solve the following exercise:

$\frac{2}{3}-\frac{1}{9}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply the fraction by 3 to get to the common denominator

00:06 Make sure to multiply both numerator and denominator

00:12 Calculate the multiplications

00:15 Subtract with the common denominator

00:24 Calculate the numerator

00:28 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:

$\frac{2}{3}-\frac{1}{9}=\text{?}$

Step-by-step solution

To solve the problem of subtracting $\frac{1}{9}$ from $\frac{2}{3}$ , we need a common denominator. Let's follow these steps:

Step 1: Identify the common denominator for the fractions $\frac{2}{3}$ and $\frac{1}{9}$ . Since $9$ is a multiple of $3$ , we use $9$ as the common denominator.
Step 2: Convert $\frac{2}{3}$ to a fraction with denominator $9$ :
To do this, multiply the numerator and the denominator of $\frac{2}{3}$ by $3$ (since $9$ divided by $3$ is $3$ ):
$\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$ .
Step 3: Subtract $\frac{1}{9}$ from $\frac{6}{9}$ :
$\frac{6}{9} - \frac{1}{9} = \frac{6 - 1}{9} = \frac{5}{9}$ .

Thus, the difference between $\frac{2}{3}$ and $\frac{1}{9}$ is $\frac{5}{9}$ .

Therefore, the correct choice from the given options is $\boxed{\frac{5}{9}}$ .

Final Answer

$\frac{5}{9}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCD to subtract fractions with different denominators
Technique: Convert $\frac{2}{3}$ to $\frac{6}{9}$ by multiplying by 3
Check: Verify $\frac{5}{9} + \frac{1}{9} = \frac{6}{9} = \frac{2}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators and denominators separately
Don't subtract $\frac{2}{3} - \frac{1}{9}$ as $\frac{2-1}{3-9} = \frac{1}{-6}$ ! This creates meaningless fractions because you can't subtract fractions without the same denominator. Always find a common denominator first, then subtract only the numerators.

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

How do I know what common denominator to use?

Look for the smallest number that both denominators divide into. Since 9 is already a multiple of 3, use 9 as your common denominator. This saves time compared to using larger multiples like 18 or 27.

Why can't I just subtract 2-1 and 3-9?

Fractions represent parts of a whole. You can only subtract parts when they're the same size (same denominator). It's like trying to subtract 2 apples from 1 orange - you need the same units first!

What if the answer doesn't match any of the choices?

Double-check your work! Make sure you found the correct common denominator and converted fractions properly. Also verify that $\frac{5}{9}$ is in simplest form - it is, since 5 and 9 share no common factors.

Is there a faster way to do this?

Once you practice, you'll quickly recognize that $\frac{2}{3} = \frac{6}{9}$ . The pattern is: multiply top and bottom by the same number to get equivalent fractions. This becomes automatic with practice!

How do I check if my answer is right?

Add your answer back to the second fraction: $\frac{5}{9} + \frac{1}{9} = \frac{6}{9} = \frac{2}{3}$ . If you get the original first fraction, you're correct!

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