Math Snap

STEP 1

What is this asking?
We need to subtract two fractions and find the simplest form of the result.
Watch out!
We can't subtract fractions unless they have the same denominator!

STEP 2

1. Find a Common Denominator
2. Subtract the Numerators
3. Simplify the Result

STEP 3

Alright, let's get these fractions speaking the same language!
We've got $\frac{11}{12}$ and $\frac{2}{3}$.
Notice that 12 is a multiple of 3: $3 \cdot 4 = 12$.
So, 12 is our common denominator!

STEP 4

We need to rewrite $\frac{2}{3}$ with a denominator of 12.
To do this, we'll multiply the top and bottom by 4.
Remember, multiplying by $\frac{4}{4}$ is the same as multiplying by one, so it doesn't change the value of the fraction, just how it looks!
$$\frac{2}{3} \cdot \frac{4}{4} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12}$$

STEP 5

Now that our fractions have the same denominator, we can subtract them!
We subtract the numerators and keep the denominator the same.
It's like subtracting apples from apples – we're subtracting twelfths from twelfths!
$$\frac{11}{12} - \frac{8}{12} = \frac{11 - 8}{12}$$

STEP 6

Let's do the subtraction: $11 - 8 = 3$.
So, we have:
$$\frac{11 - 8}{12} = \frac{3}{12}$$

STEP 7

$\frac{3}{12}$ is a correct answer, but we can simplify it!
Both 3 and 12 are divisible by 3.
Let's divide both the numerator and the denominator by 3.
Dividing by $\frac{3}{3}$ is just dividing by one, which doesn't change the value of our fraction!
$$\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}$$

The difference between $\frac{11}{12}$ and $\frac{2}{3}$ is $\frac{1}{4}$.