Math Snap

STEP 1

What is this asking?
We're asked to divide two mixed numbers, which means figuring out how many times one "fits" into the other.
Watch out!
Don't forget to convert the mixed numbers to improper fractions before dividing!

STEP 2

1. Convert to Improper Fractions
2. Divide the Fractions
3. Simplify the Result

STEP 3

Alright, let's kick things off by turning these mixed numbers into improper fractions!
Remember, a mixed number is just a whole number plus a fraction hanging out together.
We've got $3 \frac{3}{8}$ and $2 \frac{1}{4}$.

STEP 4

For $3 \frac{3}{8}$, we multiply the whole number ($3$) by the denominator ($8$), which gives us $3 \cdot 8 = 24$.
Then, we add the numerator ($3$) to this result: $24 + 3 = 27$.
This new number becomes our new numerator, and we keep the same denominator ($8$).
So, $3 \frac{3}{8}$ becomes $\frac{27}{8}$.

STEP 5

Now, let's do the same for $2 \frac{1}{4}$.
Multiply the whole number ($2$) by the denominator ($4$): $2 \cdot 4 = 8$.
Add the numerator ($1$): $8 + 1 = 9$.
Keep the same denominator ($4$).
So, $2 \frac{1}{4}$ becomes $\frac{9}{4}$.

STEP 6

Now, we're dividing $\frac{27}{8}$ by $\frac{9}{4}$.
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of $\frac{9}{4}$ is $\frac{4}{9}$ (just flip it!).

STEP 7

So, our division problem becomes: $\frac{27}{8} \div \frac{9}{4} = \frac{27}{8} \cdot \frac{4}{9}$.

STEP 8

Let’s multiply those fractions!
Multiply the numerators together: $27 \cdot 4 = 108$.
Multiply the denominators together: $8 \cdot 9 = 72$.
So, we have $\frac{108}{72}$.

STEP 9

We can simplify $\frac{108}{72}$ by finding the greatest common divisor (GCD) of $108$ and $72$.
Turns out, their GCD is $36$.

STEP 10

Now, we divide both the numerator and the denominator by $36$: $\frac{108}{36} = 3$ and $\frac{72}{36} = 2$.
This gives us the simplified fraction $\frac{3}{2}$.

STEP 11

We can write $\frac{3}{2}$ as a mixed number. $2$ goes into $3$ one time with a remainder of $1$.
So, $\frac{3}{2}$ is the same as $1 \frac{1}{2}$.

Our final answer is $1 \frac{1}{2}$.