Math Snap

STEP 1

What is this asking?
We're figuring out which of these multiplication problems give us answers less than -1, equal to -1, or greater than -1!
Watch out!
Don't mix up your negative signs – they can be sneaky little things!

STEP 2

1. Evaluate each expression
2. Categorize each result

STEP 3

Alright, let's tackle this first one!
We've got $8$ multiplied by $-\frac{1}{2}$.
Remember, multiplying by a negative flips the sign.
We can rewrite $8$ as $\frac{8}{1}$, so we have $\frac{8}{1} \cdot \left(-\frac{1}{2}\right)$.
Multiply the numerators together and the denominators together: $\frac{8 \cdot (-1)}{1 \cdot 2} = \frac{-8}{2}$.
Now, divide $-8$ by $2$ to get $-4$.
So, $8 \cdot \left(-\frac{1}{2}\right) = -4$.

STEP 4

Next up!
We've got $-3$ multiplied by $\frac{1}{3}$.
Rewriting $-3$ as $\frac{-3}{1}$, we get $\frac{-3}{1} \cdot \frac{1}{3} = \frac{-3 \cdot 1}{1 \cdot 3} = \frac{-3}{3}$.
Dividing $-3$ by $3$ gives us $-1$.
So, $-3 \cdot \left(\frac{1}{3}\right) = -1$.

STEP 5

Keep the momentum going!
We have $-\frac{7}{8}$ multiplied by $\frac{8}{7}$.
Multiplying the numerators and denominators, we get $\frac{-7 \cdot 8}{8 \cdot 7} = \frac{-56}{56}$.
Dividing $-56$ by $56$ gives us $-1$.
So, $-\frac{7}{8} \cdot \frac{8}{7} = -1$.

STEP 6

Last one!
We have $\frac{4}{5}$ multiplied by $-\frac{4}{5}$.
Multiplying across, we get $\frac{4 \cdot (-4)}{5 \cdot 5} = \frac{-16}{25}$.
Now, we can convert this fraction to a decimal by dividing $-16$ by $25$, which gives us $-0.64$.
So, $\frac{4}{5} \cdot \left(-\frac{4}{5}\right) = -0.64$.

STEP 7

We found that $8 \cdot \left(-\frac{1}{2}\right) = -4$.
Since $-4$ is less than $-1$, this expression belongs in the "Less than -1" category.

STEP 8

We calculated that $-3 \cdot \left(\frac{1}{3}\right) = -1$ and $-\frac{7}{8} \cdot \frac{8}{7} = -1$.
These belong in the "Equal to -1" category.

STEP 9

We found that $\frac{4}{5} \cdot \left(-\frac{4}{5}\right) = -0.64$.
Since $-0.64$ is greater than $-1$, this goes in the "Greater than -1" category.

Less than -1: $8 \cdot \left(-\frac{1}{2}\right) = -4$
Equal to -1: $-3 \cdot \left(\frac{1}{3}\right) = -1$ and $-\frac{7}{8} \cdot \frac{8}{7} = -1$
Greater than -1: $\frac{4}{5} \cdot \left(-\frac{4}{5}\right) = -0.64$