Studdy AI Logo
Math  /  Numbers & Operations

QuestionLess than -1 8(−12)8\left(-\frac{1}{2}\right)
Equal to -1 −3(13)-3\left(\frac{1}{3}\right) −78(87)-\frac{7}{8}\left(\frac{8}{7}\right) Greater than -1 45(−45)\frac{4}{5}\left(-\frac{4}{5}\right)

Studdy Solution

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 88 multiplied by −12-\frac{1}{2}.
Remember, multiplying by a negative flips the sign.
We can rewrite 88 as 81\frac{8}{1}, so we have 81⋅(−12)\frac{8}{1} \cdot \left(-\frac{1}{2}\right).
Multiply the numerators together and the denominators together: 8⋅(−1)1⋅2=−82\frac{8 \cdot (-1)}{1 \cdot 2} = \frac{-8}{2}.
Now, divide −8-8 by 22 to get −4-4.
So, 8⋅(−12)=−48 \cdot \left(-\frac{1}{2}\right) = -4.

STEP 4

Next up!
We've got −3-3 multiplied by 13\frac{1}{3}.
Rewriting −3-3 as −31\frac{-3}{1}, we get −31⋅13=−3⋅11⋅3=−33\frac{-3}{1} \cdot \frac{1}{3} = \frac{-3 \cdot 1}{1 \cdot 3} = \frac{-3}{3}.
Dividing −3-3 by 33 gives us −1-1.
So, −3⋅(13)=−1-3 \cdot \left(\frac{1}{3}\right) = -1.

STEP 5

Keep the momentum going!
We have −78-\frac{7}{8} multiplied by 87\frac{8}{7}.
Multiplying the numerators and denominators, we get −7⋅88⋅7=−5656\frac{-7 \cdot 8}{8 \cdot 7} = \frac{-56}{56}.
Dividing −56-56 by 5656 gives us −1-1.
So, −78⋅87=−1-\frac{7}{8} \cdot \frac{8}{7} = -1.

STEP 6

Last one!
We have 45\frac{4}{5} multiplied by −45-\frac{4}{5}.
Multiplying across, we get 4⋅(−4)5⋅5=−1625\frac{4 \cdot (-4)}{5 \cdot 5} = \frac{-16}{25}.
Now, we can convert this fraction to a decimal by dividing −16-16 by 2525, which gives us −0.64-0.64.
So, 45⋅(−45)=−0.64\frac{4}{5} \cdot \left(-\frac{4}{5}\right) = -0.64.

STEP 7

We found that 8⋅(−12)=−48 \cdot \left(-\frac{1}{2}\right) = -4.
Since −4-4 is less than −1-1, this expression belongs in the "Less than -1" category.

STEP 8

We calculated that −3⋅(13)=−1-3 \cdot \left(\frac{1}{3}\right) = -1 and −78⋅87=−1-\frac{7}{8} \cdot \frac{8}{7} = -1.
These belong in the "Equal to -1" category.

STEP 9

We found that 45⋅(−45)=−0.64\frac{4}{5} \cdot \left(-\frac{4}{5}\right) = -0.64.
Since −0.64-0.64 is greater than −1-1, this goes in the "Greater than -1" category.

STEP 10

Less than -1: 8⋅(−12)=−48 \cdot \left(-\frac{1}{2}\right) = -4
Equal to -1: −3⋅(13)=−1-3 \cdot \left(\frac{1}{3}\right) = -1 and −78⋅87=−1-\frac{7}{8} \cdot \frac{8}{7} = -1
Greater than -1: 45⋅(−45)=−0.64\frac{4}{5} \cdot \left(-\frac{4}{5}\right) = -0.64

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord