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Negative Numbers with Variables>
Negative Numbers with Variables 3Negative Numbers with Variables 3
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Question 1 of 4
1. Question
Evaluate`4a2b6a+8b` (2a+6b, 6b2a)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `a` variable (`4a6a`).Since the signs are different `(+ )` we will find the difference of the two numbers`64` `=` `2` Find the Difference `\text(Difference)` `=` `2` Insert the sign of the larger number `(6)` to the difference as well as the variable `a`.`4a6a` `=` `2a` Insert a negative sign since the larger number, `6` is negative Next, solve for the values with a `b` variable (`2b+8b`).Since the signs are different `( +)` we will find the difference of the two numbers`82` `=` `6` Find the Difference `\text(Difference)` `=` `6` Insert the sign of the larger number `(+8)` to the difference as well as the variable `b`.`2b+8b` `=` `6b` Use a positive sign since the larger number, `8` is positive Finally, combine the terms.`2a+6b` `2a+6b` 
Question 2 of 4
2. Question
Evaluate`24a^2divide6a` (4a)
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Rules for Dividing Integers
Transform the expression into a fraction to make it easier to solve.`24a^2divide6a` `=` `(24a^2)/(6a)` Simplify the fraction$$\frac{\color{#CC0000}{24}a^2}{\color{#CC0000}{6}a}$$ `=` `4``(a^2)/a` Recall, `=` `4a^(21)` Recall rules for indices `=` `4a^(1)` `=` `4a` `4a` 
Question 3 of 4
3. Question
Evaluate`m+3n18m4n+5` (17mn+5)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `m` variable (`m18m`).Since the signs are different `(+ )` we will find the difference of the two numbers`181` `=` `17` Find the Difference `\text(Difference)` `=` `17` Insert the sign of the larger number `(18)` to the difference as well as the variable `m`.`m18m` `=` `17m` Insert a negative sign since the larger number, `18` is negative Next, solve for the values with a `n` variable (`3n4n`).Since the signs are different `(+ )` we will find the difference of the two numbers`43` `=` `1` Find the Difference `\text(Difference)` `=` `1` Insert the sign of the larger number `(4)` to the difference as well as the variable `n`.`3n4n` `=` `n` Insert a negative sign since the larger number, `4` is negative Finally, combine the terms.Don’t forget to add the constant, `5`.`17mn+5` `17mn+5` 
Question 4 of 4
4. Question
Evaluate`8axx(3b)xx2` (48ab)
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Rules for Multiplying Integers
First, separate the variables from the coefficients to make the solution easier.`8xx(3)xx2xxaxxb` Next, perform the multiplication.`8xx(3)``xx2xxaxxb` `24``xx2xxaxxb` Recall, `24xx2``xxaxxb` `48``xxaxxb` Recall, `48ab` Add the variables back to the coefficient `48ab`
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