Question

math 7
directions: answer each of the following questions. show all work.

1. simplify: $\frac{1}{2}(12x - 18)$
2. simplify: -9 + (-8)
3. simplify: -15(-0.5)
4. simplify: -3(5x - 2) + 3x
5. factor: 42x - 7
6. is 0.\overline{333} rational or irrational? explain!
7. subtract 7y - 11 from 5y - 18
8. simplify: -(3x + 2) - 3(5a + 7)
9. find the area of the rectangle below.
10. list four perfect squares.

teacher use only: ____ / 10

Explanation:

Step1: Distribute the fraction

$\frac{1}{2}(12x - 18)=\frac{1}{2}\times12x-\frac{1}{2}\times18 = 6x-9$

Step2: Add negative numbers

$-9+(-8)=-9 - 8=-17$

Step3: Multiply negative numbers

$-15(-0.5)=15\times0.5 = 7.5$

Step4: Distribute and combine like - terms

$-3(5x - 2)+3x=-3\times5x+(-3)\times(-2)+3x=-15x + 6+3x=-12x + 6$

Step5: Factor out the greatest common factor

The GCF of 42x and 7 is 7. So, $42x - 7=7(6x - 1)$

Step6: Determine rationality

$0.\overline{333}=\frac{1}{3}$. A rational number is a number that can be written as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. So $0.\overline{333}$ is rational.

Step7: Subtract polynomials

$(5y - 18)-(7y - 11)=5y-18 - 7y + 11=-2y-7$

Step8: Distribute and simplify

$-(3x + 2)-3(5a + 7)=-3x-2-15a - 21=-3x-15a-23$

Step9: Find the area of a rectangle

The area of a rectangle is $A = l\times w$. Here, $A = 6(3x - 2)=18x-12$

Step10: List perfect squares

$1^2 = 1$, $2^2 = 4$, $3^2 = 9$, $4^2 = 16$

Answer:

1. $6x - 9$
2. $-17$
3. $7.5$
4. $-12x + 6$
5. $7(6x - 1)$
6. Rational, since $0.\overline{333}=\frac{1}{3}$
7. $-2y - 7$
8. $-3x-15a - 23$
9. $18x-12$
10. $1,4,9,16$