Math Essentials Review 1

Integers Operations

100

3 + (-7) =

3 + (-7) = -4

200

-6 + (-8) =

-6 + (-8) = -14

300

-19 - (-9) =

-19 - (-9) = -10

400

54 - (-27) =

54 - (-27) = 81

500

|-5|+(-16)-(-27)=

|-5|+(-16)-(-27)

=5 + (-16) + 27

= -11 + 27

= 16

Q Operations

300

1 - (-1.2) + 2.5 =

1 - (-1.2) + 2.5 

= 1 + 1.2 + 2.5

=2.2 + 2.5

=4.7

400

-1/2-1/3=

-1/2-1/3=-3/6-2/6=-5/6

500

1/6+(-1/3)-(-1/2)=

1/6+(-1/3)-(-1/2)

=1/6-2/6+3/6

=4/6-2/6

=2/6=1/3

Order of Operations

300

(-8--12)/(-2)xx(-4+(-4))

(-8--12)/(-2)xx(-4+(-4))

=4/(-2)xx(-8)

=-2xx(-8)=16

400

(-4+(-5))/(1-4)+(6--6)/-6=

(-4+(-5))/(1-4)+(6--6)/-6

=-9/(-3)+12/(-6)

=3+(-2)=1

500

(-9+12)/(9-10)-(-0.25xx32)/(-4xx0.5)=

(-9+12)/(9-10)-(-0.25xx32)/(-4xx0.5)

=3/(-1)-(-8)/(-2)

=-3-4=-7

Laws of Exponents

100

5^-2=

1/25

200

Express the answer as a positive exponent.

n^2\cdot n^-8=

1/n^6

300

a^3/a^-3xxa^-4=

a^3/a^-3xxa^-4

=a^6xxa^-4

=a^2

400

Express the answer as a positive exponent.

(b^3)^-2xxb^-5=

(b^3)^-2xxb^-5

=b^-6xxb^-5

=b^-11

=1/b^11

500

(c/d)^3/(c/d)^-2xxc^-2/d^-3=

(c/d)^3/(c/d)^-2xxc^-2/d^-3

=(c/d)^3(c/d)^2xxd^3/c^2

=c^5/d^5xxd^3/c^2

=c^3/d^2

Radical Expressions

100

Simplify 

sqrt(200)

sqrt(100)xxsqrt(2)=10sqrt(2)

200

Simplify

5sqrt(75)

5sqrt(75)=5xxsqrt(25)xxsqrt(3)

=5xx5xxsqrt(3)

=25sqrt(3)

300

Simplify

sqrt(36a^2b^3)

sqrt(36a^2b^3)

=sqrt(36)xxsqrt(a^2)xxsqrt(b^3)

=6|a|b sqrt(b)

400

Simplify

sqrt(98c^4d^5)

sqrt(98)xxsqrt(c^4)xxsqrt(d^5)

=7sqrt(2)c^2xxd^2sqrt(d)

=7c^2d^2sqrt(2d)

500

sqrt((14a^2b^-2)/(21b^2))

sqrt((14a^2b^-2)/(21b^2))

=sqrt((2a^2)/(3b^4))

=|a|/b^2sqrt(2/3)

=|a|/b^2*sqrt(6)/3