Math Jeopardy! Order of Operations Evaluating Algebraic Expressions Solving Equations Complex Fractions Simplifying Rational Expressions 10 20 30 40 50.

Math Jeopardy!Math Jeopardy!Order of Order of

OperationsOperationsEvaluating Evaluating Algebraic Algebraic

ExpressionExpressionss

Solving Solving EquationsEquations

Complex Complex FractionsFractions

Simplifying Simplifying Rational Rational

ExpressionExpressionss

10 10 10 10 1010

20 20 20 2020 2020

30 30 30 3030 3030

40 40 40 4040 4040

50 50 50 5050 5050

Simplify Simplify

2*(4+3) - 6/32*(4+3) - 6/3

using Order of using Order of Operations. Operations.

2*(4+3)-6/3=122*(4+3)-6/3=12

Simplify Simplify

8/4*2+18/4*2+1

using Order of using Order of Operations. Operations.

8/4*2+1=58/4*2+1=5

Explain the Order of Explain the Order of Operations. Operations.

Rules that describe the order that Rules that describe the order that addition, subtraction, addition, subtraction, multiplication, and division must multiplication, and division must be performed. be performed.

Order of Operations:Order of Operations:1.1. Perform operations in parenthesesPerform operations in parentheses2.2. Evaluate PowersEvaluate Powers3.3. Multiply and divide in order from Multiply and divide in order from

left to rightleft to right4.4. Add and subtract in order from Add and subtract in order from

left to rightleft to right

Simplify Simplify

20(2+6)-10(32/4)20(2+6)-10(32/4)

using Order of Operationsusing Order of Operations

20(2+6)-10(32/4)=20(8)-20(2+6)-10(32/4)=20(8)-10(8)10(8)

=160-80 =160-80

= 80= 80

Use your calculator to evaluate Use your calculator to evaluate 72(60/5)72(60/5)22-3-3

Explain how you used Order of Explain how you used Order of Operations while using your Operations while using your

calculator. calculator.

72(60/5)72(60/5)22-3=10365-3=10365

Evaluate Evaluate

8x-3 8x-3

when x=1/2. when x=1/2.

8(1/2)-3=4-38(1/2)-3=4-3

=1=1

Evaluate Evaluate

4x-1*2 4x-1*2

when x=2 and when x=3.when x=2 and when x=3.

4(2)-2=8-24(2)-2=8-2

=6=6

4(3)-2=12-104(3)-2=12-10

=2=2

EvaluateEvaluate

4(9/x)/x 4(9/x)/x

for x=12.for x=12.

4(9/12)/12=4(3/4)/124(9/12)/12=4(3/4)/12

=3/12=3/12

=1/4=1/4

The dimensions of a rectangle are The dimensions of a rectangle are given below. If the x=3 what is the given below. If the x=3 what is the perimeter of the rectangle. perimeter of the rectangle.

xx

x+2x+2

Perimeter= x+x+(x+2)+Perimeter= x+x+(x+2)+(x+2)(x+2)

=2x+2(x+2)=2x+2(x+2)

=2(3)+2(5)=2(3)+2(5)

=6+10=6+10

=16=16

Kate just bought a cell phone plan that Kate just bought a cell phone plan that will cost $10 each month plus $0.10 will cost $10 each month plus $0.10 for every minute she uses the phone. for every minute she uses the phone. In October, she used 45 minutes. In October, she used 45 minutes. How much should she expect to pay How much should she expect to pay when she gets the bill for October? when she gets the bill for October? (Write an equation for the cost, in (Write an equation for the cost, in dollars, when she uses x number of dollars, when she uses x number of minutes)minutes)

y=0.10x+10y=0.10x+10

When x=45When x=45

y=14.5y=14.5

Solve for x. Solve for x.

x-4=14x-4=14

x=18x=18

Solve for p.Solve for p.

p-5+54=-1p-5+54=-1

p+49=-1p+49=-1

p=-1-49p=-1-49

=-50=-50

Solve for a.Solve for a.

a+a-8=a+4a+a-8=a+4

a+a-a=4+8a+a-a=4+8

a=12a=12

Mars is about 48 million miles farther Mars is about 48 million miles farther away from the Sun than the Earth. away from the Sun than the Earth. Earth is about 93 million miles from Earth is about 93 million miles from the Sun. How far is Mars from the the Sun. How far is Mars from the Sun? (Make sure to set up an Sun? (Make sure to set up an equation involving x the total equation involving x the total distance, in millions of miles, Mars is distance, in millions of miles, Mars is from the Sun)from the Sun)

x-48=93x-48=93

x=93+48x=93+48

x=141x=141

Mars is 141 million miles Mars is 141 million miles from the Sun. from the Sun.

Joey is 4 years older than his little Joey is 4 years older than his little brother Tim. If the sum of their age is brother Tim. If the sum of their age is 30. How is Joey? How old is Tim? 30. How is Joey? How old is Tim? What is the equation that tells us this What is the equation that tells us this information?information?

x+(x-4)=30x+(x-4)=30

x+x=34x+x=34

x=17x=17

So Joey is 17 and Timmy So Joey is 17 and Timmy is 13. is 13.

Dividing two fractions is the Dividing two fractions is the same as…same as…

Multiplying the dividend Multiplying the dividend by the reciprocal of the by the reciprocal of the

divisor. divisor.

Simplify Simplify

(1/3)/(2/4)(1/3)/(2/4)

In other words what is one In other words what is one third divided by two third divided by two

fourths? fourths?

(1/3)/(2/4)=(1/3)*(4/2)(1/3)/(2/4)=(1/3)*(4/2)

=4/6=4/6

=2/3=2/3

Simplify Simplify

7/(2/3)7/(2/3)

In other words, what is 7 In other words, what is 7 divided by two thirds?divided by two thirds?

7/(2/3)=7*(3/2)7/(2/3)=7*(3/2)

=21/2=21/2

Simplify Simplify

(5/2)/6(5/2)/6

In other words, what is five In other words, what is five halves divided by 6?halves divided by 6?

(5/2)/6=(5/2)*(1/6)(5/2)/6=(5/2)*(1/6)

=5/12=5/12

What is a complex fraction? What are What is a complex fraction? What are the steps we should take to simplify the steps we should take to simplify a complex fraction?a complex fraction?

A complex fraction is a A complex fraction is a fraction in which the fraction in which the

numerator, the numerator, the denominator, or both denominator, or both

are fractions. are fractions.

Simplify Simplify

(6/m)-(3/2m)(6/m)-(3/2m)

(6/m)-(3/2m)(6/m)-(3/2m)

=(12/2m)-(3/2m)=(12/2m)-(3/2m)

=9/2m=9/2m

What is a rational What is a rational expression?expression?

An algebraic expression An algebraic expression that contains terms (e.g. that contains terms (e.g. x,4,(1/2)x) separated by x,4,(1/2)x) separated by operations (e.g. +,-,*,/). operations (e.g. +,-,*,/). Rational expressions can Rational expressions can be simplified by collecting be simplified by collecting

like terms.like terms.

SimplifySimplify

(3x/6)+(x/4)(3x/6)+(x/4)

(3x/6)+(x/4)(3x/6)+(x/4)

=(12x/24)+(6x/24)=(12x/24)+(6x/24)

=(18x/24)=(18x/24)

=3x/4=3x/4

Simplify Simplify

(6/4s)*(2/3)(6/4s)*(2/3)

(6/4s)*(2/3)(6/4s)*(2/3)

=12/12s=12/12s

=1/s=1/s

Stacy drove ¼ of the way to Atlanta in Stacy drove ¼ of the way to Atlanta in one day. The next day she drove 3/5 one day. The next day she drove 3/5 of the remaining distance. How much of the remaining distance. How much farther does she have to drive? farther does she have to drive?

She has drivenShe has driven(1/4)+(3/5)(3/4)(1/4)+(3/5)(3/4)

=5/20+9/20=5/20+9/20=14/20 =7/10=14/20 =7/10

This means she has 3/10 of This means she has 3/10 of the total distance left to the total distance left to

travel. travel.