warm up write an algebraic expression for 35 less than product of 4 and x. a35 + 4x b4x - 35 c35 /...
TRANSCRIPT
Warm Up
Write an algebraic expression for 35 less than product of 4 and x.A 35 + 4xB 4x - 35C 35 / 4xD 35 – 4x
The Real Number System & Writing Equations
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The Real Number System
• The Real Number System is divided into two categories: Rational and Irrational.
• Rational Numbers: Numbers, such as ½ and –3/1 that can be written as a ratio of two integers.
• Irrational Numbers: Real numbers, such as square root of 2 or , that are not rational.
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The Real Number System
• Rational Numbers: Includes integers, whole numbers, natural numbers, and numbers written as the ratio of two integers.
• Integers: {. . . – 3, – 2, – 1, 0, 1, 2, 3, . . .}
• Whole Numbers: {0, 1, 2, 3, . . .}
• Natural Numbers: {1, 2, 3, . . .}
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The Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
3
1/2-2
15%
2/3
1.456
-0.7
0
3 2
5 2
34
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The Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
31/2 -2
15%
2/3
1.456- 0.7
0
3 2
5 2
34
Integers
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The Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456- 0.7
0
3 2
5 2
34
Integers
Whole
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The Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456- 0.7
0
3 2
5 2
34
Integers
Whole
Natural
The statue of liberty sits on a pedestal that is 154 feet high. The height of the pedestal and the statue is 305 feet. If s represents the height of the statue, the following equation represents the situation.
154 + s=305
Key Words
• Words that mean equals “=“– Is– Equals– Is equal to– Is the same as– In as much as– Is identical to
Translate into equations
1. Five times the number a is equal to three times the sum of b and c
• 5a=3(b+c)
2. Nine times y subtracted from 95 equals 37.
• 95-9y=37
Four step problem solving plan
1. Explore the problem1. Read carefully2. Identify information given3. What are you asked to find
2. Plan the solution1. Define your variables
3. Solve the problem4. Examine the solution
1. Make sure your answer makes sense
Example
You know that 2,000,000 gallons of ice cream are produced in the US each day. You want to know how many days it will take to produce 40,000,000 gallons of ice cream.
Plan
1. Explore2. Plan
1. Write an equation to represent the situation. 1. Let d represent the number of days needed to produce the ice
cream.
2,000,000(d)=40,000,000
2. Solve 2,000,000(d)=40,000,000
d=20
3. ExamineIf 2,000,000 gallons of ice cream are produced in one day
2,000,000 x 20 or 40,000,000 gallons are produced in 20 days.
You Try It
The perimeter of a rectangle equals two times the length plus two times the width
1. Variables1. P=perimeter, l=length, w=width
2. Formula1. P=2l+2w
Translate into a verbal sentence
1. 3m+5=14
Three time m plus five equals fourteen
2. w+v=y2
The sum of w and v equals the square of y.