Bell Work: Simplify 4/5 + 1/2. Answer: 4/5 + ½ = 13/10 or 1 3/10.

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Presentation transcript:

Bell Work: Simplify 4/5 + 1/2

Answer: 4/5 + ½ = 13/10 or 1 3/10

{ Lesson 14: Evaluation, Solving Equations by Inspection

Constant*: A number whose value does not change. Variable*: A letter used to represent a number that has not been designated.

Sometimes we use a letter to represent an unidentified number. For example, “Four times a number s” can be expressed as 4 x s or 4s.

In the expression 4s, the number 4 is a constant, because it value does not change, and the letter s is a variable, because its value can change. If an algebraic term is composed of both constant and variable factors, we customarily write the constant factor first.

Recall that a formula is an expression or equation used to calculate a desired result. For example, the formula for the perimeter (P) of a square guides us to multiply the length of a side (s) by 4. P = 4s P = 4s

We evaluate an expression by substituting numbers in place of variables and calculating the result. For example, in the expression 4s, if we substitute 6 for s we get 4(6), which equals 24.

Example: A formula for the perimeter of a rectangle is P = 2l + 2w. Find P when l is 15 cm and w is 12 cm.

Answer: P = 2l + 2w P = 2(15cm) + 2(12cm) P = 30cm + 24cm P = 54cm

Equation*: A mathematical sentence stating that two quantities are equal. Solution*: A number that satisfies the equation or makes the equation true. In the equation 4x = 20, the solution is 5.

Example: Write and solve an equation that has one operation and one variable. Use any operation and variable you wish.

Answer: n/7 = 4; n = 28 5 x p = 25; p = 5

In this book we will learn and practice many strategies for solving equations, but first we will practice solving equations by inspection. That is, we will study equations and mentally determine the solutions.

Example: If a taxi company charges a $2 flat fee plus $3 per mile (m), then the cost (c) in dollars of a taxi ride is shown by this formula: 3m + 2 = c 3m + 2 = c Suppose that the cost of a taxi ride is $20. find the length of the taxi ride by solving the equation 3m + 2 = c.

Answer: 3m + 2 = 20 3m = 18 m = 6 6 miles

Solve each equation by inspection: a) w + 5 = 16 b) 25 – n = 11 c) d/4 = 8 d) 2a – 1 = 9 e) M – 6 = 18 f) 5x = 30 g) 12/z = 6 h) 20 = 3f – 1

Answer: a) w + 5 = 16w = 11 b) 25 – n = 11n = 14 c) d/4 = 8d = 32 d) 2a – 1 = 9a = 5 e) M – 6 = 18m = 24 f) 5x = 30x = 6 g) 12/z = 6z = 2 h) 20 = 3f – 1 f = 7

HW: Lesson 14 #1-30 Due Tomorrow