Writing and Solving a Proportion EXAMPLE 3 STEP 1 Write a proportion. Let x represent the number of floors passed in 9 seconds. Empire State Building The.

Slides:

Advertisements

Similar presentations

Solve an equation by multiplying by a reciprocal

Advertisements

Example 3 Each day, an elephant eats 5 pounds of food for every 100 pounds of its body weight. How much does a 9300 pound elephant eat per day? SOLUTION.

EXAMPLE 1 Writing Equivalent Fractions. EXAMPLE 1 Writing Equivalent Fractions Write two fractions that are equivalent to. Writing Equivalent Fractions.

Do Now: Pass out calculators. Complete EOC Review Week # 17. Have your homework out ready to check.

7 th Grade Math Ms. Richardson.  To write a percent as a fraction  You can write 16 percent as or 16%  Your turn now:  Write the percent as a fraction.

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

Solve an equation with variables on both sides

Use the cross products property EXAMPLE 1 Write original proportion = x 6 Solve the proportion =. 8 x 6 15 Cross products property Simplify. 120.

Objective The student will be able to: solve equations using multiplication and division. Designed by Skip Tyler, Varina High School.

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

Solve an “and” compound inequality

Standardized Test Practice

Standardized Test Practice

Solve a multi-step problem EXAMPLE 3 ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation.

Standardized Test Practice

People Fractions. Problem 1 of 20 Answer 1 = 10 Problem 2 of 20 Answer 2 = 5.

1.3 “Solving Linear Equations” Steps: 1.Isolate the variable. 2.To solve when there is a fraction next to a variable, multiply both sides by the reciprocal.

Writing Terminating Decimals as Fractions

EXAMPLE 2 Rationalize denominators of fractions Simplify

3.6 Solving Quadratic Equations

3.1 Solving Equations Algebra I.

SOLUTION Write a ratio EXAMPLE 1 VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches.

EXAMPLE 4 Solving an Equation with a Fraction Photography You take 16 of the 24 pictures of a roll of film on your first day of vacation. At this rate,

EXAMPLE 1 Dividing a Fraction by a Fraction a = = 3 4 1, or b. – – = = 7 (– 2) 9 – 4 = 1 4 – 2, or.

Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.

Solve an inequality using multiplication EXAMPLE 2 < 7< 7 x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > –42.

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

Use the substitution method

Do Now Pass out calculators. Have your homework out ready to check.

Objective The student will be able to: solve equations using multiplication and division.

EXAMPLE 2 Multiply by the LCD Solve. Check your solution. x – 2 x = SOLUTION x – 2 x = Multiply by LCD, 5(x – 2). 5(x – 2) x – 2 x 1 5.

Solve Fraction Equations. Designed by Skip Tyler, Varina High School EQ: How do we solve equations of fractions using multiplication and division.

ANSWER is 25% of what number ANSWER 40% 4.What percent of 90 is 36? ANSWER d = 4 ANSWER x = Solve:

EXAMPLE 2 Solving an Equation Involving Decimals 1.4x – x = 0.21 Original equation. (1.4x – x)100 = (0.21)100 Multiply each side by 100.

Solve an “and” compound inequality

Equations with fractions can be simplified by multiplying both sides by a common denominator. 3x + 4 = 2x + 8 3x = 2x + 4 x = 4 Example: Solve

Using Equivalent Ratios EXAMPLE 1 Sports A person burned about 210 calories while in-line skating for 30 minutes. About how many calories would the person.

Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide.

Example 2 Hair Growth Human hair grows about 0.7 centimeter in 2 weeks. How long does hair take to grow 14 centimeters? Writing and Solving a Proportion.

In the Real World Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding.

Solving Proportions. What’s a proportion? A proportion is when 2 ratios are equivalent For example 5/6 = 15/18.

Holt Algebra Percents 2-8 Percents Holt Algebra 1 Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Warm Up Warm Up.

Solve –3j = Check your answer. –3j = 44.7 Notice j is being multiplied by –3. j = –14.9Simplify. Check –3j = 44.7 Check your solution in the original.

1) Solve. -5t = 60 To get the variable by itself, which number needs to be moved? -5 To move the -5, you have to do the opposite operation. What operation.

Lesson 3.2 Solving Equations with Multiplication and Division

Solving Equations With Fractions

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solve a literal equation

3-1 HW:Pg #4-28eoe, 30-48e, 55, 61,

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

Objective The student will be able to:

Objective The student will be able to:

Multiply Fractions Name: _________________________________

Objective The student will be able to:

Solve an equation by combining like terms

Finding the Percent of a Number

Must Do (8/29) – (-7) 8 – 12 (-7) + (-4)

Work out (if you can, simplify your answer) 8 6.

Solve an inequality using subtraction

Solve equations using multiplication and division.

Objective The student will be able to:

Write a proportion that compares hours of work to pay.

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Algebra with Fractions 2

Presentation transcript:

Writing and Solving a Proportion EXAMPLE 3 STEP 1 Write a proportion. Let x represent the number of floors passed in 9 seconds. Empire State Building The elevators in the Empire State Building can pass 80 floors in 45 seconds.Follow the steps below to find the number of floors that the elevators can pass in 9 seconds. x = seconds floor

EXAMPLE 3 STEP 2 Solve the proportion x 9 == x = x Write original proportion. Multiply each side by 9. Simplify fraction. Simplify x = ANSWER The elevators can pass 16 floors in 9 seconds. Writing and Solving a Proportion

GUIDED PRACTICE for Example 3 ANSWER 10 floors Suppose the elevators in Example 3 could pass 70 floors in 63 seconds. How many floors could the elevator pass in 9 seconds? What If? 9.