Page 133 #14-26 ANSWERS.

Slides:



Advertisements
Similar presentations
Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation.
Advertisements

Adding and Subtracting Rational Numbers
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
4-9 Multiplying Fractions by Whole Numbers Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day.
Bell Work: Write the first 10 prime numbers.
DIVIDING RATIONAL NUMBERS
Multiplying and Dividing Integers
2-9 Equivalent Fractions and Mixed Numbers Warm Up Problem of the Day
1-2 Multiplying Rational Numbers Write each number as an improper fraction Bell Work Multiply (and think!): 4.
Copyright © Cengage Learning. All rights reserved.
Page 152 #19-38 ANSWERS.
Page 129 #24-57 ANSWERS.
3-4 Warm Up Problem of the Day Lesson Presentation
Adding, Subtracting, Multiplying, and Dividing Fractions 3-5, 3-6, 3-7
Pre-Algebra Bell Ringer 1. 10x – 5y = 2 Solve for y 2. m – n – 12 = p Solve for n 3. a – 4 < 3a x + 8 ≥ -22 – 7x.
Page 142 & Spiral Review Answers
Add positive and negative fractions and decimals.
Fractions and Decimals
Multiplying Rational Numbers
Multiplying Rational Numbers
Course Dividing Rational Numbers Warm Up Multiply – – –15 – (2.8) 4. –0.9(16.1) –14.49.
Dividing Rational Numbers
Adding and Subtracting Rational Numbers
11/18-19 Multiply Fractions & Decimals #42 LT: I will learn to multiply mixed numbers, fractions, and decimals. Today’s Plan: -Warm up & correct homework.
2-4 Multiplying Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.
3-8 Equivalent Fractions and Mixed Numbers Warm Up
Page 500 #15-32 ANSWERS.
Today’s Plan: -Warm up and Correct Homework -Multiply Fractions 12/1/10 Multiply Fractions Learning Target: -I can multiply fractions and mixed numbers.
Pre-Algebra 2-3 Multiplying and Dividing Integers 2-3 Multiplying and Dividing Integers Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day.
Page 124 #33-64 ANSWERS Student Learning Goal Chart Lesson Reflection.
Bell Work!!! a ÷ (b) 2. c × d 3. d ÷ d 4. c × b
I will be able to add and subtract fractions. Adding and Subtracting Fractions Learning Target.
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Page ?? #?-?? ANSWERS Student Learning Goal Chart Lesson Reflection.
Page 190 #1-9 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 9.
Pre-Algebra 2-3 Multiplying and Dividing Integers Today’s Learning Goal Assignment Learn to multiply and divide integers.
Page 184 #1-5 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 8.
Course Multiplying Rational Numbers Warm Up Write each number as an improper fraction
Signed Rationals. What are signed rationals? Signed rationals are rational numbers with negative and positive signs. To solve signed rational problems:
ALGEBRA READINESS LESSON 5-1 Warm Up. ALGEBRA READINESS LESSON 4-4 Warm Up.
Topic 10. What you know and what you are going to know You know how to add and subtract whole numbers, like Today you are going to learn how to.
Page ?? #?-?? ANSWERS Student Learning Goal Chart Lesson Reflections.
Bellwork Write each rational number as a fraction in simplest form.
Review of Fractions. Important Notes Leave all answers in “simplest form” No common factors in the numerator and denominator Use proper or improper fractions.
Tuesday’s Test Hints. Integers A set of Integers is shown by I. A set of Integers is shown by I. I = (…-4, -3, -2, -1, 0, 1, 2, 3, 4 …) I = (…-4, -3,
MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =
Aims: To be to be able to classify types of numbers To be able to write a surd in its simplest form To be able to add, subtract and multiply surds SURDS.
5-8 Adding and Subtracting Mixed Numbers Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day.
Page 148 #1-13 ANSWERS Pre-Algebra 3-9 Finding Square Roots Student Learning Goal Chart Lesson Reflections 3-9.
Pre-Algebra 3-7 Solving Inequalities with Rational Numbers Review/Finish Chapter 10-4 Page 517 #14-26 Solve and Graph- Due today!
5-5 Multiplying Fractions by Whole Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes.
OPERATIONS WITH INTEGERS, ADDING AND SUBTRACTING RATIONAL NUMBERS Objective: To add, subtract, multiply, and divide integers, to compare and order rational.
Bell Quiz. Objectives Multiply and Divide signed numbers. Discuss the properties of real numbers that apply specifically to multiplication. Explain the.
The set of all numbers that can be represented on a number line are called real numbers. You can use a number line to help you with addition and subtraction.
Lesson 5.3 The rational numbers. Rational numbers – set of all numbers which can be expressed in the form a/b, where a and b are integers and b is not.
Preview Warm Up California Standards Lesson Presentation.
Rational Numbers Adding Like Fractions
5.2 The Integers.
Preview Warm Up California Standards Lesson Presentation.
Mixed numbers and simplifying fractions
2-9 Equivalent Fractions and Mixed Numbers Warm Up Problem of the Day
Warm Up Change the following to a mixed number in simplest form.
Adding and Subtracting Rational Numbers
Adding and Subtracting Rational Numbers
Warm Up Write each number as an improper fraction
Adding and Subtracting Rational Numbers
Homework Corrections (page 1 of 2) A#13 / 1-1 Homework Worksheet
Adding and Subtracting Rational Numbers
Simplifying Rational Expressions
Fractions.
Presentation transcript:

Page 133 #14-26 ANSWERS

Student Learning Goal Chart Lesson Reflections

Pre-Algebra Learning Goal Students will understand rational and real numbers.

Students will understand rational and real numbers by being able to do the following: Learn to write rational numbers in equivalent forms (3.1) Learn to add and subtract decimals and rational numbers with like denominators (3.2) Learn to add and subtract fractions with unlike denominators (3.5) Learn to multiply fractions, decimals, and mixed numbers (3.3)

Today’s Learning Goal Assignment Learn to multiply fractions, decimals, and mixed numbers.

Pre-Algebra HW Page 124 #33-64 all

Multiplying Rational Numbers 3-3 Multiplying Rational Numbers Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Multiplying Rational Numbers Pre-Algebra 3-3 Multiplying Rational Numbers Warm Up Write each number as an improper fraction. 1 7 3 7 15 8 2 17 5 1. 2 2. 1 3. 3 3 8 5 2 20 3 3 43 8 4. 6 5. 5 3 8

Problem of the Day The sum of three consecutive integers is 168. What are the three integers? 55, 56, and 57

Today’s Learning Goal Assignment Learn to multiply fractions, decimals, and mixed numbers.

Kendall invited 36 people to a party Kendall invited 36 people to a party. She needs to triple the recipe for a dip, or multiply the amount of each ingredient by 3. Remember that multiplication by a whole number can be written as repeated addition. 1 4 3 4 + = Repeated addition 3 4 = Multiplication 3 • 1 1 Notice that multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator.

RULES FOR MULTIPLYING TWO RATIONAL NUMBERS If the signs of the factors are the same, the product is positive. (+) • (+) = (+) or (–) • (–) = (+) If the signs of the factors are different, the product is negative. (+) • (–) = (–) or (–) • (+) = (–)

Additional Example 1A: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. 6 7 To write as a mixed number, divide: Helpful Hint 12 5 12 5 = 2 R2 2 5 = 2 A. –8 –8 • 6 7 = –48 7 = Multiply –6 6 7 = Simplify

Additional Example 1B: Multiplying a Fraction and an Integer Multiply. Write the answer in simplest form. 1 3 B. 2 5 16 3 = 2 5(3) + 1 3 = 1 3 5 16 3 32 3 = Multiply 10 2 3 = Simplify

5 8 A. –3 –3 • 5 8 = –15 8 = –1 7 8 = Multiply Simplify Try This: Example 1A Multiply. Write the answer in simplest form. 5 8 A. –3 –3 • 5 8 = –15 8 = Multiply –1 7 8 = Simplify

Try This: Example 1B Multiply. Write the answer in simplest form. 2 5 B. 4 9 47 5 = 4 9(5) + 2 5 = 2 5 9 47 5 188 5 = Multiply 37 3 5 = Simplify

3 5 2 3 A model of is shown. Notice that to multiply fractions, you multiply the numerators and multiply the denominators. • 35 23 6 15 • = If you place the first rectangle on top of the second, the number of green squares represents the numerator, and the number of total squares represents the denominator.

To simplify the product, rearrange the six green squares into the first two columns. You can see that this is . 2 5 2 5 = 6 15 A fraction is in lowest terms, or simplest form, when the numerator and denominator have no common factors. Helpful Hint

1 8 6 7 1(6) 8(7) = 1(6) 8(7) = 3 28 = Multiply numerators. Additional Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. 1 8 6 7 A. = 1(6) 8(7) Multiply numerators. Multiply denominators. 3 4 1(6) 8(7) = Look for common factors: 2. 3 28 = Simplest form

Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. 2 3 9 2 B. – = –2(9) 3(2) Multiply numerators. Multiply denominators. 1 –1 3 1 –2(9) 3(2) = Look for common factors: 2, 3. –3 = Simplest form

Additional Example 2C: Multiplying Fractions Multiply. Write the answer in simplest form. 3 7 1 2 C. 4 1 2 3 7 4 = 31 1 7 2 Write as an improper fraction. = 31(1) 7(2) Multiply numerators. Multiply denominators. = or 2 31 14 3 14 31 ÷ 14 = 2 R3

3 5 5 8 A. 3(5) 5(8) = 3(5) 5(8) = 3 8 = Multiply numerators. Try This: Example 2A Multiply. Write the answer in simplest form. 3 5 5 8 A. = 3(5) 5(8) Multiply numerators. Multiply denominators. 1 3(5) 5(8) = Look for common factors: 5. 3 8 = Simplest form

7 8 4 7 B. – = –7(4) 8(7) –1 –7(4) 8(7) = 1 2 = – Multiply numerators. Try This: Example 2B Multiply. Write the answer in simplest form. 7 8 4 7 B. – = –7(4) 8(7) Multiply numerators. Multiply denominators. 1 –1 1 2 –7(4) 8(7) = Look for common factors: 4, 7. 1 2 = – Simplest form

C. 2 2 = = = or 2 Write as an improper fraction. Multiply numerators. Try This: Example 2C Multiply. Write the answer in simplest form. 3 5 7 9 C. 2 7 9 3 5 2 = 13 7 5 9 Write as an improper fraction. = 13(7) 5(9) Multiply numerators. Multiply denominators. = or 2 91 45 1 45 91 ÷ 45 = 2 R 1

Additional Example 3: Multiplying Decimals 2(–0.51) Product is negative with 2 decimal places. 2 • (–0.51) = –1.02 B. (–0.4)(–3.75) Product is positive with 3 decimal places. (–0.4) • (–3.75) = 1.500 = 1.5 00 You can drop the zeros after the decimal point.

A. 3.1 (0.28) 3.1 • (0.28) = 0.868 B. Multiply. (–0.4)(–2.53) Try This: Example 3 Multiply. A. 3.1 (0.28) 3.1 • (0.28) = 0.868 Product is positive with 3 decimal places. B. (–0.4)(–2.53) Product is positive with 3 decimal places. (–0.4) • (–2.53) = 1.012

Additional Example 4A: Evaluating Expressions with Rational Numbers Evaluate –3 x for the value of x. 1 8 A. x = 5 –3 x 18 –3 (5) 18 = Substitute 5 for x. –25 8 = (5) Write as an improper fraction. –125 8 = = –15 5 8 –125 ÷ 8 = –15 R5

2 B. x = –3 x 7 = –3 = = = – Evaluate –3 x for the value of x. Additional Example 4B: Evaluating Expressions with Rational Numbers Continued Evaluate –3 x for the value of x. 1 8 2 B. x = –3 x 18 7 –3 = 18 27 Substitute for x. 2 7 27 –25 8 = Write as an improper fraction. –25 • 2 8 • 7 = 1 Look for common factors: 2. 4 = – 25 28

A. y = –5 y –5 = = = = – , or – 4 Evaluate –5 y for the value of y. Try This: Example 4A Evaluate –5 y for the value of y. 3 5 67 A. y = –5 y 35 Substitute for x. 6 7 35 –5 = 67 Write as an improper fraction. –28 5 = 67 –4 –28 • 6 5 • 7 = Look for common factors: 7. 1 = – 24 5 , or – 4 45

B. y = 3 –5 y –5 (3) = = (3) = = –16 Evaluate –5 y for the value of y. Try This: Example 4B Evaluate –5 y for the value of y. 3 5 B. y = 3 –5 y 35 35 –5 (3) = Substitute 3 for y. –28 5 = (3) Write as an improper fraction. –84 5 = = –16 4 5 –84 ÷ 5 = –16 R4

Lesson Quiz: Part 1 Multiply. 1 7 1 2 7 1. 9 2 3 5 8 2. – – 5 12 3. –0.47(2.2) –1.034 1 2 45 4. Evaluate 2 (x) for x = . 2

Lesson Quiz: Part 2 5. Teri is shopping for new shoes. Her mom has agreed to pay half the cost (and all the sales tax). The shoes that Teri likes are normally $30 a pair but are on sale for off. How much money does Teri need to buy the shoes? 1 3 $10