Evaluating Algebraic Expressions

Dividing Rational Numbers

California Standards

Lesson Presentation

3. 0.05(2.8)

4. –0.9(16.1)

NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) and justify the process used.

multiplicative inverse

Two numbers whose product is 1 are multiplicative inverses , or reciprocals .

A division problem can always be rewritten as a multiplication problem by using the reciprocal of the divisor.

Additional Example 1A: Dividing Fractions

Divide. Write the answer in simplest form.

Multiply by the reciprocal.

No common factors.

Simplest form

Additional Example 1B: Dividing Fractions

Write as an improper fraction.

No common factors

Check It Out! Example1A

Check It Out! Example1B

When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10.

1 decimal place

Find 0.384 ÷ 0.24. Estimate the reasonableness of your answer.

Additional Example 2: Dividing Decimals

0.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer.

0.24 ) 0.384

Then divide as a whole number.

0.384 ÷ 0.24 = 1.6

Estimate: 40 ÷ 20 = 2

The answer is reasonable.

Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer.

Check It Out! Example 2

0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer.

0.25 ) 0.65

0.65 ÷ 0.25 = 2.6

Estimate: 60 ÷ 20 = 3

for n = 0.15

Substitute 0.15 for n.

Additional Example 3: Evaluating Expressions with Rational Numbers

Evaluate the expression for the given value of the variable.

When n = 0.15, = 35.

0.15 ) 5.25

0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.

for n = 0.12

Substitute 0.12 for n.

Check It Out! Example 3

When n = 0.12, = 30.

0.12 ) 3.60

0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.

Additional Example 4: Problem Solving Application

A muffin recipe calls for cup of oats.

You have cup of oats. How many batches of muffins can you bake using all of the oats you have?

Understand the Problem

The number of batches of muffins you can bake is the number of batches using the oats that you have. List the important information :

The amount of oats is cup.

One batch of muffins calls for cup of oats.

Additional Example 4 Continued

Set up an equation.

Make a Plan

Let n = number of batches.

You can bake 1 batches of the muffins.

One cup of oats would make two batches so 1 is a reasonable answer.

Check It Out! Example 4

A ship will use of its total fuel load for a typical round trip. If there is of a total fuel load on board now, how many complete trips can be made?

It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now.

The number of complete trips the ship can make is the number of trips that the ship can make with the fuel on board.

List the important information :

Check It Out! Example 4 Continued

Amount of fuel on board

Amount of fuel for one trip

Number of trips

Let t = number of trips.

You can complete 3¾ trips, or 3 complete trips.

A full tank will make the round trip 6 times, and is a little more than , so half of 6, or 3, is a reasonable answer.

Lesson Quiz

2. –14 ÷ 1.25

4. Evaluate for x = 6.3.

3. 3.9 ÷ 0.65

A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)?

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## Rational & Irrational Numbers

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## Rational Numbers Mathematics- Grade 7.

Published by Ruth Howard Modified over 8 years ago

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## Presentation on theme: "Rational Numbers Mathematics- Grade 7."— Presentation transcript:

Multiplying and Dividing Real Numbers; Properties of Real Numbers

Thinking Mathematically

LESSON 2 FRACTIONS. Learning Outcomes By the end of this lesson, students should be able to: ◦ Understand types of fractions. ◦ Convert improper fractions.

Factors, Fractions, and Exponents

Rational Numbers and Decimals

Operations on Rational Expressions Digital Lesson.

Scientific Notation.

Unit 1: Number Sense Minds On. Unit 1: Number Sense Learning Goals: I can convert between mixed and improper fractions I can perform all four operations.

Lesson 1-3: Mult/Div Real #s

Definitions from the Text, sections 1.1 – 1.4

Lesson 2 Operations with Rational and Irrational Numbers

Section 1.1 Numbers and Their Properties.

Multiplying and Dividing Real Numbers. Language Goal Students should be able to explain how to perform multiplication and division with real numbers.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.3 The Rational Numbers.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 5 Number Theory and the Real Number System.

Operations With Decimals

2.1 Integers Natural (Counting) Numbers: 1, 2, 3, 4, …

Pharmacology I Math Review.

Converting, Comparing and Ordering Rational Numbers

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## (7th) Rational Numbers in a PowerPoint Presentation

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7th Grade Math Rational Numbers in a PowerPoint Presentation

This slideshow lesson is very animated with a flow-through technique. I developed the lesson for my 7th grade class, Pre-Pre-Algebra, but it can also be used for upper level class reviews. This lesson teaches how to understand that a rational number is an integer divided by an integer, convert rational numbers to decimals, and order fractions and decimals.

This lesson has SKELETON NOTES , notes that have the problem only. I used this with our 1-1 district devices. This will allow for the students to follow the lesson easier. There are 6 slides per page with plenty of room for notetaking. They are in a pdf format for easy printing too. A Word document is included for you to EDIT i f you won’t be doing all of the problems so you can shorten it. I also made another version of skeleton notes that is only one or two sheets long in a pdf. When I printed off skeleton notes for the whole class this is what I used. It is also editable so you can delete the problems and rearrange the skeleton notes however you want.

NEW : The lesson is in an editable format so you can tailor the lesson to your class. The problems and clipart can’t be edited due to the TOU and to maintain the copyright integrity of the product. If you need an alternative version because your country uses different measurements, units, or slight wording adjustment for language differences just email me at [email protected]. I am respond to email quickly.

The presentation has 61 slides with LOTS of whiteboard practice. Use as many or as few of the problems to help your students learn each concept. For more PowerPoint lessons & materials visit Preston PowerPoints .

Students often get lost in multi-step math problems. This PowerPoint lesson is unique because it uses a flow-through technique, guided animation, that helps to eliminate confusion and guides the student through the problem. The lesson highlights each step of the problem as the teacher is discussing it, and then animates it to the next step within the lesson. Every step of every problem is shown, even the minor or seemingly insignificant steps. A helpful color-coding technique engages the students and guides them through the problem (Green is for the answer, red for wrong or canceled numbers, & blue, purple & sometimes orange for focusing the next step or separating things.) Twice as many examples are provided, compared to a standard textbook. All lessons have a real-world example to aid the students in visualizing a practical application of the concept.

This lesson applies to the Common Core Standard:

The Number System 7.NS.2b, 7.NS.2d

Apply and extend previous understandings of operations with fractions.

2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Are you looking for the 7th Grade Rational Numbers Bundle? Click here!

This resource is for one teacher only. You may not upload this resource to the internet in any form. Additional teachers must purchase their own license. If you are a coach, principal or district interested in purchasing several licenses, please contact me for a district-wide quote at [email protected]. This product may not be uploaded to the internet in any form, including classroom/personal websites or network drives.

*This lesson contains 28 problems. Each problem in this lesson uses several pages in order to achieve the animated flow-through technique.

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## Rational numbers in the number line - Best PowerPoint Presentation | Lumos Learning

Rational numbers in the number line, - by gracerobledo2.

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Rational numbers in the number line is related to Grade 7 and focuses on standards 7.NS.A.2.B. This Lumos presentation viewer page not only allows you to view and download Rational numbers in the number line but also view questions, videos, apps, books and other resources related to 7.NS.A.2.B.

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Dividing Rational Numbers

Jul 16, 2014

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Rational Numbers ~. Dividing Rational Numbers. Dividing Rational Numbers. RULES: 1. When multiplying or dividing integers with the same signs, the answer will be Positive . Dividing Rational Numbers. RULES:

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## Presentation Transcript

Rational Numbers ~ Dividing Rational Numbers

Dividing Rational Numbers RULES: 1. When multiplying or dividing integers with the same signs, the answer will be Positive.

Dividing Rational Numbers RULES: 1. When multiplying or dividing integers with the same signs, the answer will be Positive. 2. When multiplying or dividing integers with different signs, the answer will be Negative.

Rules for Dividing Rational Numbers: Dividing two integers with the same signs: ÷ Positive Positive= Positive + + + ÷ = ÷ Negative Negative= Positive + - - + ÷ =

Rules for Dividing Rational Numbers: Dividing two integers with different signs: ÷ Positive Negative= Negative - - + ÷ = ÷ NegativePositive= Negative - - + ÷ =

-48 ÷ 6= 24 ÷ -6= -63 ÷ -9= Try some. Find the quotient. Remember the rules for dividing rational numbers.

Try some. -48 ÷ 6= -8 - - + 24 ÷ -6= -4 - - + -63 ÷ -9= 7 - - +

Dividing Rational Numbers Use the same rules for multiplying as dividing. [Remember that division by zero is undefined.] -32 ÷ 8 = -48 ÷ (-6) = -56 ÷ (-4) = -140 ÷ 5 = -4 8 14 -28

Dividing Rational Numbers Example Solve x = -52 ¸ (-4). x = -52 ¸ (-4) The dividend and the divisor have the same sign.

Dividing Rational Numbers Example Solve x = -52 ¸ (-4). x = -52 ¸ (-4) x = 13 The dividend and the divisor have the same sign. The quotient is positive.

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 -4

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 -9

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 • 3. -27 ¸ (-9)

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 • 3. -27 ¸ (-9) 3

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 • 3. -27 ¸ (-9) • 4. 27 ¸ 9

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 • 3. -27 ¸ (-9) • 4. 27 ¸9 3

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 • 3. -27 ¸ (-9) • 4. 27 ¸ 9 • 5. 63 ¸ (-3)

Dividing Rational Numbers • Practice: • 1. -60 ¸ 15 • 2. 45 ¸ -5 • 3. -27 ¸ (-9) • 4. 27 ¸ 9 • 5. 63 ¸ (-3) -21

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## Multiplying and Dividing Rational Numbers

Multiplying and Dividing Rational Numbers. Rational Numbers. The term Rational Numbers refers to any number that can be written as a fraction. This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers.

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## Dividing Numbers

Dividing Numbers. Crossing the GREAT divide. What is a reciprocal?. Mixed numbers and integers must be put into improper fraction form to find the reciprocal!. When reciprocals (also called multiplicative inverses) are multiplied, the product is +1!. Find the reciprocal of these numbers!.

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## 2.5 Dividing Rational Numbers

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## 4.1, 4.3: Multiplying and Dividing Rational Numbers

4.1, 4.3: Multiplying and Dividing Rational Numbers. LEQ: How do we multiply and divide fractions?. Multiplying Rational Numbers occurs frequently in daily life: Ex) Interest on a loan equals the principal ( $8500) times the rate ( 5. 5%) times the time ( 2.5 years)

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## RATIONAL NUMBERS

RATIONAL NUMBERS. Fractions. INTEGERS. WHAT IS AN INTEGER? The integers consist of the positive natural numbers ( 1 , 2 , 3 , …), their negatives (−1, −2, −3, ...) and the number zero . . RATIONAL NUMBERS. WHAT IS A RATIONAL NUMBER?

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## Effects of multiplying and dividing two rational numbers

Effects of multiplying and dividing two rational numbers. If you multiply a positive rational number by a number greater than one, the product is greater than the given positive rational number. Example: 5 * 2 = 10. Multiply.

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## Dividing Rational Expressions

Dividing Rational Expressions. Dividing Fractions. Rules for Dividing Rational Expressions. Change to multiplication and use the reciprocal of the divisor (2 nd fraction). Factor. Reduce. Multiply your remaining factors. Check to see if you can reduce again. #1 Divide and simplify.

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## Dividing Whole Numbers

Dividing Whole Numbers. Common Core Standards. Homework. Number Talk. Warm up. Dividing by two digit s divisors. Steps to Divide. 468 ÷ 18. 538 ÷ 22. Guided Practice. Independent Practice. Closure. Remember to estimate before dividing.

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## Rational Numbers ~ Subtracting Rational Numbers

Rational Numbers ~ Subtracting Rational Numbers. Rational Numbers. SUBTRACTING RATIONAL NUMBERS. SUBTRACTING RATIONAL NUMBERS.

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RATIONAL NUMBERS. By: Bazen Kokeb Stanford Ms. Manuel. Objective. The topics covered in this presentation will help you understand and learn more about Rational Numbers in order to use it in real life situations. Key Terms (Vocabulary).

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## 2-3 Multiplying and Dividing Rational Numbers

2-3 Multiplying and Dividing Rational Numbers. Ex. 1 Multiplying. Same Signs Always positive answer 2(2) = 4 or -2(-2) = 4 Different Signs Always a negative answer 4(-6) = -24 Simplify -10(-5) = 50. Ex 1. Cont. Your practice -2/3(3/4) = -6/12 = -1/2. Ex. 2 Evaluating.

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## Rational Numbers

Number: Rational Numbers & Indices. By the end of this lesson you will be able to explain and calculate the following: A Rational Number An Irrational Number Order of Operations. Rational Numbers. Real Numbers. We use numbers such as integers, fractions and decimals every day.

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Rational Numbers. The root word of ratio nal is ratio. Ratios are fractions. Any number that can be written as the quotient (a fraction) of two integers is a rational number. However, the denominator cannot be 0. 1. 2. 3. 0.25. -5. 0.333. are rational numbers. -. 10. -. -. 15.

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Dividing Rational Expressions. When P,Q,R and S are polynomials with Q=0, S=0 and R=0 P/Q ÷ R/S=RR/QS flip R/S to S/R and multiply. Examples. =. =. =.

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Rational Numbers. Any number that can be written as a fraction. 1, 2, 3, …. 2.7. 7.0145. –5. 0. Integers. All whole and numbers and their opposites, zero. –5. 1, 2, 3, …. 0. Whole Numbers. All counting numbers and zero. 1, 2, 3, …. 0. Natural or Counting Numbers.

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## DIVIDING RATIONAL NUMBERS

DIVIDING RATIONAL NUMBERS. Division means multiplying by the reciprocal. RULE FOR DIVISION. BEFORE DIVIDING, ALL MIXED NUMBERS AND INTEGERS MUST BE EXPRESSED AS IMPROPER FRACTIONS “LEAVE” “CHANGE” “FLIP”. “LEAVE” “CHANGE” “FLIP”. SIMPLIFY BEFORE YOU MULTIPLY!. DIVIDING RATIONAL NUMBERS.

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## 2.3 Multiplying/Dividing Rational Numbers

2.3 Multiplying/Dividing Rational Numbers. Multiplying and Dividing. Note: Rules are way easier than adding and subtracting. If two numbers have the same sign , the answer is positive. If two numbers have different signs , the answer is negative. Examples:.

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## Practicing Adding/subtracting/Multiplying and Dividing Rational Numbers

Practicing Adding/subtracting/Multiplying and Dividing Rational Numbers. Tell me the steps to solve this problem : 3 – 7 x (-8. How is this problem the same? 3.25 - x (-. 3.25 - x ( -. 3 – 7 x (-8. How are these different?

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## Dividing Complex Numbers

Dividing Complex Numbers. Before we begin. Last time we learned about the “imaginary numbers.” Numbers like 4 i and -3 i are called “pure imaginary” because no real number has been put with them.

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## COMMENTS

Rational numbers. Education. 1 of 13. Download now. Rational numbers ppt - Download as a PDF or view online for free.

Rational Numbers - Week 5. Please look at each slide. Be sure to click on each link. Each link has a video or a game to help learn this standard. There will be practice problems each day for students (slide 2) The Cool Downs will be used as our task this week. Lesson 3 - Monday and Tuesday.

Dividing Rational Numbers. When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10. 13.2.

Rational and Irrational Numbers lesson plans. Free Clipart. Free Templates. Lots of Lessons - Math. Pete's PowerPoint Station is your destination for free PowerPoint presentations for kids and teachers about Rational & Irrational Numbers, and so much more.

Free Google Slides theme and PowerPoint template. When we talk about "rational numbers", we do not mean numbers that are sensible and able to think thoroughly, but numbers that can be expressed as fractions of two integers. Time to start your math lesson about operations on rational numbers! To lessen the burden of coming up with a cool design ...

Free Google Slides theme, PowerPoint template, and Canva presentation template. Get your students excited about math with our engaging PowerPoint and Google Slides template, perfect for middle school educators! This presentation template makes teaching the concepts of rational and irrational numbers not just easy, but super interactive.

Presentation Transcript. Rational Numbers • The integers which are in the form of p/q where q is not equal to 0 are known as rational numbers. Examples - 5/8; -3/14; 7/-15; -6/-11 • Natural numbers - They are counting numbers. • Integers - Natural numbers, their negative and 0 form the system of integers. • Fractional numbers - the ...

6. Additive identity property: When 'o' is added to any rational number the sum of the rational number is becomes itself, If x is a rational number then 𝒙 + 𝟎 = 𝟎 + 𝒙 = 𝒙 . EXAMPLE: let 𝑥 = 5 4 LHS= 5 4 + 0 = 5 4 RHS=0 + 5 4 = 5 4 As LHS = RHS so this property valids. Zero is called the identity element in Addition . Additive inverse property: The negative of a rational ...

Rational Numbers All rational numbers are written as a RATIO. Example 1. During a recent regular season, a Texas Ranger baseball player had 126 hits and was at bat 399 times. Write a fraction in the simplest form to represent the ratio of the number of hits to the number of at bats. =. Rational Numbers.

Rational Numbers. May 8, 2014 •. 107 likes • 56,403 views. Manisha Keim. Rational Numbers PPT for Class VIII, Properties of Rational Numbers: Commutative, Distributive, Associative, etc. Education Technology Business. 1 of 8. Rational Numbers - Download as a PDF or view online for free.

Download ppt "Rational Numbers Mathematics- Grade 7." Module Objectives Know the meaning, standard form and equivalents of rational numbers, Develop the skill of representing the rational numbers on a number line, Know the comparison of rational numbers, finding rational numbers between any two rational numbers, Know the operations on rational ...

Free Google Slides theme and PowerPoint template. Embark on an exciting mathematical adventure with your middle schoolers and teach them the difference between rational and irrational numbers! Guide your students through simple explanations and fun, hands-on activities with this fully editable Google Slides and PowerPoint template.

Designed for 7th graders, this lively and whimsical Google Slides and PowerPoint resource brings math to life. Its geometric patterns and creative design ensure learning is engaging and enjoyable. From fractions to decimals, this template will make every math lesson a thrilling journey. It's much more than a presentation; it's a launchpad for ...

Topic - Rational Numbers By- Srinivas, Sri Ragavan, Vignesh, Syed & Shreeram Introduction By - Shreeram Introduction Rational Numbers are the numbers that can be expressed in the form of p/q, where p and q are integers and is q not equal to zero. ... Understanding 30-60-90 sales plans and incorporating them into a presentation; April 13, 2024 ...

Description. 7th Grade Math Rational Numbers in a PowerPoint Presentation. This slideshow lesson is very animated with a flow-through technique. I developed the lesson for my 7th grade class, Pre-Pre-Algebra, but it can also be used for upper level class reviews. This lesson teaches how to understand that a rational number is an integer divided ...

Give reasons for your answers — Every natural number is a whole number. 1. 2. Every integer is a whole number. 3. Every rational number is a whole number Answer: 1. True 2. False, because -5, -6 are integers but not whole numbers 3. False, because h, 3/5 or -4/9 are not whole numbers.

This Lumos presentation viewer page not only allows you to view and download Rational numbers in the number line but also view questions, videos, apps, books and other resources related to 7.NS.2.B. Rational numbers in the number line is related to Grade 7 and focuses on standards 7.NS.A.2.B. This Lumos presentation viewer page not only allows ...

Free Google Slides theme and PowerPoint template. Making Math accessible and fun can be a challenge, but it's by no means an impossible task: with this template for seventh grade students, rational numbers can become as interesting as any other subject! Its look is inspired in that of a file folder, and the barrage of colors on display in ...

Rational Numbers • A real number that can be written as: • A fraction or ratio of two integers - • A repeating 0.5757... 1.2 or terminating decimal 0. 45 • An integer - 25 A number must be written in one of these three forms in order to be classified as RATIONAL. Squares • Another example of a RATIONAL number is a perfect square and ...

Multiplying and Dividing Rational Numbers. Multiplying and Dividing Rational Numbers. Rational Numbers. The term Rational Numbers refers to any number that can be written as a fraction. This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers. 2.58k views ...