Illustrative Math Alignment: Grade 6 Unit 9
Putting it All Together
Lesson 4: How Do We Choose?
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Numerical Expressions--Order of Operations--Example 11 | Math Example--Numerical Expressions--Order of Operations--Example 11
Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division. Because addition is commutative, adding from left to right, or right to left, gives you the same result. The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Order of Operations--Example 12 | Math Example--Numerical Expressions--Order of Operations--Example 12
Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division. Because addition is commutative, adding from left to right, or right to left, gives you the same result. The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Order of Operations--Example 13 | Math Example--Numerical Expressions--Order of Operations--Example 13
Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division. Because addition is commutative, adding from left to right, or right to left, gives you the same result. The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Order of Operations--Example 14 | Math Example--Numerical Expressions--Order of Operations--Example 14
Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division. Because addition is commutative, adding from left to right, or right to left, gives you the same result. The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations. |
Numerical Expressions |
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Math Clip Art--Order of Operations 01 | Math Clip Art--Order of Operations 01
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 02 | Math Clip Art--Order of Operations 02
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 03 | Math Clip Art--Order of Operations 03
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 04 | Math Clip Art--Order of Operations 04
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 05 | Math Clip Art--Order of Operations 05
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 06 | Math Clip Art--Order of Operations 06
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 07 | Math Clip Art--Order of Operations 07
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 08 | Math Clip Art--Order of Operations 08
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 09 | Math Clip Art--Order of Operations 09
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 10 | Math Clip Art--Order of Operations 10
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 11 | Math Clip Art--Order of Operations 11
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 12 | Math Clip Art--Order of Operations 12
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 13 | Math Clip Art--Order of Operations 13
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Clip Art--Order of Operations 14 | Math Clip Art--Order of Operations 14
This is part of a collection of math clip art images that focus on the order of operations. —Press PREVIEW to see the clip art image.—To see the complete collection of images on this topic, click on this link.Watch the following video on Order of Operations. (The transcript is included.) Video Transcript
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Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 1 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 1TopicExponents DescriptionShows Example 1 with the expression 32. The solution explains how to simplify by multiplying 3 by itself according to the exponent. Example 1: Simplify 32. Multiply 3 by itself two times: 3•3 = 9. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 2 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 2TopicExponents DescriptionShows Example 2 with the expression 43. The solution explains the simplification by multiplying 4 three times. Example 2: Simplify 43. Multiply 4 by itself three times: 4•4•4 = 64. In general, the topic of exponents involves understanding how repeated multiplication can be expressed more compactly. The examples provided in this collection allow students to see the step-by-step breakdown of how to simplify various exponential expressions, which can include positive and negative bases, fractional bases, and negative exponents. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 3 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 3TopicExponents DescriptionShows Example 3 with the expression 54. The solution details multiplying 5 four times. Example 3: Simplify 54. Multiply 5 by itself four times: 5•5•5•5 = 625. In general, the topic of exponents involves understanding how repeated multiplication can be expressed more compactly. The examples provided in this collection allow students to see the step-by-step breakdown of how to simplify various exponential expressions, which can include positive and negative bases, fractional bases, and negative exponents. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 4 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 4TopicExponents DescriptionShows Example 4 with the expression 106. The solution simplifies by multiplying 10 six times. Example 4: Simplify 106. Multiply 10 by itself six times: 10•10•10•10•10•10 = 1,000,000. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 5 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 5TopicExponents DescriptionShows Example 5 with the expression (-1)2. The solution explains the result by multiplying -1 by itself. Example 5: Simplify (-1)2. Multiply -1 by itself two times: (-1)•(-1) = 1. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 6 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 6TopicExponents DescriptionShows Example 6 with the expression (-5)3. The solution demonstrates multiplying -5 three times. Example 6: Simplify (_5)3. Multiply -5 by itself three times: (-5)•(-5)•(-5) = -125. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 7 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 7TopicExponents DescriptionShows Example 7 with the expression (-6)4. The solution explains multiplying -6 by itself four times. Example 7: Simplify (-6)4. Multiply -6 by itself four times: (-6)•(-6)•(-6)•(-6) = 1296. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 8 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 8TopicExponents DescriptionShows Example 8 with the expression 23•32. The solution demonstrates using order of operations to simplify each term separately, then multiply. Example 8: Simplify 23•32. Evaluate each exponential term separately, then multiply: 8•9 = 72. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9TopicExponents DescriptionShows Example 9 with the expression (-1)2•43. The solution explains simplifying each term individually before multiplying. Example 9: Simplify (-1)2•43. Evaluate each exponential term separately, then multiply: 1•64 = 64. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 10 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 10TopicExponents DescriptionShows Example 10 with the expression (-3)3•54. The solution uses order of operations to evaluate each term before multiplying. Example 10: Simplify (-3)3•54. Evaluate each exponential term separately, then multiply: -27•625= -16,875. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 11 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 11TopicExponents DescriptionExample 11 shows how to simplify (1/2)2. The image illustrates multiplying 1/2 by itself due to the exponent of 2. Example 11: Simplify (1/2)2. Multiply one-half two times. Solution: (1/2) * (1/2) = 1/4. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 12 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 12TopicExponents DescriptionExample 12 shows how to simplify (1/3)4. The image illustrates multiplying 1/3 four times due to the exponent of 4. Example 12: Simplify (1/3)4. Multiply one-third four times. Solution: (1/3) * (1/3) * (1/3) * (1/3) = 1/81. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 13 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 13TopicExponents DescriptionExample 13 shows how to simplify (-1/3)3. The image illustrates multiplying -1/3 three times due to the exponent of 3. Example 13: Simplify (-1/3)3. Multiply negative one-third three times. Solution: (-1/3) * (-1/3) * (-1/3) = -1/27. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 14 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 14TopicExponents DescriptionExample 14 shows how to simplify 2-1. The image illustrates rewriting 2-1 as the reciprocal of 2 raised to the first power. Example 14: Simplify 2-1. Negative exponents are written as reciprocals. Solution: 2-1 = 1/2. |
Numerical Expressions |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 15 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 15TopicExponents DescriptionExample 15 shows how to simplify 2-2. The image illustrates rewriting 2-2 as the reciprocal of 2 raised to the second power. Example 15: Simplify 2-2. Negative exponents are written as reciprocals. Solution: 2-2 = 1/(22) = 1/4. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 1 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 2 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 3 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 4 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 5 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 6 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 7 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 8 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 9 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 10 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 1 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 2 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 3 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 4 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 5 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 6 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 7 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
