Illustrative Math Alignment: Grade 6 Unit 7
Rational Numbers
Lesson 1: Positive and Negative Numbers
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Numerical Expressions--Dividing Integers: Example 13 | Math Example--Numerical Expressions--Dividing Integers: Example 13TopicNumerical Expressions DescriptionThis example demonstrates the division of two positive integers: 12 ÷ 5. The solution shows that dividing two positive integers results in a positive quotient, which in this case is a mixed number. The calculation is presented as: 12 / 5 = 2 2/5. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 14 | Math Example--Numerical Expressions--Dividing Integers: Example 14TopicNumerical Expressions DescriptionThis example illustrates the division of a positive integer by a negative integer: 14 ÷ (-6). The solution demonstrates that dividing a positive by a negative results in a negative quotient, which in this case is a mixed number. The calculation is presented as: 14 / -6 = -2 1/3. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 15 | Math Example--Numerical Expressions--Dividing Integers: Example 15TopicNumerical Expressions DescriptionThis example demonstrates the division of a negative integer by a positive integer: -18 ÷ 4. The solution shows that dividing a negative by a positive results in a negative quotient, which in this case is a fraction. The calculation is presented as: -18 / 4 = -9/2 = -4 1/2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 16 | Math Example--Numerical Expressions--Dividing Integers: Example 16TopicNumerical Expressions DescriptionThis example illustrates the division of two negative integers: (-9) ÷ (-6). The solution demonstrates that dividing two negative integers results in a positive fraction. The calculation is presented step-by-step: (-9) ÷ (-6) = -9 / -6 = -3 / -2 = 1 1/2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 17 | Math Example--Numerical Expressions--Dividing Integers: Example 17TopicNumerical Expressions DescriptionThis example demonstrates the division of three positive integers: 20 ÷ 2 ÷ 4. The solution shows that dividing three positive integers results in a positive mixed number quotient. The calculation is presented step-by-step: 20 ÷ 2 ÷ 4 = 20 / 2 / 4 = 10 / 4 = 2 1/2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 18 | Math Example--Numerical Expressions--Dividing Integers: Example 18TopicNumerical Expressions DescriptionThis example illustrates the division of three integers: 48 ÷ 6 ÷ (-3). The solution demonstrates that dividing two positive integers and one negative integer results in a negative mixed number quotient. The calculation is presented step-by-step: 48 ÷ 6 ÷ (-3) = 48 / 6 / (-3) = 8 / (-3) = -2 2/3. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 19 | Math Example--Numerical Expressions--Dividing Integers: Example 19TopicNumerical Expressions DescriptionThis example demonstrates the division of three integers: 24 ÷ (-6) ÷ 2. The solution shows that dividing two positive integers and one negative integer results in a negative quotient. The calculation is presented step-by-step: 24 ÷ (-6) ÷ 2 = 24 / (-6) / (2) = -4 / 2 = -2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 2 | Math Example--Numerical Expressions--Dividing Integers: Example 2TopicNumerical Expressions DescriptionThis example illustrates the division of a positive integer by a negative integer: 14 divided by -7. The solution demonstrates that when dividing one integer by another, the result is a rational number. In this case, when dividing a positive integer by a negative integer, the quotient is negative. The calculation is presented as 14 ÷ (-7) = 14 / -7 = -2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 20 | Math Example--Numerical Expressions--Dividing Integers: Example 20TopicNumerical Expressions DescriptionThis example demonstrates the division of three integers: (-72) / 2 / 5. The solution shows that dividing a negative integer by two positive integers results in a negative mixed number quotient. The calculation is presented step-by-step: (-72) / 2 / 5 = -72 / (2 * 5) = -36 / 5 = -7 1/5. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 21 | Math Example--Numerical Expressions--Dividing Integers: Example 21TopicNumerical Expressions DescriptionThis example demonstrates the division of three integers: 125 / (-25) / (-2). The solution shows that dividing a positive integer by two negative integers results in a positive mixed number quotient. The calculation is presented step-by-step: 125 / (-25) / (-2) = 125 / (25 * -2) = -5 / -2 = 2 1/2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 22 | Math Example--Numerical Expressions--Dividing Integers: Example 22TopicNumerical Expressions DescriptionThis example illustrates the division of three integers: (-144) / 12 / (-5). The solution demonstrates that dividing a negative integer by a positive integer and then by a negative integer results in a positive fraction. The calculation is presented step-by-step: (-144) / 12 / (-5) = -144 / (12 * -5) = -12 / -5 = 2 2/5. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 23 | Math Example--Numerical Expressions--Dividing Integers: Example 23TopicNumerical Expressions DescriptionThis example demonstrates the division of three integers: (-150) / (-5) / 4. The solution shows that dividing a negative integer by a negative integer and then by a positive integer results in a positive mixed number quotient. The calculation is presented step-by-step: (-150) / (-5) / 4 = -150 / -5 / 4 = 30 / 4 = 7 1/2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 24 | Math Example--Numerical Expressions--Dividing Integers: Example 24TopicNumerical Expressions DescriptionThis example illustrates the division of three negative integers: (-108) ÷ (-2) ÷ (-7). The solution demonstrates that dividing three negative integers results in a negative mixed number quotient. The calculation is presented step-by-step: (-108) ÷ (-2) ÷ (-7) = -108 / -2 ÷ (-7) = 54 / -7 = -7 5/7. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 3 | Math Example--Numerical Expressions--Dividing Integers: Example 3TopicNumerical Expressions DescriptionThis example demonstrates the division of a negative integer by a positive integer: -18 divided by 6. The solution shows that when dividing one integer by another, the result is a rational number. In this case, when dividing a negative integer by a positive integer, the quotient is negative. The calculation is presented as (-18) ÷ 6 = -18 / 6 = -3. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 4 | Math Example--Numerical Expressions--Dividing Integers: Example 4TopicNumerical Expressions DescriptionThis example illustrates the division of two negative integers: -9 divided by -3. The solution demonstrates that when dividing one integer by another, the result is a rational number. In this case, when dividing two negative integers, the quotient is positive. The calculation is presented as (-9) ÷ (-3) = -9 / -3 = 3. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 5 | Math Example--Numerical Expressions--Dividing Integers: Example 5TopicNumerical Expressions DescriptionThis example demonstrates the division of three positive integers: 20 ÷ 2 ÷ 5. The solution shows that dividing three positive integers results in a positive quotient. The calculation is presented step-by-step: 20 ÷ 2 ÷ 5 = 20 / 2 ÷ 5 = 10 / 5 = 2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 6 | Math Example--Numerical Expressions--Dividing Integers: Example 6TopicNumerical Expressions DescriptionThis example demonstrates the division of three integers: 48 ÷ 6 ÷ (-4). The solution shows that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: 48 ÷ 6 ÷ (-4) = 48 / 6 ÷ (-4) = 8 / -4 = -2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 7 | Math Example--Numerical Expressions--Dividing Integers: Example 7TopicNumerical Expressions DescriptionThis example illustrates the division of three integers: 24 ÷ (-6) ÷ 2. The solution demonstrates that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: 24 ÷ (-6) ÷ 2 = -4 / 2 = -2. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 8 | Math Example--Numerical Expressions--Dividing Integers: Example 8TopicNumerical Expressions DescriptionThis example demonstrates the division of three integers: (-72) ÷ 2 ÷ 6. The solution shows that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: (-72) ÷ 2 ÷ 6 = -72 / 2 ÷ 6 = -36 / 6 = -6. |
Numerical Expressions |
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Math Example--Numerical Expressions--Dividing Integers: Example 9 | Math Example--Numerical Expressions--Dividing Integers: Example 9TopicNumerical Expressions DescriptionThis example illustrates the division of three integers: 125 ÷ (-25) ÷ (-5). The solution demonstrates that dividing three integers, two negative and one positive, results in a positive quotient. The calculation is presented step-by-step: 125 ÷ (-25) ÷ (-5) = -5 / -5 = 1. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 1 | Math Example--Numerical Expressions--Multiplying Integers: Example 1TopicNumerical Expressions DescriptionExample 1 demonstrates the multiplication of two positive integers: 3 × 5. The solution shows that when multiplying two positive numbers, the result is always positive. In this case, 3 × 5 = 15. Numerical expressions are fundamental in mathematics, representing values through various operations like addition, subtraction, multiplication, and division. This collection of examples illustrates different scenarios of integer multiplication, helping students recognize patterns and develop strategies for solving numerical problems effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 10 | Math Example--Numerical Expressions--Multiplying Integers: Example 10TopicNumerical Expressions DescriptionExample 10 illustrates the multiplication of three integers: -5, 4, and -6. The solution demonstrates that when multiplying three integers with two negative numbers and one positive number, the result is positive. In this case, (-5) × 4 × (-6) = 120. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 11 | Math Example--Numerical Expressions--Multiplying Integers: Example 11TopicNumerical Expressions DescriptionExample 11 shows the multiplication of three integers: -7, -5, and 8. The solution demonstrates that when multiplying three integers with two negative numbers and one positive number, the result is positive. In this case, (-7) × (-5) × 8 = 280. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 12 | Math Example--Numerical Expressions--Multiplying Integers: Example 12TopicNumerical Expressions DescriptionExample 12 demonstrates the multiplication of three negative integers: -6, -2, and -8. The solution shows that when multiplying three negative numbers, the result is negative. In this case, (-6) × (-2) × (-8) = -96. This collection of examples covers various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations of negative integers, students can recognize patterns and develop a solid foundation for more complex mathematical operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 2 | Math Example--Numerical Expressions--Multiplying Integers: Example 2TopicNumerical Expressions DescriptionExample 2 illustrates the multiplication of a positive integer by a negative integer: 4 × (-6). The solution demonstrates that when multiplying a positive number by a negative number, the result is always negative. In this case, 4 × (-6) = -24. This collection of examples covers various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, students can recognize patterns and develop a solid foundation for more complex mathematical operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 3 | Math Example--Numerical Expressions--Multiplying Integers: Example 3TopicNumerical Expressions DescriptionExample 3 demonstrates the multiplication of a negative integer by a positive integer: (-7) × 6. The solution shows that when multiplying a negative number by a positive number, the result is always negative. In this case, (-7) × 6 = -42. This collection of examples explores various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, students can recognize patterns and develop a solid foundation for more complex mathematical operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 4 | Math Example--Numerical Expressions--Multiplying Integers: Example 4TopicNumerical Expressions DescriptionExample 4 shows the multiplication of two negative integers: (-8) × (-3). The solution demonstrates that when multiplying two negative numbers, the result is always positive. In this case, (-8) × (-3) = 24. This collection of examples covers various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, students can recognize patterns and develop a solid foundation for more complex mathematical operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 5 | Math Example--Numerical Expressions--Multiplying Integers: Example 5TopicNumerical Expressions DescriptionExample 5 illustrates the multiplication of three positive integers: 2 × 4 × 5. The solution demonstrates that when multiplying multiple positive numbers, the result remains positive. In this case, 2 × 4 × 5 = 40. This collection of examples explores various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, including multiple factors, students can recognize patterns and develop a solid foundation for more complex mathematical operations. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 6 | Math Example--Numerical Expressions--Multiplying Integers: Example 6TopicNumerical Expressions DescriptionExample 6 demonstrates the multiplication of three integers, including a negative number: 3 × 6 × (-4). The solution shows that when multiplying multiple numbers with one negative factor, the result is negative. In this case, 3 × 6 × (-4) = -72. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 7 | Math Example--Numerical Expressions--Multiplying Integers: Example 7TopicNumerical Expressions DescriptionExample 7 presents the multiplication of three integers with a negative number in the middle: 2 × (-5) × 6. The solution demonstrates that the position of the negative number doesn't affect the result, which is negative when there's an odd number of negative factors. In this case, 2 × (-5) × 6 = -60. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 8 | Math Example--Numerical Expressions--Multiplying Integers: Example 8TopicNumerical Expressions DescriptionExample 8 depicts the multiplication of three integers with a negative number at the beginning: (-6) × 3 × 5. The solution shows that the position of the negative number doesn't affect the result, which is negative when there's an odd number of negative factors. In this case, (-6) × 3 × 5 = -90. |
Numerical Expressions |
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Math Example--Numerical Expressions--Multiplying Integers: Example 9 | Math Example--Numerical Expressions--Multiplying Integers: Example 9TopicNumerical Expressions DescriptionExample 9 demonstrates the multiplication of three integers: 9, -3, and -4. The solution shows that when multiplying three integers with two negative numbers and one positive number, the result is positive. In this case, 9 × (-3) × (-4) = 108. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 06 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 06TopicIntegers DescriptionThis example demonstrates the operation: Subtract: 14 - 5. The solution states to subtract them like whole numbers. 14 - 5 = 9. Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 07 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 07TopicIntegers DescriptionThis example demonstrates the operation: Subtract: 8 - 10. The solution 8 = 10 = -2. Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 08 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 08TopicIntegers DescriptionThis example demonstrates the operation: Subtract: 16 - 16. The solution shows that 16 - 16 = 0. Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 09 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 09TopicIntegers DescriptionThis example demonstrates the operation: Subtract: 8 - (-3). The solution shows that it is rewritten as addition: 8 + 3 = 11. Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 10 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 10TopicIntegers DescriptionThis example demonstrates the operation: Subtract: -3 - 5. Solution: Subtracting a positive integer from a negative integer results in a negative difference. -3 - 5 = -8. Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 11 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 11TopicIntegers DescriptionThis example demonstrates the operation: Subtract: -8 - (-3). Solution involves rewriting the subtraction as an addition statement. -8 + 3 = -5. Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 12 | Two Integers: Example 12 TopicIntegers DescriptionThis example demonstrates the operation of subtracting two negative integers: -4 - (-6). The solution shows that when subtracting a negative integer, it can be rewritten as an addition statement: -4 + 6 = 2. Integer operations are crucial in mathematics as they provide foundational skills for more advanced topics. This collection explores various examples of integer subtraction, highlighting how rules apply across different scenarios. Such variety helps learners grasp concepts effectively. |
Numerical Expressions |
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Math Example--Numerical Expressions--Subtracting Two Integers: Example 13 | Math Example--Numerical Expressions--Subtracting Two Integers: Example 13TopicIntegers DescriptionThis example demonstrates subtracting a negative integer from another negative integer: -7 - (-7). The solution involves rewriting the subtraction as an addition statement, resulting in -7 + 7 = 0. Integer operations are fundamental in mathematics, providing essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such variety helps learners grasp concepts effectively. |
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 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 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--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--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 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 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 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 |
