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ACC Module #2 Unit 2.1

ACC Module #2 Unit 2.1

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ACC Module #2 Unit 2.1

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  1. DemingEarly College High SchoolUnit 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.1 Rational numbers

  2. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers Integers are the whole numbers together with their negatives. They include numbers like 5, 24, 0, -6 and 15. They DO NOT include fractions or numbers that have digits after the decimal point.Rational numbers are all numbers that can be written as a fraction using integers. A fraction is written as x/y and represents the quotient of x being divided by y. .

  3. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers Examples of rational numbers include and .The number on the top is called the numerator, and the number on the bottom is called the denominator. Because every integer can be written as a fraction with a denominator of 1, they are also rational numbers. Repeating numbers are also rational numbers(i.e. and 6.4444).

  4. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers An irrational number is a real number that is not rational. For example, are irrational numbers because they can not be expressed as a quotient of two integers.

  5. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers Classify the following as rational or irrational: This number is irrational because it is the square root of an integer that is not a perfect square. It cannot be expressed as a quotient of two integers. This number is rational because it can be expressed as a quotient of two integers. This number is irrational because it is the difference of an irrational number and a rational number.

  6. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers When adding integers and negative rational numbers, there are some basic rules to determine if the solution is negative or positive. Adding two positive numbers results in a positive number: 3.3 + 4.8 = 8.1 Adding two negative numbers results in a negative number: (-8) + (-6) = -14 .

  7. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers Adding one positive and one negative number requires taking the absolute values and finding the difference between them. Then, the sign of the number that has the higher absolute value is used. For example, (-9) + 11, has a difference of absolute values of 2. The final solution is +2 because 11 has the higher absolute value. Another example is 9 + (-11), which has a difference of absolute values of 2. The final solution is -2 because 11 has the higher absolute value. .

  8. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers When subtracting integers and negative rational numbers, one has to change the problem to adding the opposite and then applying the rules of addition. Subtracting two positive numbers is the same as adding one positive and one negative number. For example, 4.9 – 7.1 is the same as 4.9 + (-7.1). The solution is -2.2 since the absolute value of -7.1 is greater. .

  9. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers Another example is 8.5 – 6.4 which is the same as 8.5 + (-6.4). The solution is 2.1 since the absolute value of 8.5 is greater. Subtracting a positive number from a negative number results in a negative value. For example, (-12) - 7 is the same as (-12)+(-7) with a solution of -19. .

  10. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers Subtracting a negative number from a positive number results in a positive value. For example, 12 - (-7) is the same as 12 + 7 = 19. And 8 – (-5) is the same as 8 + 5 =13. .

  11. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers What is the result of each of the following? 1) 7 + 14 2) (-6) + (-5) . 3) 10 + (-3) 4) 15 – 6.5

  12. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers What is the result of each of the following? 1) 7 + 14 21 2) (-6) + (-5) -11 . 3) 10 + (-3) 7 15 + (-6.5) = 8.5 4) 15 – 6.5

  13. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers For multiplication and division of integers and rational numbers, if both numbers are positive or both numbers are negative, the result is a positive value. For example, 3 x 13 has a solution of +39 since both numbers are positive. For example, (-1.7)(-4) has a solution of +6.8 since both numbers are negative values. .

  14. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers If one number is positive and another number is negative, the result is a negative value. For example, (-15) / 5 has a solution of -3 since there is one negative number. And since there is one negative Number. .

  15. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers What is the result of each of the following? 1) 7 x 14 2) (-6) x (-5) . 3) 10 x (-3) 4) -15 x 6

  16. Unit 2.0 QAS 2.1 Rational Numbers 2.1.1 Computation with Integers and Negative Rational Numbers What is the result of each of the following? 1) 7 x 14 98 2) (-6) x (-5) 30 . 3) 10 x (-3) -30 -90 4) -15 x 6

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