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ACC. Module #1 Unit 1.1

ACC. Module #1 Unit 1.1

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ACC. Module #1 Unit 1.1

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  1. DemingEarly College High SchoolModule 1.0 Arithmetic Unit 1.1 Whole Number and Fraction Operations

  2. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Addition combines two quantities together. With whole numbers, this is two sets of things and merging them into one, then counting the results. For example 4 + 3 = 7. When adding numbers the order does not matter: 3 + 4 = 7, also. Longer lists of whole numbers can also be added together. The result of adding numbers is called the sum. With fractions, the number on the top is the numerator and the number on the bottom is the denominator. To add fractions, the denominator must be the same – a common denominator. To find a common denominator, the existing numbers on the bottom must be considered, and the lowest number they will both multiply into must be determined.

  3. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Consider the following equation:The numbers 3 and 6 both multiply into 6. Three can be multiplied by 2, and 6 can be multiplied 1. The top and bottom of each fraction must be multiplied by the same number. Then the numerators are added together to get a new numerator.

  4. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions What if the denominators are not multiples of each other? Consider the following equation:Since the numbers of the denominator are not multiples of each other, we can find the common denominator of the fractions by multiplying the denominators together. The numbers 3 and 7 are multiplied and the result is 21. We must divide each denominator into the common denominator to get the number we multiply both the numerator and denominator by.

  5. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Ok – now you try it.1. Add:

  6. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Ok – now you try it.1. Add: Answer:

  7. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Ok – now you try it.2. Add:

  8. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Ok – now you try it.2. Add: Answer:

  9. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Ok – now you try it.3. Add

  10. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.1 Addition With Whole Numbers and Fractions Ok – now you try it.3. Add Answer:

  11. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions Subtraction is taking one quantity away from another, so it is the opposite of addition. The expression 4 – 3 means taking 3 away from 4. So, 4 – 3 = 1. In this case, the order does matter, since it entails taking one quantity away from the other, rather than just putting two quantities together. To subtract fractions, the denominators must be the same – a common denominator . Again, to find a common denominator, the existing numbers on the bottom must be considered, and the lowest number they will both multiply into must be determined. Then, subtract the numerators to get a new numerator

  12. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions There are 3 simple steps to subtract fractions: Step 1. Make sure the bottom numbers (the denominators) are the same. Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator. Step 3. Simplify the fraction (if needed).

  13. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions Consider the following equation:The numbers 6 and 3 both multiply into 6. Six can be multiplied by 1, and 3 can be multiplied 2. The top and bottom of each fraction must be multiplied by the same number. Then the numerators are added together to get a new numerator.

  14. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions Consider the following equation:The numbers 6 and 3 both multiply into 6. Six can be multiplied by 1, and 3 can be multiplied 2. The top and bottom of each fraction must be multiplied by the same number. Then the numerators are added together to get a new numerator.

  15. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions Ok – now you try it.1. Subtract:

  16. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions Ok – now you try it.1. Subtract:

  17. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.2 Subtraction With Whole Numbers and Fractions Ok – now you try it.3. Subtract: Answer:

  18. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions When multiplying fractions, common factors can cancel or divide into one another, when factors that appear in the numerator of one fraction and the denominator of the other fraction. The number 3 and 9 have a common factor of 3, so that factor can be divided out. Same Sign: The product of two numbers with the same sign is positive. Different Signs: The product of two numbers with different signs is negative.

  19. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions Ok – now you try it.1. Multiply: 6 x 17 = ? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. Multiply: -5 x -4 = ?

  20. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions Ok – now you try it.1. Multiply: 6 x 17 = ? Answer: 17 x 6 102 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. Multiply: -5 x -4 = ? Answer: -5 x -4 Same signs = positive +20

  21. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions 3. Multiply: -0.5(-0.4) = ? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. Multiply: -3(-9) = ?

  22. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions 3. Multiply: -0.5(-0.4) = ? Answer: -0.5 x -0.4 Same signs = positive +0.20 Keep track of decimal point - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. Multiply: -3(-9) = ? Answer: -3 x -9 Same signs = positive +27

  23. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions 5. Multiply these fractions: 1 / 6 x 5 /12 = ? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 6. Multiply:

  24. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.3 Multiplication With Whole Numbers and Fractions 5. Multiply these fractions: 1 / 6 x 5 /12 = ? Answer: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 6. Multiply: Answer: Different signs = negative

  25. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions Division is the opposite of multiplication. With whole numbers, it means splitting up one number into sets of equal sizes. For example, 16 / 8 is the number of sets of eight things that can be made out of sixteen things. Thus, 16 / 8 = 2. As with subtraction, the order of the numbers will make a difference, here. The answer to a division problem is called the quotient, while the number in front of the division sign is called the divisor.

  26. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions Ok – now you try it.1. Divide: 24 / 3 = ? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. Divide:

  27. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions Ok – now you try it.1. Divide: 24 / 3 = ? Answer: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. Divide: Answer: Different signs = negative

  28. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions 3. Divide: 24 / 12 = ? - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. Divide:

  29. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions 3. Divide: 24 / 12 = ? Answer: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. Divide: Answer: Different signs = negative

  30. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions To divide fractions, the first fraction must be multiplied by the reciprocal of the second fraction. Then the numerators are multiplied together as well as the denominators. [The reciprocal of the fraction is . Here is an example: CAUTION: Division by 0 is undefined. However, dividing 0 by a nonzero number gives the quotient of 0. For example: is undefined, but = 0 (because 0 x 6 = 0)

  31. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions 1. Divide: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. Divide:

  32. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions 1. Divide: Answer: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2. Divide: Answer:

  33. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions 3. Divide: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. Divide:

  34. Unit 1.0 Arithmetic 1.1 Whole Number and Fraction Operations 1.1.4 Division With Whole Numbers and Fractions 3. Divide: Answer: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -- - - - - - - - - - -- - - -- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4. Divide: Answer:

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