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PRESENTATION 1 Whole Numbers

PRESENTATION 1 Whole Numbers. PLACE VALUE. The value of any digit depends on its place value Place value is based on multiples of 10 as follows:. TEN THOUSANDS. HUNDRED THOUSANDS. THOUSANDS. HUNDREDS. UNITS. MILLIONS. TENS. 2 , 6 7 8 , 9 3 2.

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PRESENTATION 1 Whole Numbers

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  1. PRESENTATION 1Whole Numbers

  2. PLACE VALUE • The value of any digit depends on its place value • Place value is based on multiples of 10 as follows: TEN THOUSANDS HUNDRED THOUSANDS THOUSANDS HUNDREDS UNITS MILLIONS TENS 2 , 6 7 8 , 9 3 2

  3. ESTIMATING • Used when an exact mathematical answer is not required • A rough calculation is called estimating or approximating • Mistakes can often be avoided when estimating is done before the actual calculation • When estimating, exact values are rounded

  4. ROUNDING • Used to make estimates • Rounding Rules: • Determine place value to which the number is to be rounded • Look at the digit immediately to its right • If the digit to the right is less than 5, replace that digit and all following digits with zeros • If the digit to the right is 5 or more, add 1 to the digit in the place to which you are rounding. Replace all following digits with zeros

  5. ROUNDING EXAMPLES • Round 612 to the nearest hundred Since 1 is less than 5, 6 remains unchanged Answer: 600 • Round 175,890 to the nearest ten thousand 7 is in the ten thousands place value, so look at 5. Since 5 is greater than or equal to 5, change 7 to 8 and replace 5, 8, and 9 with zeros Answer: 180,000

  6. ADDITION OF WHOLE NUMBERS • The result of adding numbers is called the sum • The plus sign (+) indicates addition • Numbers can be added in any order

  7. PROCEDURE FOR ADDING WHOLE NUMBERS • Example: Add 763 + 619 • Align numbers to be added as shown; line up digits that hold the same place value • Add digits holding the same place value, starting on the right: 9 + 3 = 12 • Write 2 in the units place value and carry the one

  8. PROCEDURE FOR ADDING WHOLE NUMBERS • Continue adding from right to left • Therefore, 763 + 619 = 1,382

  9. SUBTRACTION OF WHOLE NUMBERS • Subtraction is the operation which determines the difference between two quantities • It is the inverse or opposite of addition • The minus sign (–) indicates subtraction

  10. PROCEDURE FOR SUBTRACTING WHOLE NUMBERS • Example: Subtract 917 – 523 • Align digits that hold the same place value • Start at the right and work left: 7 – 3 = 4

  11. PROCEDURE FOR SUBTRACTING WHOLE NUMBERS • Since 2 cannot be subtracted from 1, you need to borrow from 9 (making it 8) and add 10 to 1 (making it 11) • Now, 11 – 2 = 9; 8 – 5 = 3 • Therefore, 917 – 523 = 394

  12. MULTIPLICATION OF WHOLE NUMBERS • Multiplication is a short method of adding equal amounts • There are many occupational uses of multiplication • The times sign (×) is used to indicate multiplication

  13. PROCEDURE FOR MULTIPLICATION • Example: Multiply 386 × 7 • Align the digits on the right • First, multiply 7 by the units of the multiplicand: 7×6 = 42 • Write 2 in the units position of the answer

  14. PROCEDURE FOR MULTIPLICATION • Multiply the 7 by the tens of the multiplicand: 7 × 8 = 56 • Add the 4 tens from the product of the units: 56 + 4 = 60 • Write the 0 in the tens position of the answer

  15. PROCEDURE FOR MULTIPLICATION • Multiply the 7 by the hundreds of the multiplicand: 7 × 3 = 21 • Add the 6 hundreds from the product of the tens: 21 + 6 = 27 • Write the 7 in the hundreds position and the 2 in the thousands position • Therefore, 386 × 7 = 2,702

  16. DIVISION OF WHOLE NUMBERS • In division, the number to be divided is called the dividend • The number by which the dividend is divided is called the divisor • The result is the quotient • A difference left over is called the remainder

  17. DIVISION OF WHOLE NUMBERS • Division is the inverse, or opposite, of multiplication • Division is the short method of subtraction • The symbol for division is ÷ • The long division symbol is • Division can also be expressed in fraction form such as 20 99

  18. DIVISION WITH ZERO • Zero divided by a number equals zero • For example: 0 ÷ 5 = 0 • Dividing by zero is impossible; it is undefined • For example: 5 ÷ 0 is not possible

  19. PROCEDURE FOR DIVISION • Example: Divide 4,505 ÷ 6 • Write division problem with divisor outside long division symbol and dividend within symbol • Since 6 does not go into 4, divide 6 into 45. 45  6 = 7; write 7 above the first 5 in number 4505 as shown • Multiply: 7 × 6 = 42; write this under 45 • Subtract: 45 – 42 = 3

  20. PROCEDURE FOR DIVISION • Bring down the 0 • Divide: 30  6 = 5; write the 5 above the 0 • Multiply: 5 × 6 = 30; write this under 30 • Subtract: 30 – 30 = 0 • Since 6 cannot divide into 5, write 0 in the answer above the 5. Subtract 0 from 5 and 5 is the remainder • Therefore 4505  6 = 750 r5

  21. ORDER OF OPERATIONS • All arithmetic expressions must be simplified using the following order of operations: • Parentheses • Raise to a power or find a root • Multiplication and division from left to right • Addition and subtraction from left to right

  22. ORDER OF OPERATIONS • Example: Evaluate (15 + 6) × 3 – 28 ÷ 7 21 × 3 – 28 ÷ 7 63 – 4 63 – 4 = 59 • Therefore: (15 + 6) × 3 – 28 ÷ 7 = 59 • Do the operation in parentheses first (15 + 6 = 21) • Multiply and divide next (21 ×3 = 63) and (28 ÷ 7 = 4) • Subtract last

  23. PRACTICAL PROBLEMS • A 5-floor apartment building has 8 electrical circuits per apartment. There are 6 apartments per floor. How many electrical circuits are there in the building?

  24. PRACTICAL PROBLEMS • Multiply the number of apartments per floor times the number of electrical outlets • Multiply the number of floors times the number of outlets per floor obtained in the previous step • There are 240 outlets in the building

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