PRESENTATION 1Whole Numbers

PLACE VALUE

•The value of any digit depends on its place value

•Place value is based on multiples of 10 as follows:

UNITSTENSHUNDREDSTHOUSANDS TENTHOUSANDS

HUNDREDTHOUSANDSMILLIONS

2 , 6 7 8 , 9 3 2

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

ROUNDING

•Used to make estimates•Rounding Rules:o Determine place value to which the number is to be rounded o 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

ROUNDING EXAMPLES

•Round 612 to the nearest hundredSince 1 is less than 5, 6 remains unchanged

Answer: 600

•Round 175,890 to the nearest ten thousand7 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

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

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

PROCEDURE FOR ADDING WHOLE NUMBERS

•Continue adding from right to left

•Therefore, 763 + 619 = 1,382

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

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

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

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

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

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

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

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

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

DIVISION WITH ZERO

•Zero divided by a number equals zeroo For example: 0 ÷ 5 = 0

•Dividing by zero is impossible; it is undefinedo For example: 5 ÷ 0 is not possible

PROCEDURE FOR DIVISION•Example: Divide 4,505 ÷ 6o Write division problem with divisor outside long division symbol

and dividend within symbolo Since 6 does not go into 4, divide 6 into 45.

45 6 = 7; write 7 above the first 5 in number 4505 as showno Multiply: 7 × 6 = 42; write this under 45o Subtract: 45 – 42 = 3

PROCEDURE FOR DIVISIONo Bring down the 0o Divide: 30 6 = 5; write the 5 above the

0o Multiply: 5 × 6 = 30; write this under 30o Subtract: 30 – 30 = 0o Since 6 cannot divide into 5, write 0 in the

answer above the 5. Subtract 0 from 5 and 5 is the remainder

o Therefore 4505 6 = 750 r5

ORDER OF OPERATIONS

•All arithmetic expressions must be simplified using the following order of operations:1.Parentheses2.Raise to a power or find a root3.Multiplication and division from left to right4.Addition and subtraction from left to right

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

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?

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