Business Math Day 1

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Business Math Day 1

• Whole Numbers and Decimals

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Learning Objectives

• Read decimals
• Write decimals
• Round decimals
• Add decimals
• Subtract decimals
• Multiply decimals
• Divide decimals

• Read whole numbers
• Write whole numbers
• Round whole numbers
• Add whole numbers
• Subtract whole numbers
• Multiply whole numbers
• Divide whole numbers

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1.1.1 Read whole numbers

• Our system of numbers, the decimal number system
  uses 10 symbols called digits 0,1, 2, 3, 4, 5,
  6, 7, 8, and 9.
• Place-value system a number system that
  determines the value of a digit by its position
  in a number.

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How to read whole numbers

• Beginning with the ones place on the right, the
  place values are grouped in digits of three
  places.
• For example 145,874,322
• Each group is called a period.

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Understanding place value

• Each period has a name and a ones place, a tens
  place and a hundreds place
• In a number, the first period from the left may
  have fewer than three digits.
• In many cultures, the periods are separated by
  commas.

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Read whole numbers

• Identify the period name of the leftmost group.
• Read the three digit number from left to right.
• Name the period.
• 34,786,654 would read thirty four million seven
  hundred eighty six thousand six hundred fifty
  four.

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Note these exceptions

• Do not read or name a period that is all zeros.
• 34,000,892 would read thirty four million eight
  hundred ninety two.
• Do not name the units period (892).

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When reading whole numbers, remember that

• The period name will be read at each comma.
• Period names are read in the singular
  (thousand not thousands).
• Hundreds is not a period name.
• Do not say the word and when reading whole
  numbers.
• Calculator displays ordinarily do not show
  commas insert when writing the number.

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1.1.2 Write whole numbers.

• Begin recording digits from left to right.
• Insert a comma at each period name.
• Every period after the first period must have
  three digits.
• Insert zeros as necessary.

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Heres an example

• Seven million, three hundred three thousand,
  nine hundred twenty eight.
• 7, million
• 303, thousand
• 928 (units)
• is written 7,303,928.

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1.3.3 Rounding whole numbers

• Rounding to a specific place
• Identify the place
• (nearest hundred, for example)
• Look at the number immediately to the right.
• Is it 5 or higher? Round up.
• Is it 4 or lower? It stays the same.
• All digits to the right of the specified place
  become zeros.

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Try these examples

• Round to the nearest hundred
• 2,345 12,517 234,567 12,345,078
• And the answers are
• 2,300 12,500 234,600 12,345,100

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1.2.1 Add whole numbers.

• Write the numbers in a vertical column, aligning
  digits according to their places.
• Beginning with the ones column, add the place
  digits.
• Add, if necessary, to the tens column.
• Repeat the operation, adding to the hundreds
  column, if necessary until you have reached the
  farthest column of digits to the left.

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Key Terms

• Addends numbers being added
• Sum or total The answer or result of addition.
• Commutative property of addition two or more
  numbers can be added in either order without
  changing the sum
• Associative property of addition When more than
  two numbers are being added, the addends can be
  grouped by two at a time in any way.

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Try this example

• Add the ones column
• Place the 8 the bottom of the ones column
• Carry the 2 to the tens column
• Place the 4 in the tens column.
• Carry the 2.
• Finish the operation
• Answer 64,948

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Estimating

• Estimate to find a reasonable approximate
  answer for a calculation.
• Use estimating as a quick tool when an exact
  number is not required.
• Round whole numbers to the place desired for an
  estimate.

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Try this example

• What was the weeks total to the nearest hundred?
• Answer 3,200

• Sales for last weeks concession stand
• Monday 219
• Tuesday 877
• Wednesday 455
• Thursday 614
• Friday 980

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1.2.2. Subtracting whole numbers

• The order of the numbers is important so
  therefore, subtraction is not commutative.
• 8 3 ? 3 8
• Grouping in subtraction is important.
  Subtraction is not associative.
• (8 - 3) -1 5 1 4 but
• 8 - (3 -1) 8 - 2 6
• 4 ? 6

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Key Terms

• Minuend the beginning amount or number that a
  second number is being subtracted from.
• Subtrahend the number being subtracted.
• Difference the answer or result of subtracting
• Borrow regroup digits in the minuend by
  borrowing 1 from the digit to the left of the
  specified place and adding 10 to the specified
  place.

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Using rounding in subtraction

• Subtract 128 from 1,345 by rounding each number
  to the nearest hundred to estimate the
  difference.
• 128 would become 100.
• 1,345 would become 1,300.
• The estimated difference would be 1,200.

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Try this example

• Borrow 1 from the tens column.
• Subtract 8 from 13.
• Borrow 1 from the hundreds column
• Subtract 9 from 18
• Borrow 1 from the thousands column
• Subtract 5 from 11
• Answer 695

• Subtract

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1.2.3 Multiplying whole numbers

• Numbers can be multiplied in any order without
  affecting the result.
• 8 x 3 x 4 4 x 3 x 8
• 96 96

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Key terms

• Multiplicand the number being multiplied
• Multiplier the number multiplied by
• Factor each number involved in multiplication
• Product the answer or result of multiplication
• Partial product the product of one digit of the
  multiplier and the entire multiplicand

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Multiply these numbers

• Multiply

• Identify each

Multiplicand Multiplier Partial product Partial
product Product
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Try these examples(without using a calculator)

• 123 x 466 ?
• Answer 57,318
• 67 x 120 ?
• Answer 8,040
• 348 x 27 ?
• Answer 9,396

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1.2.4 Divide whole numbers

• Division is used to find the number of equal
  parts a whole quantity can be separated into.
• A 40 tip is shared equally among 5 servers. How
  much does each server receive?
• 40 5 servers 8 each

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Key Terms

• Dividend the number being divided or the total
  quantity
• Divisor The number to divide by
• Quotient The answer or result of the operation
• Whole-number part of the quotient the quotient
  without regard to its remainder
• (continued on the next slide)

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Key Terms

• Remainder of quotient a number that is smaller
  than the divisor that remains after division is
  complete.
• Partial dividend the part of the dividend that
  is being considered at a given step of the
  process.
• Partial quotient the quotient of the partial
  dividend and the divisor.

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Remainders

• There will be a remainder if an amount is too
  small to be further divided by the divisor.
• For example 152 3 50 R 2
• That amount may be expressed as a remainder (R
  2), a fraction, or a decimal.

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How to divide whole numbers

• 1235 5 ?
• 1. Beginning with its leftmost digit, identify
  the first group of digits of the dividend that is
  larger than or equal to the divisor.
• Is it 1? No.
• Is it 12? Yes.
• 5 goes into 12 two times. Place the 2 above the
  2 in the dividend.
• (Go on to next slide)

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Division step by step

• 2. Multiply 2 by the divisor. Place 10 under the
  12 and subtract. The result is 2.
• 3. Bring down the following digit which is 3 and
  divide 5 into 23. The result is 4.
• 4. Place the 4 directly above the 3 in the
  dividend. Multiply 4 by the divisor.
• (Go on to next slide)

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Finish the problem

• 5. Place 20 under the 23 and subtract. The
  result is 3.
• 6. Bring down the last digit which is 5 and
  divide 5 into 35. The result is 7. Place 7
  directly above the 5.
• 7. You have finished and the answer is 247.

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Try these examples(without a calculator)

• 6,750 cases of detergent will be distributed
  evenly to 25 local stores. How many will each
  receive?
• Answer 270
• 420 bottles of fabric softener in the warehouse
  are packed a dozen to case. How many cases are
  there in the warehouse?
• Answer 35

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3.1 Decimals and the Place Value System

• Read and write decimals
• Round decimals
• 1.2345 rounded to the nearest tenth is 1.2

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3.1.1 Read and write decimals

• Our money system, based on the dollar, uses the
  decimal system.
• Moving one place from right to left increases the
  value ten times.
• Moving one place from left to right, causes the
  value of the digit to become ten times smaller.

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How much is 0.1?

• It is one part of a 10-part whole.
• 0.1 is read one tenth
• If this chart represented a dollar, the white
  segment would be equal to 0.10.

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The decimal point

• Separates the whole number part from the decimal
  part, as the number extends from left to right.
• 34.7 is read thirty four and seven tenths
• or 34 point 7.

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Place value names

• The first place to the right of the decimal point
  is tenths. (0.1)
• Second place is hundredths. (0.01)
• Third place is thousandths. (0.001)
• Fourth place is ten-thousandths. (0.0001)
• and so on.

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Place value names
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How to read or write a decimal

• 3.12 Three and twelve hundredths
• 9.067 Nine and sixty-seven thousandths.
• 4.5 Four and five tenths.
• Read the whole number part first, saying and
  to indicate the beginning of the decimal part of
  the number.

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Reading decimals as money amounts

• When reading numbers that represent money
  amounts, read whole numbers as dollars.
• Decimal amounts are read as cents.
• 35.98 is read thirtyfive dollars and 98 cents.

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3.1.2 Round to a specific decimal place

• 1. Find the digit in the specified place.
• 2. Look at the next digit to the right.
• If this digit is less than 5, eliminate it and
  all digits to its right.
• If the digit is 5 or more, add 1 to the digit in
  the specified place, and eliminate all digits to
  its right.

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Try these examples

• Round to the nearest tenth
• 12.456
• 12.5
• 31,343.387
• 31,343.4
• 346.2778
• 346.3

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3.2 Operations with decimals

• Add and subtract decimals
• Multiply decimals
• Divide decimals
• 3.234 6.8 ?

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Add and subtract decimals

• Write the numbers in a vertical column, aligning
  digits according to their places.
• Attach extra zeros to the right end of each
  number so each number has the same quantity of
  digits.
• Add or subtract as though the numbers are whole
  numbers.
• Place the decimal point in the sum or difference
  to align with the decimal point in the respective
  operation.

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Be orderly to avoid mistakes.
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Add zeros where necessary

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Try these examples.(Without using your
calculator)

• 7.098 2.6 0.8 13.999
• 24.497
• 10.008 7.6
• 2.408
• .976 - .04217
• .93383

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3.2.2 Multiply decimals

• Multiply the decimal numbers as though they are
  whole numbers.
• Count the digits in the decimal parts of both
  decimal numbers.
• Place the decimal point in the product so that
  there are as many digits in its decimal part as
  there are digits you counted in the previous
  step.
• If necessary, attach zeros to the left end of the
  product to place the decimal point accurately.

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Look at this example.

• 3.45 x 4.082
• How many places are there to the right of the
  decimal point?
• Five so, the answer will have five places to the
  right of the decimal.
• The answer is 14.08290
• The last zero can be dropped and the answer would
  be 14.0829.

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Try these examples(Without using your calculator)

• 2.4 x .06
• 0.144
• 3.07 x 8.008
• 24.58456
• .01 x 1.001
• 0.01001

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3.2.3 Divide decimals

• Divide a decimal by a whole number
• Place a decimal point for the quotient directly
  above the decimal point in the dividend.
• Divide as though the decimal points are whole
  numbers.
• 3.4 divided by 3 ?

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Try these examples(Without using your calculator)

• 12.4 6
• 2.06 (repeating)
• 36.5 2
• 18.25
• 192.45 50
• 3.849

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Try this word problem

• Jill wants to buy a bottle of detergent. If a
  100-ounce bottle costs 6.49 and a 50- ounce
  bottle costs 3.99, which would be the better buy
  on cost per ounce basis? What are those amounts?
• Answer The 50 - ounce bottle has a cost of
  .0798 per ounce while the 100-ounce bottle has a
  cost of .0649 per ounce. The bigger bottle is a
  better buy.

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Divide by a decimal

• Change the divisor to a whole number by moving
  the decimal point to the right, counting the
  places as you go.
• Use a caret ( ) to show the new position of the
  decimal point.
• Move the decimal point in the dividend to the
  right as many places as you moved the divisor.
• Place the decimal point for the quotient directly
  above the new decimal point for the dividend.
• Divide as you would divide a whole number.

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Try these examples.Without using your calculator)

• 12.3 .06
• 205
• 15 .004
• 3,750
• 20.765 .08
• 259.5625

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Try these word problems.

• Bill Sullivan has an hourly rate of 14.32 and
  his gross weekly pay was 572.80. How many hours
  did he work?
• 40 hours
• Jan Stevens has an hourly rate of 7.75 per hour
  and her gross weekly pay was 193.75. How many
  hours did she work last week?
• 25 hours

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Resources

• All resources can be found on
• The resource drive (Resource\BM\Math)
• Online labs can be found at
• http//linux.herzing.ca/kim
• (as of July 30, this link only works from school
  network support is to have it up online by the
  end of this week)

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Lab work / Homework

• Lab work
• Online Lab 1
• Homework due at the end of the week
• Chapter 3 Exercises Set A