Section 1.6 Division Review:

Transcription

1 Section 1.6 Division Review: Quotient 2 / 2 8, 2 Dividend Divisor Quotient also we can do it this way :2 Divisor 8 Dividend Checking Division: Quotient X Divisor + Remainder = Dividend Translation: The answer to the division problem times the number you divided by, plus the remainder, should equal the number you divided into. /2 leaves no remainder, so remainder = 0 8x2 +0 = What about /? R1 Check: Quotient X Divisor + Remainder = Dividend 5 x + 1 = 15+1= yes

2 For example: If 62 people had the winning lottery ticket for $1,400, how much would each person receive? Divide 1,400 by Remainder R28 Each would receive $506, and there would be $28 leftover. Who get s it? Where do we start? We first only look at the first few digits of the dividend, which is What is the smallest number among those digits that 62 can go into? is too small 1 is too small. 14 is big enough. The first digit of the quotient will be above the 4. Now choose a number that you think when multiplied by 62, will be close to 14. How? Estimate by rounding 62 down to 60, and rounding 14 down to 00. We know 00/60 = 0/6 = 5, so let s try 5 x 62, which is 10. This is close to 14. Subtract = does not go into 4 so bring down the next digit of 1400, which is 0. Does 62 go into 40? No, so we must put a 0 in that place value after 5. (There must be a digit in the quotient (answer) above every digit in the dividend. So we must put a 0 before going to the next digit). Now bring down the next digit of 1400, which is 0. This gives us 400. Does 62 go into 400? Rounding down to estimate we know 60x6=60, which is getting close, and 62x6=72, this is the closest we re gong to get to 400 without going over, so let s try 6. Subtract = 28. There are no more digits to bring down, so 28 is the remainder.

3 Division Properties: Division is the inverse of multiplication. That is, does the opposite of what multiplying does. a(b) = c a = c/b b = c/a If a times b is c, then c/b answers the question, c times what equals b? and c/a answers the question, c times what equals a? Division with 0 If a represents any nonzero number, 0/a = 0 If a represents any nonzero number, a/0 is undefined. 0/0 is undetermined. More Division Properties a/1 = a a/a = 1 (provided that a 0) Example: A total of 2 girls tried out for a city volleyball program. How many girls should be put on the team roster if the following requirements must be met? 1)All the teams must have the same number of players. (find a number that goes exactly into 2, so there is no remainder) 2) A reasonable number of players on a team is 7 to 10 (divide 2 players by 7 players per team, then 8, then 9, then 10). But don t bother with 10 because we know 10 doesn t go exactly into 2. ) There must be an even number of teams. (The quotient must be EVEN). 6<7, and there are no more digits left to carry down, so 6 is the remainder and 2 is not exactly divisible by goes exactly into 2, but the quotient is 27, which is ODD. (Does not meet rd req.) This meets all requirements: 9 players per team leaves no remainder, 9 is an acceptable number for a team (which is a number between 7 and 10), and the number of teams is, which is an even number.

4 ORDER OF OPERATIONS Please: do all operations within parentheses and other grouping symbols (such as [ ], or operations in numerators and denominators of fractions) from innermost outward. Excuse: calculate exponents My,Dear: do all multiplications and divisions as they occur from left to right Aunt,Sally: do all additions and subtractions as they occur from left to right. Example: (8-6) 2 Expression in parentheses gets calculated first = (2) 2 Next comes all items with exponents = (4) Next in order comes multiplication. Multiplication and Division always come before addition or division, even if to the right. = Now when choosing between when to do addition and when to do subtraction, always go from left to right, so do 20-2 first, because the subtraction is to the left of the addition. = 18 + Now finally we can do the addition. = 0 Example 9 on p.50 Evaluate: Numerator Denominator 2(1) 2 2 2(1) (8) 2 1 Think of the numerator and denominator of this fraction as each being their own grouping. In fact, you must use parentheses when doing these operations on a calculator. Put parentheses around the numerator, then use the button for the fraction bar, then put parentheses around the denominator. Also, some calculators do not recognize (2 2 ) as multiplication, and there is a special button for exponents; so you might have to use ( (2 x y ) )

5 Arithmetic Mean (Average) To find the mean of a set of objects, divide the sum of the object s values by the number of objects. In 2005 USC had a perfect season of winning games (not including the ROSE BOWL on Jan. 4, 2006!). Find their average margin of victory (difference between winning and losing scores). DATE OPPONENT W/L SCORE ATTEND Sep, 2005 at Hawai`i W Sep 17, 2005 ARKANSAS W *Sep, 2005 at # Oregon W *Oct 01, 2005 at #14 Arizona State W *Oct 08, 2005 ARIZONA W Oct 15, 2005 at #9 Notre Dame W *Oct 22, 2005 at Washington W *Oct 29, 2005 WASHINGTON STATE W *Nov 05, 2005 STANFORD W *Nov, 2005 at California W Nov 19, 2005 # FRESNO STATE W *Dec 0, 2005 #11 UCLA BRUINS W Taken from (617) (70 17) (45 1) (8 28) (42 21) (4 1) (51 ) (55 1) (51 21) (5 10) (50 42) (66 19) Average Average Margin of Victory was approx. 29 points.