BASIC MATH 9: COMPUTATION CONT. -- MULTIPLICATION, DIVISION, ETC.

GREAT WAY TO DIVIDE

(EVEN IN LONG DIVISION): 525 / 8 500 / 8 = ? THINK IN 10s: 8 x ?10s = 500 8 x 6 10s = 480 etc

.006 / .3 =

1. move decimal over to right of three, do likewise with .006, then divide: .02 2. estimation: .3 x .1 = .03 (too high) .3 x .01 = .003 (too low) .3 x .02 - .006 Yes 3. 6/1000 / 3/10 = 6/1000 x 10/3 = 10s cancel, leaving 6/100 x 1/3 = 2/100 x 1 = .02 *remember: when dividing fractions by fractions, convert to multiplication by taking reciprocal 1/2 / 4 is same as saying 1/2 x 1/4 (or 4 X y = 1/2) likewise, 1/2 / 1/4 is same as 1/2 x 4 or 1/4 X y = 1/2

DIVIDING FRACTIONS ILLUSTRATION: 1/2 / 6

1/2 / 6 IS SAYING 1/2 DIVIDED BY 6; ALSO 1/6 OF 1/2, OR 1/2 X 1/6.

10 TO 1 = 10 TO 2 10 TO 3 10 TO 4

10 100 1000 10,0001

1,000,000 / 10 = 100,000 / 10 = 10,000 / 10 = 1,000 / 10 = 100 / 10 = 10 / 10 =

10 100,000s in 1,000,000 10 10,000s in 100,000 10 1000s in 10,000 10 100s in 1000 10 10s in 100 1 10 in 10

DIVISION: 14/2=7 TERMS:

14 = DIVIDEND, 2 = DIVISOR, 7 = QUOTIENT

4 3/4 / 1 1/2 =

19/4 / 3/2 = 19/4 x 2/3 (2/3 used to cancel out 3/2) 4 and 2 reduced by factor of 2 19/2 x 1/3 = 19/6 or 3 1/6

***WHY AND HOW DO WE MOVE DECIMALS OVER WHEN DOING LONG DIVISION?

24.00 / .16 A COUPLE REASONS: 1. 24 / .16 IS SAYING: .16 X y = 24, so may multiply both sides by 100 to simplify finding the answer. also: 2. 24/ .16, like any fraction, may be multiplied by any number as long as both the numerator and denominator are multiplied by it. (in this case, 100):) (may simply computing)

3/4 / 1/8 = 3/4 x 8 (or 8/1) 4 and 8 are reduced answer

3/4 x 8 (or 8/1) 4 and 8 are reduced answer = 6

WHEN DIVIDING WITH TENS OR MULTIPLES OF 10, EASY WAY TO COMPUTE: EX 320,000 320,000 / 40 320,000 / 4000 (NOTE OTHERS LIKE 320,000 / 4 = 80,000)

32/4 = 8, TAKE AWAY ONE ZERO (SINCE DIVISOR HAS ZERO): 8000. WITH SECOND PROBLEM, TAKE AWAY 3 ZEROS SINCE DIVISOR HAS 3 ZEROS. ANSWER IS 80 (NOTE OTHERS LIKE 320,000 / 4 = 80,000) UNDERSTANDING: EACH ADDITIONAL POWER OF TEN IN THE DIVISOR (EACH EXTRA "0") REDUCES THE QUOTIENT BY A POWER OF TEN, SINCE THAT'S WHAT IT'S BEING DIVIDED BY.:) CAN ALSO BE THOUGHT OF AS: 320000/4X10 OR 32 X 10,000 / 4 X 10 OR 32 X 10 X 1000 / 4 X 10 IN EVERY CASE, THE NUMBERS CANCEL OUT, LEAVING 8000. ****IT IS AMAZING THAT ANY (?)NUMBER MULTIPLIED BY 10 WILL BE ITSELF WITH A ZERO ADDED.

4 LBS TRAIL MIX. YOU WANT TO PUT IN BAGS SO THAT THERE IS 2/3 POUND IN EACH BAG. HOW MANY BAGS CAN YOU FILL?

4 / 2/3 = 2/3X = 4 = 4 X 3/2 (RECIPROCAL) = 6 BAGS OR SIMPLY: 4 / 2/3 = (MULTIPLY BOTH NUM AND DEN BY RECIPROCAL OF 2/3: 3/2; THIS RENDERS: 4 X 3/2 / 1 = 6

DIVIDING WITH FRACTIONS

7/8 / 3 = is same as 7/8 x 1/3, since to cancel the three to "simplify", one must multiply it by its reciprocal, 1/3 (for den and num) - 3 x 8 redefines the parts/type

DIVIDING WITH EASY NUMBERS BY 10 BY 100 BY 50 BY 25 BY 5 BY 4

BY 10: MOVE DECIMAL POINT IN THE DIVIDEND ONE PLACE TO THE LEFT. BY 100: move the decimal point in the dividend two places to the left BY 50: divide by 100 then multiply by 2: 1000: 1000/100 = 10 x 2 = 20 by 25: divide by 100 then multiply by 4 by 5: divide by 10 then multiply by 2 by 4: divide by 2 twice :):):)

USING COMPATIBLE NUMBERS TO ESTIMATE QUOTIENTS: COMPATIBLE: 8,200,000 / 223:

COMPATIBLE: NUMBERS THAT WORK WELL TOGETHER; IN DIVISION, THEY ARE NUMBER PAIRS THAT ARE EASY TO DIVIDE. 8 MILLION DIVIDED BY 200 = 40,000

MULTIPLYING MIXED NUMBERS

GREAT ILLUSTRATION. NOTICE IN FIRST EX HOW DENOMINATORS CREATE NEW INTERPRETATION OF THE WHOLE, IN TERMS OF PARTS: NAMELY 7X9=63.

RECIPROCALS DEFINITION NUMBER PAIRS _________________

RECIPROCALS DEFINITION NUMBER PAIRS THAT HAVE A PRODUCT OF 1 !!! SO, 3/8 AND 8/3 ARE RECIPROCALS. THEIR PRODUCT IS 1. ETC.

UNDERSTANDING PLACES IN LONG DIVISION, PARTICULARLY WHEN FILLING A PLACE WITH ZERO: 1316/12 =

START WITH 1000s. How many 12000s go into 1 thousand? none. Move to 100s. How many 12 hundreds go into 13 hundreds (1300)? 1. 1316 - 1200 = 116. NOW, HOW MANY 12 TENS WILL GO INTO 11 (OF 116) TENS? NONE. PUT ZERO IN THE PLACE. MOVE TO ONES. HOW MANY 12 ONES WILL GO INTO 116? 12 X 9 = 108. FINISH PROBLEM...ETC.:)