Mt. S.A.C. Learn 48 & 49 Basic Math Vocab.

SUBTRACTING FRACTION WITH DIFFERENT DENOMINATORS

FIND THE LCD WRITE EACH FRACTION AS AN EQUIVALENT FRACTION DENOMINATOR 18. SUBTRACT THE SECOND NUMERATOR FROM THE FIRST NUMERATOR AND WRITE THE DIFFERENCE OVER THE THE COMMON DENOMINATOR.

EQUIVALENT FRACTIONS

FRACTIONS THAT REPRESENT THE SAME NUMBER. 8/12 IS THE SAME AS 2/3

LIKE FRACTIONS

FRACTIONS WITH THE SAME DENOMINATOR .

SIMILAR GEOMETRIC FIGURES

GEOMETRIC FIGURES WITH THE SAME SHAPE IN WHICH THE RATIOS OF THE LENGTHS OF THEIR CORRESPONDING SIDES ARE EQUAL.

STEPS FOR SUBTRACTING FRACTIONS WITH DIFFERENT DENOMINATORS

STEP1. FIND THE LCD OF THE FRACTIONS. STEP2. WRITE EACH FRACTION AS AN EQUIVALENT FRACTION WITH A DENOMINATOR EQUAL TO THE LCD FOUND IN STEP1. STEP3. FOLLOW THE STEPS FOR SUBTRACTING LIKE FRACTIONS.

STEPS FOR COMPARING FRACTIONS

STEP1. FIND THE LCD OF THE FRACTIONS. STEPS 2. WRITE EACH FRACTION AS AN EQUIVALENT FRACTION WITH A DENOMINATOR EQUAL TO THE LCD. STEP3. COMPARE THE NUMERATORS. A. 2/3 AND 5/8 = 2 X 8 OVER 3 X 8 = 16/24 5 X 3 OVER 8 X 3 = 15/24 = 5/8 < 2/3

RULES FOR CONVERTING A FRACTION INTO A DECIMAL

DIVIDE THE NUMERATOR BY THE DENOMINATOR. IF NECESSARY, WRITE ADDITIONAL ZEROS TO THE RIGHT OF THE LAST DIGIT FOLLOWING THE DECIMAL POINT IN THE DIVIDEND TO ALLOW THE DIVISION TO CONTINUE. ALSO, IF NECESSARY, INSERT ZEROS AS PLACEHOLDERS IN THE QUOTIENT TO GET CORRECT NUMBER OF DECIMAL PLACES.

THE THREE WAYS TO SET UP A DIVISION PROBLEM.

DIVIDEND DV BY DIVISOR =QUOTIENT DIVIDEND OVER DIVISOR =QUOTIENT DIVIDEND IS ON THE INSIDE DIVISOR IS ON THE RIGHT SIDE AND THE QUOTIENT IS ON THE TOP.

TWO METHODS TO FINE FACTORS OF ANY NUMBER. STOP WHEN IT BEGINS TO REPEAT.

18 DV- 1 = 18 18 X 1 = 18 18 DV- 2 = 9 9 X 2 = 18 18 DV- 3 = 6 6 X 3 = 18 18 DV- 4 = _ 4 X _ = _ 18 DV- 5 =_ 5 X _ = _ 18 DV- 6 = 3 6 X 3 = 18

THE FIRST UNDER 30 PRIME NUMBERS

2,3,5,7,11,17,19,23,29,

COMMON DENOMINATOR

A COMMON MULTIPLE OF ALL THE DENOMINATORS FOR A SET OF FRACTIONS.

RATIO

A COMPARISON OF TWO QUANTITIES BY DIVISION. 3/2 3:2 AND 3 TO 2

REPEATING DECIMAL

A DECIMAL WHOSE EXPANSION CONTINUES INDEFINITELY WITH A REPEATING DIGIT OR A REPEATING BLOCK OF DIGITS.

NON-TERMINATING DECIMAL

A DECIMAL WHOSE EXPANSION DOSE NOT END.

TERMINATING DECIMAL

A DECIMAL WHOSE EXPANSION ENDS

PRIME FACTORIZATION

A FACTORIZATION OF A NATURAL NUMBER IN WHICH EACH FACTOR IS PRIME. 2X3X3=2X3 TO THE 2ND POWER= 18

FRACTION SIMPLIFIED TO LOWEST TERMS

A FRACTION IN WHICH THE NUMERATOR AND DENOMINATOR HAVE NO COMMON FACTOR OTHER THAN 1. 6/9=2X3/3X3

IMPROPER FRACTION

A FRACTION IN WHICH THE NUMERATOR IS GREATER OR EQUAL TO THE DENOMINATOR. 15/11 19/7 2/2

PROPER FRACTION OR COMMON FRACTION.

A FRACTION IN WHICH THE NUMERATOR IS LESS THEN THE DENOMINATOR. 1/2 3/16 9/32

DECIMAL FRACTION

A FRACTION WHOSE DENOMINATOR IS A POWER OF 10.

VARIABLE

A LETTER OR SOME OTHER SYMBOL THAT REPRESENTS A NUMBER WHOSE VALUE IS UNKNOWN

PROPORTION

A MATHEMATICAL STATEMENT SHOWING THAT TWO RATIOS ARE EQUAL.

COMPOSITE NUMBERS

A NATURAL NUMBER GREATER THAN 1 THAT HAS MORE THAN TWO FACTORS(DIVISORS).

PRIME NUMBER OR PRIME

A NATURAL NUMBER GREATER THAN ONE THAT HAS ONLY TWO FACTORS (DIVISORS), NAMELY 1 AND ITSELF

FRACTION

A NUMBER OF THE FORM A OVER B WHERE A AND B ARE WHOLE NUMBERS AND B IS NOT ZERO. A/B

MIXED NUMBER

A NUMBER THAT COMBINES A WHOLE NUMBER AND A FRACTION. 1 3/8 7 11/16 15 13/28

FACTOR OF A NUMBER

A NUMBER THAT DIVIDES THE GIVEN NUMBER EVENLY.

DECIMAL NUMBER OR DECIMAL

A NUMBER WRITTEN IN DECIMAL NOTATION.

COMPLEX FRACTION

A QUOTIENT OF THE FORM A/B WHERE BOTH ARE FRACTIONS AND WHERE B IS NOT ZERO. LIKE 1 HALF IS OVER 4 FIFTHS 1/2 / 4/5

PERCENT

A RATIO OF A PART TO 100.

RATE

A RATIO THAT COMPARES TWO QUANTITIES THAT HAVE DIFFERENT KINDS OF UNITS

MULTIPLY FRACTIONS IN AN APPLICATION PROBLEM

A. A CHOCOLATE CHIP RECIPE REQUIRES 2/3 OF A CUP OF BROWN SUGAR. IF YOU WANT TO MAKE HALF THE NUMBER OF COOKIES, HOW MANY CUPS OF BROWN SUGAR WOULD YOU NEED? THE PROBLEM CONTAINS A KEY WORD half INDICATING MULTIPLICATION BY 1/2. 2 IS A COMMON FACTOR OF THE NUMERATORS OF THE FIRST FRACTION AND THE DENOMINATOR OF THE SECOND FRACTION. DIVIDE EACH BY THE COMMON FACTOR 2. MULTIPLY THE NUMERATORS. MULTIPLY THE DENOMINATORS. EXPRESS THE MIXED NUMBER AS AN IMPROPER FRACTION. MULTIPLY THE NUMERATORS.MULTIPLY THE DENOMINATORS. WRITE THE RESULT AS A MIXED NUMBER. 2/3 X 1/2 = 1/3 X 1/1= 1/3 CUP OF BROWN SUGAR

PRIME FACTOR TREE

AN ILLUSTRATION THAT SHOWS THE PRIME FACTORIZATION OF A COMPOSITE NUMBER. 18 2 9

MULTIPLYING FRACTIONS, MIXED NUMBERS, OR WHOLE NUMBERS

CONVERT EACH NUMBER AS AN IMPROPER FRACTION. MULTIPLY THE NUMERATORS THAN MULTIPLY THE DENOMINATORS.WRITE THE RESULT AS A MIXED NUMBER. A. 3 3/4 X 5 1/2= 15/4 X 11/2= 165/8 = 20 5/8 DIVIDE TO CONVERT TO A MIXED #. B. 12 5/6 X 4 = 77/6 X 4/1 = 77/3 X 2/1 154/ 3 = 51 1/3

DIVIDE FRACTION IN AN APPLICATION PROBLEM.

HOW MANY METAL PLATES, EACH 2 3/4 INCHES THICK, WILL FIT IN A STORAGE CONTAINER THAT IS 27 1/2 INCHES HIGH? TO FIND THE NUMBER OF METAL PLATES THAT WILL FIT IN THE CONTAINER DIVIDE BY THE HEIGHT AND THE THICKNESS OF EACH PLATE. MUTLIPLY 55/2 BY 11/4, THE RECIPROCAL OF 4/11. DIVIDE 2 THE DENOMINATOR OF THE FIRST FRACTION, AND 4, THE NUMERATOR OF THE 2ND FRACTION,BY THE THE COMMON FACTOR OF 2. ALSO, DIVIDE 55, THE NUMERATOR OF THE FIRST FRACTION AND 11, THE DENOMINATOR OF THE 2ND FRACTION, BY THE COMMON FACTOR OF 11. MULTIPLY 27 1/2 DV- 2 3/4= 55/2 DV- 4/11= 5/1 X 2/1 = 10/1= 10

DIVIDING A DECIMAL BY A POWER OF 10 SUCH AS 10,100,1000.....

MOVE THE DECIMAL POINT IN THE DIVIDEND TO THE LEFT THE SAME NUMBER OF PLACES AS THERE ARE ZEROS IN THE POWER OF 10 INSERT THE ZEROS,IF NECESSARY.

DIVIDING A DECIMAL BY A POWER OF 10 SUCH AS 0.1,0.01,0.001.....

MOVE THE DECIMAL POINT IN THE DIVIDEND TO THE RIGHT THE SAME NUMBER OF PLACES AS THERE ARE DECIMAL POWER OF 10. INSERT ZEROS, INSERT ZEROS, AS NECESSARY.

MULTIPLYING A DECIMAL BY A POWER OF 10 SUCH AS 0.1,0.01,0.001.....

MOVE THE DECIMAL POINT TO THE LEFT THE SAME NUMBER OF PLACES AS THERE ARE DECIMAL PLACES IN THE DECIMAL POWER OF 10. INSERT ZEROS, AS NECESSARY.

MULTIPLYING A DECIMAL BY A POWER OF 10 SUCH AS 10,100,1000.....

MOVE THE DECIMAL POINT TO THE RIGHT THE SAME NUMBER OF PLACES AS THERE ARE ZEROS IN THE POWER OF 10 . INSERT ZEROS ,AS NECESSARY.

RULES FOR CONVERTING A DECIMAL TO A PERCENT

MULTIPLY THE DECIMAL BY 100%. ALTERNATIVELY, MOVE THE DECIMAL POINT TWO PLACES TO THE RIGHT AND APPEND A PERCENT SIGN.

RULES FOR CONVERTING A PERCENT TO A DECIMAL

MULTIPLY THE NUMBER PRECEDING THE PERCENT SIGN BY 0.01.ALTERNATIVELY, DROP THE PERCENT SIGN AND MOVE THE DECIMAL TWO PLACES TO THE LEFT

ORDER OF OPERATION!! OR P.E.M.D.A.S OR PLEASE EXCUSE MY DEAR AUNT SALLY

STEP1 P = PERFORM ALL OPERATIONS WITHIN ANY GROUPING SYMBOLS : PARENTHESES ( ), BRACKETS [ ], AND CURLY BRACES { },WHEN GROUPING SYMBOLS OCCUR WITHIN GROUPING SYMBOLS , BEGIN WITH THE INNER MOST GROUPING SYMBOLS. STEP2 E= EVALUATE ALL EXPONENTIAL EXPRESSIONS. STEP3 MD= PREFORM AS THEY APPEAR LEFT TO RIGHT MULTIPLICATION AND DIVISION STEP4 AS= PREFORM AS THEY APPEAR LEFT TO RIGHT FOR ADDITION AND SUBTRACTION

STEPS FOR SOLVING A PROPORTION

STEP1. ASSIGN A VARIABLE TO THE UNKNOWN QUANTITY. STEP2. CROSS MULTIPLY TO FIND THE CROSS PRODUCT. STEP3. SEPARATE THE CROSS PRODUCTS BY AN EQUAL SIGN TO FORM AN EQUATION. STEP4. DIVIDE BOTH SIDES OF THE EQUATION BY THE NUMBER THAT MULTIPLIES THE VARIABLE. N STEP5.SIMPLIFY, IF POSSIBLE. STEP6.VERIFY THE ANSWER BY REPLACING THE UNKNOWN IN THE ORIGINAL PROPORTION WITH THE ANSWER, AND CHECK THAT THE CROSS PRODUCT ARE EQUAL.

ALTERNATE METHOD FOR ADDING MIXED NUMBERS.

STEP1. CHANGE EACH MIXED NUMBER T AN IMPROPER FRACTION. STEP2. FIND THE LCD ,AND WRITE EACH FRACTION AS AN EQUIVALENT FRACTION WITH THE LCD. STEP3. FOLLOW THE RULES FOR ADDING LIKE FRACTIONS. STEP4. COVERT TO A MIXED NUMBER AND SIMPLIFY. 3 1/5 + 6 3/5 = 16/5 + 33/5 = 49/5= 9 4/5

ALTERNATE METHOD FOR SUBTRACTING MIXED NUMBERS

STEP1. CHANGE THE MIXED NUMBER TO AN IMPROPER FRACTION. STEP2. FIND THE LCD, AND WRITE THE FRACTION AS AN EQUIVALENT FRACTION WITH THE LCD STEP3. FOLLOW THE RULES FOR SUBTRACTING LIKE NUMBERS. STEP4. CONVERT THE ANSWER TO A MIXED NUMBER AND SIMPLIFY. EXAMPLES: 8 6/7 - 3 2/7= 62/7 - 23/7= 39/ 7 = 5 4/7 3 3/4 - 2 1/6= 15/4 -13/6 = 15 X 3 OVER 4 X= 15 --13 X 2 OVER 6 X 2 45/12=26/12 19/12= =1 7/12

STEPS FOR CONVERTING A FRACTION TO A PERCENT

STEP1. CONVERT THE FRACTION TO A DECIMAL. STEP2. CONVERT THE DECIMAL TO A PERCENT.

STEPS FOR WRITING AN IMPROPER FRACTION AS A MIXED NUMBER OR WHOLE NUMBER.

STEP1. DIVIDE THE NUMERATOR BY THE DENOMINATOR. STEP2. A. IF THERE IS NO REMAINDER, THEN THE IMPROPER FRACTION IS EQUAL TO THE QUOTIENT FOUND IN STEP1. B. IF THERE IS A REMAINDER, THEN THE IMPROPER FRACTION CAN BE WRITTEN AS FOLLOWS. QUOTIENT REMAINDER/DIVISOR ( Q R/D ) 1 1/2 A. 30 OVER 5 = 30/5 A. 30/5= 30 DV- 5 = 6 B. 9 OVER 2 = 9/2 B. 9/2= 9 DV- 2 = 4 WITH THE REMAINDER OF 1 SO WE WRITE AS 4 1/2 A. 6 B. 9/2= 4 1/2

STEPS FOR SIMPLIFYING BEFORE MULTIPLYING FRACTION

STEP1. FIND THE COMMON FACTOR THAT DIVIDES EVENLY INTO ONE OF THE NUMERATOR AND ONE OF THE DENOMINATORS DIVIDE THE IDENTIFIED NUMERATOR AND DENOMINATOR BY THIS COMMON FACTORS. STEP2. REPEAT STEP 1 UNTIL THERE ARE NO MORE COMMON FACTORS. STEP3. MULTIPLY THE REMAINING FACTORS IN THE NUMERATORS AND IN THE DENOMINATORS

STEPS FOR ADDING FRACTIONS WITH DIFFERENT DENOMINATORS

STEP1. FIND THE LCD OF THE FRACTIONS. STEP2. WRITE EACH FRACTION AS AN EQUIVALENT FRACTION WITH A DENOMINATOR EQUAL TO THE LCD FOUND IN STEP 1. STEP3. FOLLOW THE STEPS FOR ADDING LIKE FRACTIONS. B. 3/8 + 5/7+ 1/2 = 3 X 7 + 5 X 8 + 1 X 28 OVER 8 X 7 + 7 X 8 + 2 X 28 = 21/56 + 40/56 + 28/56 = 21 + 40 + 28= OVER 56 = 89/56 DIVIDE = 1 33/56

STEPS FOR SIMPLIFYING A FRACTION

STEP1. IDENTIFY AND DIVIDE OUT ANY FACTORS COMMON TO THE NUMERATOR AND THE DENOMINATOR. USE THE GREATER COMMON FACTOR IF YOU CAN IDENTIFY IT. STEP2. IF A COMMON FACTOR REMAINS IN THE NUMERATOR AND DENOMINATOR OF THE RESULTING FRACTION, REPEAT STEP 1 UNTIL THE FRACTION IS SIMPLIFIED TO LOWEST TERMS. A.48/54= 24/27= 8/9

STEPS FOR ROUNDING DECIMALS TO A SPECIFIED PLACE.

STEP1. IDENTIFY THE PLACE TO THE RIGHT OF THE DECIMAL POINT TO WITCH THE DECIMAL IS TO BE ROUNDED. STEP2. IF THE DIGIT TO THE RIGHT OF THE SPECIFIED PLACE IS 4 OR LESS,THE DIGIT REMAINS THE SAME . IF THE DIGIT TO THE RIGHT OF THE SPECIFIED PLACE IS 5 OR MORE, INCREASE THE DIGIT BY ONE.CARRY, IF NECESSARY STEP3. DELETE THE DIGIT IN EACH PLACE AFTER THE SPECIFIED PLACE.

STEPS FOR SUBTRACTING MIXED NUMBERS

STEP1. IF THE DENOMINATORS OF THE FRACTIONS ARE DIFFERENT,WRITE EACH FRACTION AS EQUIVALENT FRACTION WITH A DENOMINATOR EQUAL TO THE LCD OF THE ORIGIN AL FRACTIONS. STEP2. A. IF THE FRACTION PART OF THE FIRST MIXED NUMBER IS LESS THAN THE FRACTION PART OF THE SECOND MIXED NUMBER, BORROW 1 FROM THE WHOLE NUMBER PART AND ADD IT IN THE FORM OF LCD/LCD TO THE FRACTION PART. B. IF THE FIRST NUMBER IS A WHOLE NUMBER, BORROW 1 FROM THE WHOLE NUMBER AND ADD THIS IN THE FORM OF LCD/ LCD TO ONE ESS THAN THE WHOLE NUMBER. STEP3. SUBTRACT THE FRACTIONS PARTS. STEP4. SUBTRACT THE WHOLE NUMBER PART. STEP 5. SIMPLIFY,IF POSSIBLE.

STEPS FOR FINDING THE LCM: ALTERNATE METHOD

STEP1. LIST THE NUMBERS FOR WHICH WE ARE TRYING TO FIND THE LCM IN A ROW DRAW A UPSIDE DOWN DIVISION BOX AROUND THE NUMBERS. STEP2. FIND THE PRIME FACTOR FOR AT LEAST ONE OF THESE NUMBERS. WRITE THIS PRIME FACTOR TO THE LEFT OF THE BOX. STEP3. CONSIDER THE QUOTIENT OF EACH NUMBER IN THE BOX AND THE PRIME FACTOR FROM STEP2. IF THE NUMBER IS EVENLY DIVISIBLE BY THE PRIME FACTOR, WRITE THE QUOTIENT BELOW THE NUMBER IF NOT, WRITE THE NUMBER ITSELF. PLACE A NEW BOX AROUND THIS NEW ROW OF NUMBERS STEP4. REPEAT STEP2 &3 UNTIL A ROW OF 1'S REMAINS. STEP5. CALCULATE THE PRODUCT OF THE PRIME FACTORS TO THE LEFT OF EACH BOX THIS IS THE LCM.

STEPS FOR DETERMINING WHETHER TWO RATIOS ARE PROPORTIONAL USING CROSS PRODUCTS.

STEP1. MULTIPLY THE DENOMINATOR OF THE FIRST RATIO BY THE NUMERATOR OF THE SECOND RATIO STEP2. MULTIPLY THE NUMERATOR OF THE FIRST RATIO BY THE DENOMINATOR OF THE SECOND RATIO. STEP3. DETERMINE WHETHER OR NOT THE CROSS PRODUCT ARE EQUAL. A. IF THE CROSS PRODUCTS ARE EQUAL, THE RATIOS ARE PROPORTIONAL, AND WE CAN WRITE A PROPORTION. B. IF THEY ARE NOT EQUAL, THE RATIOS ARE NOT PROPORTIONAL,AND WE CANNOT WRITE A PROPORTION.

STEPS FOR DIVIDING BY THE RECIPROCAL OF THE DIVISOR.

STEP1. MULTIPLY THE DIVIDEND BY THE RECIPROCAL OF THE DIVISOR, THAT IS,WHERE B,C, AND D ARE NOT ZERO. STEP2. SIMPLIFY, IF POSSIBLE. A/B DV- C/DB = A/B X D/C = 4/5 DV- 2/3 = 4/5 X 3/2 = 2/5 X 3/1 = 6/5 = 1 1/5

STEPS FOR MULTIPLYING FRACTIONS

STEP1. MULTIPLY THE NUMERATOR TO FROM AND NEW NUMERATOR. STEP2. MULTIPLY THE DENOMINATOR TO FORM A NEW DENOMINATOR. STEP3. SIMPLIFY, IF POSSIBLE. IN GENERAL WE HAVE THE FOLLOWING: A/B X C/D = A X C OVER B X D A. 5/7 X 3/4 = 5 X 3 = 15 7 X 4 =28 = 15/28

STEPS FOR WRITING A MIXED NUMBER AS AN IMPROPER FRACTION

STEP1. MULTIPLY THE WHOLE NUMBER PART BY THE DENOMINATOR OF THE FRACTION PARTAND ADD THE NUMERATOR OF THE FRACTION PART TO THIS PRODUCT. WRITE AN IMPROPER FRACTION. THE NUMERATOR IS THE RESULT OF STEP 1. THE DENOMINATOR IS THE ORIGINAL DENOMINATOR. DO THE MA! 5 2/3= 5X3+2 OVER 3 5X3=15+2= 17 = 17 OVER 3 17/3

STEPS FOR MULTIPLYING DECIMALS

STEP1. MULTIPLY WITHOUT REGARD TO THE DECIMAL POINTS. THAT IS, MULTIPLY THE FACTORS AS THOUGH THEY ARE WHOLE NUMBERS. STEP2. DETERMINE THE TOTAL NUMBER OF DECIMAL PLACES IN BOTH OF THE FACTORS. STEP3. PLACE THE DECIMAL POINT IN THE RESULTING PRODUCT SO THAT THE NUMBER OF PLACES TO THE RIGHT OF THE DECIMAL POINT IS EQUAL TO THE TOTAL DETERMINED IN STE 2. IF NECESSARY, INSERT ZEROS AS PLACEHOLDERS TO GET THE CORRECT NUMBER OF DECIMAL PLACES. ANY INSERTED ZERO WILL BE ON THE IMMEDIATE RIGHT OF THE DECIMAL POINT.

STEPS FOR SOLVING AN APPLICATION PROBLEM USING A PROPORTION

STEP1. READ AND UNDERSTAND THE PROBLEM. ASSIGN A VARIABLE TO THE UNKNOWN QUANTITY. STEP2. SET UP A PROPORTION. KEEP LIKE UNITS IN THEIR RESPECTIVE NUMERATORS AND DENOMINATORS. STEP3. SOLVE AND VERIFY THE PROPORTION. STEP4. STATE THE ANSWER.

STEPS FOR ESTIMATING WHEN ADDING OR SUBTRACTING DECIMALS

STEP1. ROUND EACH DECIMAL TO SPECIFIED PLACE. STEP2. ADD OR SUBTRACT.

STEPS FOR SUBTRACTING LIKE FRACTIONS

STEP1. SUBTRACT THE SECOND NUMERATOR FROM THE FIRST NUMERATOR AND WRITE THIS DIFFERENCE OVER THE COMMON DENOMINATOR. STEP2. SIMPLIFY, IF POSSIBLE.

STEPS FOR COMPARING TWO DECIMAL NUMBERS

STEP1. WRITE THE DECIMALS ONE ABOVE ANOTHER SO THAT THEIR DECIMAL POINTS ARE VERTICALLY ALIGNED. STEP2. COMPARE THE WHOLE NUMBERS SIDES. IF ONE IS GREATER THEN THE OTHER ,THEN THE ENTIRE DECIMAL IS GREATER. IF THEY ARE EQUAL, CONTINUE TO THE NEXT STEP. STEP3.COMPARE THE DIGITS TO THE RIGHT 0F THE DECIMAL POINT IN THE CORRESPONDING PLACES FROM LEFT TO RIGHT. A. IF THE DIGITS ARE THE SAME, MOVE RIGHT ONE PLACE TO THE NEXT DIGIT. IF NECESSARY, INSERT ZEROS AFTER THE LAST DIGIT TO THE RIGHT OF THE DECIMAL POINT TO CONTINUE THE COMPARISON. B. IF THE DIGITS ARE NOT THE SAME, THE LARGER DIGIT CORRESPONDS TO THE LARGER DECIMAL.

STEPS FOR ADDING DECIMALS

STEP1. WRITE THE DECIMALS SO THAT THE DECIMAL POINTS ARE VERTICALLY ALIGNED.IF NECESSARY, INSERT EXTRA ZEROS TO THE RIGHT OF THE LAST DIGIT AFTER THE DECIMAL POINT SO THAT EACH ADDEND HAS THE SAME NUMBER OF DECIMAL PLACE. STEP 2 ADD AS WITH WHOLE NUMBERS .CARRY, IF NECESSARY. STEP3. PLACE THE DECIMAL POINT IN THE SUM SO THAT IT IS VERTICALLY ALIGNED WITH THE DECIMAL POINTS OF THE ADDENDS.

STEPS FOR FINDING THE LCM USING PRIME FACTORIZATION

STEP1. WRITE THE PRIME FACTORIZATION OF EACH NUMBER. STEP2. WRITE THE PRODUCT OF THE PRIME FACTORS WITH EACH FACTOR APPEARING THE GREATEST NUMBER OF TIMES THAT IT OCCURS IN ANY ONE FACTORIZATION. 8= 2X2X2 12=2X2X3 2X2X2X3 LCM=2X2X2X3=24

STEPS FOR SIMPLIFYING A FRACTION USING PRIME FACTORIZATION

STEP1. WRITE THE PRIME FACTORIZATIONS OF THE NUMERATOR AND THE DENOMINATOR. STEP2. DIVIDE OUT ANY FACTORS COMMON TO THE NUMERATOR AND DENOMINATOR. STEP3. MULTIPLY THE REMAINING FACTORS IN THE NUMERATOR AND IN THE DENOMINATOR TO DETERMINE THE SIMPLIFIED FRACTION. A. 28/50= 2X2X7 OVER 2X5X5 = 1X2X7 OVER 1X5X5 = 14/25

STEPS FOR DIVIDING A DECIMAL BY A WHOLE NUMBER

STEP1. WRITE THE PROBLEM IN LONG DIVISION FORMAT STEP2. DIVIDE AS IF WORKING WITH WHOLE NUMBER S. PLACE THE DECIMAL POINT IN THE QUOTIENT DIRECTLY ABOVE THE DECIMAL POINT IN IN THE DIVIDEND. STEP3. IF NECESSARY, WRITE ADDITIONAL ZEROS TO THE RIGHT OF THE LAST DIGIT FOLLOWING THE DECIMAL POINT IN THE DIVIDEND TO ALLOW THE DIVISION TO CONTINUE.

STEPS FOR DIVIDING A DECIMAL OR WHOLE NUMBER BY A DECIMAL

STEP1. WRITE THE PROBLEM IN LONG DIVISION FORMAT. STEP2. WRITE AN EQUIVALENT DIVISION PROBLEM WITH A WHOLE NUMBER DIVISOR. IN PARTICULAR, MOVE THE DECIMAL POINT IN THE DIVISOR TO THE RIGHT AS MANY PLACES AS NECESSARY UNTIL THE DIVISOR IS A WHOLE NUMBER OF PLACES TO RIGHT STEP 3. DIVIDE . PLACE THE DECIMAL POINT IN THE QUOTIENT DIRECTLY ABOVE THE MOVED DECIMAL POINT IN THE DIVIDED

STEPS FOR WRITING A UNIT PRICE

STEP1. WRITE THE RATE IN FRACTION NOTATION WITH THE PRICE AS THE NUMERATOR AND THE QUANTITY (NUMBER OF ITEMS OR UNITS) AS THE DENOMINATOR. STEP2. DIVIDE THE NUMERATOR BY THE DENOMINATOR. STEP3. ROUND TO THE NEAREST CENT, IF NECESSARY.

STEPS FOR WRITING A UNIT RATE

STEP1. WRITE THE RATE IN THE FRACTION NOTATION WITH THE UNITS INCLUDED. STEP2. DIVIDE THE NUMERATOR BY THE DENOMINATOR. STEP3. ROUND AS SPECIFIED, IF NECESSARY.

STEP FOR SIMPLIFYING A RATIO THAT CONTAINS DECIMALS

STEP1. WRITE THE RATIO IN FRACTION NOTATION STEP2. REWRITE AS A RATIO OF WHOLE NUMBERS. TO DO SO,MULTIPLY THE RATIO BY 1 IN THE FORM N/N,WHERE N IS A POWER OF 10 LARGE ENOUGH TO REMOVE ANY DECIMALS IN BOTH THE NUMERATOR AND THE DENOMINATOR. STEP3 SIMPLIFY, IF POSSIBLE.

STEPS TO SIMPLIFYING A RATIO

STEP1. WRITE THE RATIO IN FRACTION NOTATION. STEP2. SIMPLIFY, IF POSSIBLE.

STEPS FOR SIMPLIFYING A RATIO THAT CONTAINS A COMBINATION OF FRACTIONS, MIXED NUMBERS, OR WHOLE NUMBERS.

STEP1. WRITE THE RATIO IN FRACTION NOTATION.EP STEP2. CONVERT EACH MIXED NUMBER AND EACH WHOLE NUMBER TO AN IMPROPER FRACTION. STEP3. DIVIDE THE FRACTIONS BY MULTIPLYING THE NUMERATOR BY THE RECIPROCAL OF THE DENOMINATOR. STEP4. SIMPLIFY, IF POSSIBLE

STEPS FOR WRITING A DECIMAL A DECIMAL WORD FORM AND STANDARD FORM.

STEP1. WRITE THE WHOLE NUMBER PART IN WORDS. STEP2. WRITE THE WORD "AND" IN PLACE OF THE DECIMAL POINT. STEP3. WRITE THE DECIMAL PART IN WORD AS THOUGH IT WERE A WHOLE NUMBER, WITHOUT ANY COMMAS, FOLLOWED BY THE NAME OF THE LAST DIGIT

PERCENT SIGN

THE % SYMBOL.

DENOMINATOR

THE BOTTOM NUMBER OF A FRACTION. /B

RECIPROCAL OF THE FRACTION A/B

THE FRACTION B/A WHERE A # 0 AND B # 0, IS THE FRACTION B/A.

GREATEST COMMON FACTOR

THE LARGEST FACTOR SHARED BY TWO OR MORE NUMBERS.

LEAST COMMON DENOMINATOR OR LCD

THE LEAST COMMON MULTIPLE (LCM) OF ALL THE DENOMINATOR FOR A SET OF FRACTIONS.

FRACTION BAR

THE LINE BETWEEN THE NUMERATOR AND THE DENOMINATOR. / OR ---

MULTIPLE OF A NUMBER

THE PRODUCT OF THE GIVEN NUMBER AND ANY NATURAL NUMBER. 2X1=2 2X2=4 2X3=6 2X4=8 2X5=10

TERMS OF RATIO

THE QUANTITIES BEING COMPARED.

LEAST COMMON MULTIPLE OR LCM

THE SMALLEST MULTIPLE SHARED BY A SET OF TWO OR MORE NUMBERS. LIKE THE SMALLEST COMMON MULTIPLE OF 2,4, AND 5 IS: 20 2= 2,4,6,8,10,12,14,16,18,20 4= 4,8,12,16,20,24,28,32,36,40 5= 5,10,15,20,25,30,35,40,45,50

NUMERATOR

THE TOP NUMBER OF A FRACTION. A/

ADDING MIXED NUMBERS

TO ADD MIXED NUMBERS WE MUST FIRST ADD THE FRACTIONS AND THEN THE WHOLE NUMBERS. AS AN EXAMPLE, CONSIDER 3 1/5 + 6 3/5. WE VERTICALLY FORMAT THE MIXED NUMBERS AS SHOWN. 3 1/5 3 1/5 + 6 3/5 + 6 3/5 = 4/5 = 9 4/5

RULES FOR CONVERTING A DECIMAL FRACTION TO A DECIMAL

TO CONVERT A DECIMAL,WRITE THE WHOLE NUMBER IN THE NUMERATOR AND MOVE THE DECIMALS TO THE LEFT AS MANY THERE ARE ZEROS IN THE POWER OF TEN IN THE DENOMINATOR. 61/100 61. = .61 61/100=0.61 831/100,000 831.=0.00831 831/100,000=0.00831

RULES FOR CONVERTING A TERMINATING DECIMAL TO A FRACTION':

TO CONVERT A TERMINATING DECIMAL TO A FRACTION , WRITE THE WHOLE NUMBER FORMED BY THE DIGITS TO THE RIGHT OF THE DECIMAL POINT AS THE NUMERATOR, AND WRITE THE POWER OF 10 THAT HAS AS MANY ZEROS AS PLACES IN THE DECIMAL AS THE DENOMINATOR.SIMPLIFY IF POSSIBLE A. 0.23 = 23/100 B. 0.007 = 7/1000 C. 12.5 = 12 5/10 = 12 1/2 D.43.025 = 43 25/1000 = 43 1/40

FACTOR

TO EXPRESS A QUANTITY AS A PRODUCT. 1X18=18 2X9=18 3X6=18

RULES FOR WRITING AN EQUIVALENT FRACTION WITH A LARGE DENOMINATOR.

TO FIND AN EQUIVALENT FRACTION FOR A/B WITH A LARGER DENOMINATOR , MULTIPLY BOTH THE NUMERATOR AND DENOMINATOR BY THE SAME NONZERO WHOLE NUMBER, N. IN GENERAL, WE HAVE THE FOLLOWING: A/B= A X N OVER B X N A. 2/3 WITH A DENOMINATOR OF 15. = 2 X 5 OVER 3 X 5 = 10 / 15

SUBTRACT MIXED NUMBERS

TO SUBTRACT MIXED NUMBERS, FIRST SUBTRACT THE FRACTION PARTS AND THE WHOLE NUMBERS. AS AN EXAMPLE, CONSIDER 8 6/7 - 3 2/7. 8 6/7 8 6/7 - 3 2/7 -3 2/7 = 4/7 =5 4/7

DIVIDE FRACTIONS, MIXED NUMBERS , OR WHOLE NUMBERS.

WRITE THE DIVIDEND AND THE DIVISOR AS AN IMPROPER FRACTIONS. MULTIPLY 73/6 BY 1/3 THE RECIPROCAL OF 3/1. EXPRESS THE IMPROPER FRACTION AS A MIXED NUMBER. 12 1/6 DV- 3 = 73/6 DV- 3/1= 73/18 = 4 1/18

RULES FOR CONVERTING A PERCENT TO A FRACTION

WRITE THE NUMBER PRECEDING THE PERCENT SIGN OVER 100.M MANIPULATE THE RATIO TO GET A WHOLE NUMBER IN THE NUMERATOR. SIMPLIFY, IF NECESSARY. THE RESULTING FRACTION, IF POSSIBLE.

COMMON MULTIPLE

`A MULTIPLE THAT IS SHARED BY TWO OR MORE NUMBERS. LIKE COMMON MULTIPLE OF 4 AND 6 ARE: 12,24,AND 36 4 = 4,8,12,16,24,28,32,36,40 6 = 6,12,18,24,30,36,42,48,54,60

commission

a form of compensation based on a percent of sales.

sales tax

a state tax based on the retail price or rental cost of certain items.

how to solve a percent problem as an equation

base in a percent problem, the quantity that represent the total. amount in a percent problem, the quantity that represent the portion of the total. percent equation an equation of the form amount= percent x base. ex a. = amount b= is percent c= base a. what number is 80% of 1500? | k | = 80 x 1500 k. = 0.08 x 1500 = 1200 b. 15 is what percent of 125? 15 = | p | x 125 15 = p x 125 15/125 = 125p/125 p= 15/125 p= 0.12 = 12% c. 70 is 35% of what number? 70 = 35% x | b | 70 = 35% x b 70 = 0.35 x b 70/0.35 = 0.35b/0.35 b = 70/0.35= 200

write a percent problem as an equation

is,are, was, will be, results in, yields = the meaning is equal. of = the meaning is to multiply what,what number, what percent, = the meaning is its unknown, assign a variable like x n u any letter you choose. a. what number is 3% of 150? | k | = 3 x 150 b. 500 is what percent of 6000? 500 = | s | x 6000 c. 62 is 5% of what number? 62 = 5 x | z |

how to solve a percent proportion

solve a percent proportion in the same way we solved a proportion in section 4.3. write each percent proportion as a proportion and solve. a. what percent of 850 is 510? | percent | base amount amount/base = part/100 = 510/850 = p/100 = 850 x p = 510 x 100 = 850p = 51,000 = 85op/ 850 = 51000/850 = p= 60 = 60% of 850 is 510.

steps for finding the percent of change

step1. find the change amount. a. if a quantity increases, subtract the original quantity from the new quantity. b. if a quantity decreases, subtracts the new quantity from the original quantity. step2. divide the change amount from step1 by the original quantity. convert the result to a percent . in general, use the following formula and convert the quotient to a percent. percent change - change amount / original amount.

steps to write and solve a percent problem as a proportion.

step1. identify the amount,base, and part. step2. assign a variable to the unknown. substitute the know quantities and the variable in the percent proportion. step3. simplify the ratios in the percent proportion, if possible. step4. cross multiply to find the cross products. set the cross products equal. step5. divide both sides of the equation by the number that multiplies the variable.

steps for calculating the new amount after a percent change part 1

step1. if the quantity increases, add the percent increase to 100"%. if the quantity decreases,subtract the percent decreases from 100% step2. solve for the new amount by solving either a percent equation or a percent proportion involving the percent from step1 and the original amount.(the base). what is 722 decreased by 50% 100% - 50% =50% what is 50% 0f 722 a = 0.5 x 722 a = 361 722 decreased by 50% is 361.