TEAS 2019 MATHEMATICS:

SUBTRACTING MIXED NUMBERS:

CONVERT EACH MIXED NUMBERS TO AN IMPROPER FRACTION, GET A COMMON DENOMINATOR, AND THEN SUBTRACT NUMERATORS.

WHICH IS LARGEST VALUE? 0.49, 3/5, 1/2, 0.55

CONVERT FRACTIONS TO DECIMALS: 3/3 = 0.6 1/2 = 0.5 0.55 PLACE ORDERS FROM SMALLEST TO LARGEST: 0.49 < 0.5 <0.55 <0.6 3/5 IS THE LARGEST NUMBER

PLACE IN ORDER FROM LEAST TO GREATEST: 2/5, -0.7, 0.35, -3/2, 0.46

CONVERT FRACTIONS TO DECIMALS: 2/5 = 0.4 -3/2 = 1.5 -3/2 < -0.7 < 0.35 < 2/5 < 0.46

RULES OF POSITIVE/NEGATIVE NUMBERS:

(+) + (-) = THE SIGN OF THE LARGER NUMBER (-) + (-) = NEGATIVE NUMBER (-) X (-) OR (-) / (-) = POSITIVE NUMBER (-) X (+) IR (-) / (+) = NEGATIVE NUMBER (+) + (+) OR (+) X (+) OR (+) / (+) = POSITIVE NUMBER

WHAT IS THE SUM OF -65 AND -32?

(-) + (-) = (-) -65 + -32 = -97

WHAT IS THE VALUE OF -16 DIVIDED BY 2.5?

(-) / (+) = (-) -16 / 2.5 = -6.4

FIND THE PRODUCT OF -10 AND 47:

(-) X (+) = (-) -10 X 47 = -470

IS THE PRODUCT OF -7 AND 4 LESS THAN -7, BETWEEN -7 AND 4, OR GREATER THAN 4?

(-) X (+) = (-) -7 X 4 = -28, WHICH IS LESS THAN -7

JEAN HAS 7.4 GALLONS OF GAS IN HER TANK. AFTER DRIVING, SHE HAS 6.8 GALLONS. HOW MANY GALLONS OF GAS DID SHE USE?

0.6 GAL

2/5 / 1 1/5 =

1 1/5 = 6/5 = 2/5 X 5/6 = 10/30 = 1/3

ORDER OF OPERATIONS:

1. PARENTHESIS - PERFORM FIRST 2. EXPONENTS - AFTER PARETHESIS, DO THIS 3. MULTIPLICATION 4. DIVISION - CARRIED OUT LEFT TO RIGHT 5. ADDITION 6. SUBTRACTION - ALSO FROM LEFT TO RIGHT

A RECIPE CALLS FOR 1/4 CUP OF SUGAR. IF 8 1/2 BATCHES OF THE RECIPE ARE NEEDED, HOW MANY CUPS OF SUGAR WILL BE USED?

1/4 X 8 1/2 CONVERT MIXED NUMBER: 8 1/2 = 17/2 1/4 X 17/2 = 17/8 = 2 1/8

SIMPLIFY 121/ 77

121 AND 77 SHARE 11 AS COMMON FACTOR. DIVIDE EACH BY 11: 121/77 = 11/11 X 11/7 = 11/7

FIND THE SUM OF 17.07 + 2.52

19.59

WHAT IS THE PRODUCT OF 0.25 AND 1.3?

25 X 13 = 325 THERE ARE 2 DIGITS AFTER THE DECIMAL IN 0.25 AND ONE DIGIT AFTER 1.3 - THEREFORE THE PRODUCT SHOULD HAVE 3 DIGITS AFTER THE DECIMAL - 0.325

WHAT PLACE IS EACH DIGIT VALUE? 5,124.068

5 - THOUSANDS 1 - HUNDREDS 2 - TENS 4 - ONES .0 - TENTHS 6 - HUNDREDTHS 8 - THOUSANDTHS

REAL NUMBER:

A NUMBER THAT CAN BE REPRESENTED BY A POINT ON A LINE. REAL NUMBERS INCLUDE ALL RATIONAL AND IRRATIONAL NUMBERS.

PROPORTIONS:

AN EQUATION WHICH STATES THAT 2 RATIOS ARE EQUAL. PROPORTIONS ARE USUALLY WRITTEN AS 2 FRACTIONS JOINED BY AN EQUAL SIGN (A/B = C/D), BUT THEY CAN ALSO BE WRITTEN USING COLONS (A: B: C: D). IN PROPORTION, UNITS MUST BE THE SAME IN BOTH NUMERATOR AND DENOMINATOR. OFTEN YOU WILL BE GIVEN 3 VALUES AND ASKED TO FIND 4TH. - IN THESE PROBLEMS YOU CAN SOLVE FOR MISSING VALUE BY CROSS-MULTIPLYING - MULTIPLY THE NUMERATOR OF EACH FRACTION BY DENOMINATOR OF OTHER TO GET AN EQUATION WITH NO FRACTIONS. YOU CAN SOLVE EQUATION USING BASIC ALGEBRA. A/B = C/D --> AD = BC

NUMERATOR:

APPEARS ABOVE THE BAR IN A FRACTION

DENOMINATOR:

APPEARS BELOW THE BAR IN A FRACTION.

RATIONAL NUMBERS:

CAN BE REPRESENTED AS A FRACTION. ANY DECIMAL PART MUST TERMINATE OR RESOLVE INTO A REPEATING PATTERN. EX: 0.7, 1/2, 012.36

ADDING/SUBTRACTING POSITIVE/NEGATIVE NUMBERS:

CAN USE A NUMBER LINE TO EASILY FIND RESULT: WHEN ADDING 2 NUMBERS, WHETHER THEY ARE POSITIVE OR NEGATIVE, COUNT TO THE RIGHT. WHEN SUBTRACTING, COUNT TO THE LEFT. ADDING A NEGATIVE VALUE IS THE SAME AS SUBTRACTING. SUBTRACTING A NEGATIVE VALUE IS THE SAME AS ADDING.

IRRATIONAL NUMBERS:

CANNOT BE REPRESENTED AS A FRACTION. IRRATIONAL DECIMAL NUMBER NEVER ENDS AND NEVER RESOLVES INTO A REPEATING PATTERN. EX: N, 3/7, SQUARE ROOT OF 2)

FIND 0.8 / 0.2

CHANGE 0.2 TO 2 BY MOVING THE DECIMAL ONE SPACE TO RIGHT. THEN MOVE THE DECIMAL ONE SPACE TO THE RIGHT ON THE DIVIDEND - 0.8 BECOMES 8. DIVID 8 BY 2 - 8 / 2 = 4

FIND THE QUOTIENT WHEN 40 IS DIVIDED BY 0.25

CHANGE THE DIVISOR TO A WHOLE NUMBER: 0.25 BECOMES 25. CHANGE THE DIVIDEND TO MATCH THE DIVISOR BY MOVING THE DECIMAL TWO SPACES TO THE RIGHT, SO 40 BECOMES 4000. DIVIDE 4000 BY 25 - 4000 / 25 = 160

SABRINA HAS 2/3 OF A CAN OF RED PAINT. HER FRIEND HAS 1/6 OF A CAN. HOW MUCH RED PAINT DO THEY HAVE COMBINED?

COMMON DENOMINATOR: 6

DIVIDING FRACTIONS:

CONVERT ANY MIXED NUMBER INTO IMPROPER FRACTION. INVERT THE SECOND FRACTION SO THE DENOMINATOR AND NUMERATOR ARE SWITCHED. MULTIPLY NUMERATORS TOGETHER AND DENOMINATORS TOGETHER.

MULTIPLYING FRACTIONS

CONVERT ANY MIXED NUMBERS INTO IMPROPER FRACTIONS AND MULTIPLY NUMERATOR TOGETHER AND DENOMINATOR TOGETHER. REDUSE TO LOWEST FORM.

CONVERT 37/5 INTO A MIXED NUMBER:

DIVIDE NUMERATOR BY DENOMINATOR 37 / 5 = 7 WITH A REMAINDER OF 2 BUILD A MIXED NUMBER WITH THE WHOLE NUMBER AND THE NEW NUMERATOR: 37/5 = 7 2/5

2/3 - 1/5 = ?

FIND COMMON DENOMINATOR: 15 2/3 - 1/5 = 10/15 - 3/15 = 7/15

AN ITEM ORIGINALLY PRICED $55 IS MARKED 25% OFF. WHAT IS THE SALE PRICE?

FIND SALE PRICE, WHICH MEANS YOU NEED TO SOLVE FOR THE AMOUNT OF CHANGE FIRST. AMOUNT OF CHANGE = ORIGINAL AMOUNT X PERCENT CHANGE = 55 X 0.25 - 13.75 USING THIS AMOUNT, YOU CAN FIND NEW PRICE. SINCE IT'S ON SALE, WE KNOW THE AOUNT WILL COST LESS THAN ORIGINAL PRICE. 55 - 13.75 = $41.25

(5) EXPONENT 2 / 5 + 4 X 2

FIRST CALCULATE EXPONENTIAL EXPRESSIONS: (25) / 5 + 4 X 2 SECOND, CALCULATE DIVISION AND MULTIPLICATION FROM LEFT TO RIGHT: 5 + 8 FINALLY, DO ADDITION AND SUBTRACTION: 5 + 8 = 13

-(2)EXPONENT 2 - (4 + 7)

FIRST COMPLETE OPERATIONS WITHIN PARENTHESIS: -(2) EXPONENT 2 - (11) SECOND CALCULATE EXPONENTIAL EXPRESSION: -(4) - (11) FINALLY, DO ADDITION AND SUBTRACTION: -4 - 11 = -15

`(5/2 x 4) + 23 - 4 TO THE SECOND EXPONENT

FIRST COMPLETE WITHIN PARENTHESIS: (10) + 23 - 4 TO THE SECOND EXPONENT SECOND, CALCULATE EXPONENTIAL EXPRESSION: (10) + 23 - 16 FINALLY, DO ADDITION AND SUBTRACTION FROM LEFT TO RIGHT: 10 + 23 - 16 33 - 16 = 17

15 X (4 + 8) - 3 TO THE THIRD EXPONENT

FIRST COMPLETE WITHIN PARENTHESIS: 15 X (12) - 3 TO THE THIRD EXPONENT SECOND, CALCULATE VALUE OF EXPONENTIAL EXPRESSIONS: 15 X (12) - 27 THIRD, CALCULATE DIVISION AND MULTIPLICATION FROM LEFT TO RIGHT: 180 - 27 FINALLY, DO ADDITION AND SUBTRACTION FROM LEFT TO RIGHT: 180 - 27 = 153

A GOLF SHOP PAYS ITS WHOLESALER $40 FOR A CERTAIN CLUB, AND THEN SELLS IT TO A GOLFER FOR $75. WHAT IS THE MARKUP RATE?

FIRST, CALCULATE THE AMOUNT OF CHANGE: 75 - 40 = 35 NOW SET UP EQUATION & SOLVE (NOTE THAT MARKUP RATE IS ANOTHER WAY OF SAYING PERCENTAGE CHANGE): PERCENT CHANGE = AMOUNT OF CHANGE / ORIGINAL AMOUNT = 35/40 = 0.875 = 87.5%

2 1/3 - 3/2 = ?

FRACTION SUBTRACTION WITH A MIXED NUMBER - CONVERT MIXED NUMBER TO IMPROPER FRACTION: 7/3 - 3/2 = COMMON DENOMINATOR: 6 14/6 - 9/6 = 5/6

IMPROPER FRACTION:

FRACTION WITH A NUMERATOR LARGER THAN OR EQUAL TO ITS DENOMINATOR. CAN BE CONVERTED INTO MIXED NUMBERS BY DIVIDING THE NUMERATOR BY DENOMINATOR. THE RESULTING WHOLE NUMBER IS PLACED TO THE LEFT OF THE FRACTION AND THE REMAINDER BECOMES NEW NUMERATOR (DENOMINATOR DOES NOT CHANGE).

NATURAL NUMBER:

GREATER THAN 0 AND HAS NO DECIMAL OR FRACTION ATTACHED. SOMETIMES CALLED COUNTING NUMBERS EX: 1,2,3,4,...

7/8 / 1/4 =

INVERT SECOND FRACTION. 7/8 X 4/1 = 28/8 = 7/2

FRACTIONS:

MADE UP OF 2 PARTS

DIVIDING DECIMALS:

MOVE THE DECIMAL POINT IN THE DIVISOR (NUMBER YOU'RE DIVIDING BY) UNTIL IT'S A WHOLE NUMBER. YOU CAN THEN MOVE THE DECIMAL TO THE DIVIDEND (NUMBER YOU'RE DIVIDING INTO) THE SAME NUMBER OF PLACES IN THE SAME DIRECTION. FINALLY, DIVIDE THE NEW NUMBERS NORMALLY.

THE RATIO OF STUDENT TO TEACHERS IN A SCHOOL IS 15:1. IF THERE ARE 38 TEACHERS, HOW MANY STUDENTS ATTEND THE SCHOOL?

MULTIPLY BOTH SIDES OF THE RATIO BY DESIRED VALUE TO FIND NUMBER OF STUDENTS THAT CORRESPOND TO HAVING 38 TEACHERS 15 STUDENTS/1 TEACHER X 38 TEACHERS = 570 STUDENTS

CONVERT DECIMAL TO PERCENTAGE:

MULTIPLY IT BY 100. IF YOU'VE READ 5 PAGES (THE PART) OF A 10 PAGE ARTICLE (THE WHOLE), YOUV'E READ 5/10 = 0.5 = 50% (THE PERCENT SIGN (%) IS USED ONCE THE DECIMAL HAS BEEN MULTIPLIED BY 100) *** WHEN SOLVING THESE PROBLEMS, THE UNITS FOR THE PART AND THE WHOLE SHOULD BE THE SAME. IF YOU'RE READING A BOOK, SAYING YOU'VE READ 5 PAGES OUT OF 15 CHAPTERS DOESN'T MAKE SENSE.

WHAT IS THE PRODUCT OF 1/2 AND 6/8?

MULTIPLY NUMERATORS TOGETHER AND DENOMINATORS TOGETHER THEN REDUCE: 1/12 X 6/8 = 6/96 = 1/16 SOMETIMES EASIER TO REDUCE FRACTIONS FIRST: 1/12 X 6/8 = 1/12 X 3/4 = 3/48 = 1/16

MULTIPLYING/DIVIDING NEGATIVE/POSITIVE NUMBERS:

MULTIPLYING 2 NUMBERS WITH THE SAME SIGN GIVES A POSITIVE RESULT, AND MULTIPLYING 2 NUMBERS WITH DIFFERENT SIGNS GIVES A NEGATIVE RESULT. SAME RULES APPLY FOR DIVISION.

WHOLE NUMBERS:

NATURAL NUMBERS AND THE NUMBER 0. EX: 0,1,2,3,4,...

FIND THE SUM OF 9/16, 1/2 AND 7/4

NEED TO FIND COMMON DENOMINATOR: 16 1/2 X 8/8 = 8/16 7/4 X 4/4 = 28/16 9/16 + 8/16 + 28/16 = 45/16

MIXED NUMBERS:

NEW NUMBER FROM CONVERTING AN IMPROPER FRACTION. IT CONTAINS A WHOLE NUMBER AND A FRACTION. CAN BE TURNED INTO IMPROPER FRACTIONS THROUGH REVERSE PROCESS - MULTIPLY THE WHOLE NUMBER BY THE DENOMINATOR AND ADD THE NUMERATOR TO GET THE NEW NUMERATOR.

NUMERATOR:

NUMBER ABOVE THE WRITTEN LINE IN FRACTION

DENOMINATOR:

NUMBER BELOW THE LINE IN A FRACTION.

COMPARISON OF RATIONAL NUMBERS:

NUMBER COMPARISON PROBLEMS PRESENT NUMBERS IN DIFFERENT FORMATS AND ASK WHICH IS LARGER OR SMALLER, OR WHETHER THE NUMBERS ARE EQUIVALENT. THE IMPORTANT STEP IN SOLVING THESE PROBLEMS IS TO CONVERT THE NUMBER TO SAME FORMAT SO THAT IT IS EASIER TO SEE HOW THEY COMPARE. IF NUMBERS ARE GIVEN IN THE SAME FORMAT, OR AFTER THEY HAVE BEEN CONVERTED, DETERMINE WHICH NUMBER IS SMALLER OR IF THE NUMBERS ARE EQUAL. REMEMBER WITH NEGATIVE NUMBERS ARE HIGHER NUMBERS ARE ACTUALLY SMALLER.

DECIMALS AND FRACTIONS:

NUMBERS ARE WRITTEN USING THE BASE-10 SYSTEM WHERE EACH DIGIT (THE NUMERIC SYMBOLS 0-9) IN A NUMBER IS WORTH TEN TIMES AS MUCH AS THE NUMBER TO THE RIGHT OF IT. FOR EX: IN NUMBER 37 - EACH DIGIT HAS A PLACE VALUE BASED ON ITS LOCATION. THE 3 IS IN THE TENS PLACE, AND SO HAS A VALUE OF 30, AND THE 7 IS IN THE ONES PLACE, SO IT HAS A VALUE OF 7.

WHAT PERCENT OF 65 IS 39?

PERCENT = PART/WHOLE = 39/65 = 0.6 OR 60%

INTEGERS:

POSITIVE AND NEGATIVE NATURAL NUMBERS AND 0. EX: 0,....(-4,-3,)

ADDING AND SUBTRACTING FRACTIONS:

REQUIRES COMMON DENOMINATOR. TO GET THIS: YOU CAN MULTIPLY EACH FRACTION BY 1. WITH FRACTIONS, ANY NUMBER OVER ITSELF (EX: 5/5, 12/12) IS EQUIVALENT TO 1, SO MULTIPLYING BY SUCH FRACTION CAN CHANGE THE DENOMINATOR WITHOUT CHANGING THE VALUE OF THE FRACTION. ONCE DENOMINATOR ARE SAME, THE NUMERATOR CAN BE SUBTRACTED/ADDED.

JIM SPENT 30% OF HIS PAYCHECK AT THE FAIR. HE SPENT $15 ON A HAT, $30 FOR A SHIRT, AND $20 PLAYING GAMES. HOW MUCH WAS HIS CHECK? (ROUND TO NEAREST DOLLAR)

SET UP APPROPRIATE EQUATION AND SOLVE. WHOLE = PART/PERCENT = 15 + 30 + 20 / 0.30 = 216.67 = $217

A COMPUTER SOFTWARE RETAILER MARKS UP ITS GAMES 40% ABOVE WHOLESALE PRICE WHEN IT SELLS THEM TO CUSTOMERS. FIND THE PRICE OF A GAME FOR A CUSTOMER IF THE GAME COSTS THE RETAILER $25.

SET UP EQUATION AND SOLVE. AMOUNT OF CHANGE = ORIGINAL AMOUNT X PERCENT CHANGE = 25 X 0.4 = 10 IF THE AMOUNT CHANE IS 10, THAT MEANS THE STORE ADDS A MARK UP OF $10, SO THE GAME COSTS $25 + $10 = $35

45 IS 15% OF WHAT NUMBER?

SET UP EQUATION AND SOLVE. DON'T FORGET TO CHANGE 15% TO A DECIMAL. WHOLE = PART/PERCENT = 45/0.15 = 300

GRANT NEEDS TO SCORE 75% ON AN EDAM. IF HE HAS 45 QUESTIONS, HOW MANY QUESTIONS DOES HE NEED TO ANSWER CORRECTLY?

SET UP EQUATION AND SOLVE. REMEMBER TO CONVERT 75% TO DECIMAL VALUE. PART = WHOLE X PERCENT = 45 X 0.75 = 33.75 - HE NEEDS TO ANSWER AT LEAST 34 QUESTIONS CORRECTLY

ONE ACRE OF WHEAT REQUIRES 500 GALLONS OF WATER. HOW MANY ACRES CAN BE WATERED WITH 2600 GALLONS?

SET UP EQUATION: 1 ACRE/500 GAL = x ACRES/2600 GAL SOLVE FOR x: x ACRES = 1 ACRE X 2600 GAL/ 500 GAL x = 26/5 OR 5.2 ACRES

A TRAIN TRAVELING 120 MILES TAKES 3 HOURS TO GET TO ITS DESTINATION. HOW LONG WILL IT TAKE FOR A TRAIN TO TRAVEL 180 MILES?

SET UP PROPORTION: 120 MILES/3 HOURS = 180 MILLES/ X HOURS ** IT DOES NOT MATTER WHICH VALUE IS PLACED IN NUMERATOR OR DENOMINATOR AS LONG AS ITS THE SAME ON BOT SIDES. - SOLVE FOR MISSING QUANTITY THROUGH CROSS-MULTIPLYING. 120 MILES X x HOURS = 3 HOURS X 180 MILES x HOURS = (3 HOURS_ X (180 MILES)/ 120 MILES x = 4.5 HOURS

A STORE CHARGES 40% MARKUP ON SHOES IT SELLS. HOW MUCH DID THE STORE PAY FOR A PAIR OF SHOES PURCHASED BY A CUSTOMER FOR $63?

SOLVING FOR ORIGINAL PRICE, BUT IT'S TRICKY B/C YOU DON'T KNOW THE AMOUNT OF CHANGE, YOU ONLY HAVE THE NEW PRICE. TO SOLVE, CREATE EXPRESSION FOR AMOUNT OF CHANGE. ORIGINAL AMOUNT = x AMOUNT OF CHANGE = 63 - x PLUG VALUES INTO EQUATION: ORIGINAL AMOUNT = AMOUNT OF CHANGE / PERCENT CHANGE x= 63 - x / 0.4 LAST STEP IS TO SOLVE FOR x : 0.4x = 63 - x 1.4x = 63 x = 45 STORE PAID $45 FOR THE SHOES.

MULTIPLYING DECIMALS:

START BY MULTIPLYING NORMALLY. YOU CAN THEN DETERMINE THE PLACEMENT OF DECIMAL POINTS IN THE RESULT BY ADDING NUMBERS OF DIGITS AFTER THE DECIMAL IN EACH OF THE NUMBERS YOU MULTIPLIED TOGETHER.

RATIOS:

TELLS YOU HOW MANY OF ONE THING EXIST IN RELATION TO THE NUMBER OF ANOTHER THING. UNLIKE FRACTIONS, RATIOS DO NOT GIVE A PART RELATIVE TO A WHOLE, INSTEAD THEY COMPARE TWO VALUES. EX:IF YOU HAVE 3 APPLES AND 4 ORANGES , THE RATIO OF APPLES TO ORANGES IS 3 TO 4. RATIOS CAN BE WRITTEN USING WORDS (3 TO 4), FRACTIONS (3/4) OR COLONS (3:4) ***WHEN WORKING WITH RATIOS IMPORTANT THING TO CONSIDER IS UNITS OF VALUES BEING COMPARED. MAY BE ASKED TO REWRITE RATIO USING SAME UNITS ON BOTH SIDES EX: YOU MIGHT HAVE TO REWRITE THE RATIOR 3 MINUTES TO 7 SECONDS AS 180 SECONDS TO 7 SECONDS.

CONVERT 0.45 INTO A FRACTION:

THE LAST NUMBER IN THE DECIMAL IS IN THE HUNDREDTHS PLACE - 0.45 = 45/100 THEN REDUCE FRACTION DOWN TO LOWEST COMMON DENOMINATOR. HERE, BOTH 45 AND 100 CAN BE DIVIDED BY 5: 45/100 = (45 / 5) / (100 / 5) = 9/20

SIMPLEST FORM:

THE NUMERATOR AND THE DENOMINATOR SHARE NO COMMON FACTORS.

PERCENTAGES:

THE RATIO OF A PART TO THE WHOLE MULTIPLIED BY 100. EQUATION FOR PERCENT AGES CAN BE REARRANGED TO SOLVE FOR EITHER THE PART, THE WHOLE, OR THE PERCENT. PERCENT = PART/WHOLE PART = WHOLE X PERCENT WHOLE = PART/PERCENT IN THIS EQUATION ABOVE ^ THE PERCENT SHOLD ALWAYS BE EXPRESSED AS A DECIMAL.

PERCENTAGE CHANGE:

THESE PROBLEMS WILL ASK YOU TO CALCULATE HOW MUCH A GIVEN QUANTITY CHANGED. THE PROBLEMS ARE SOLVED IN A SIMILAR WAY TO REGULAR PERCENTAGE PROBLEMS, EXCEPT THAT INSTEAD OF USING THE PART YOU'LL USE THE AMOUNT OF CHANGE. SIGN OF THE AMOUNT OF CHANGE IS IMPORTANT: IF THE ORIGINAL AMOUNT HAS INCREASED THE CHANGE WILL BE POSITIVE, AND IF IT HAS DECREASED THE CHANGE WILL BE NEGATIVE. IN THE EQUATION BELOW, THE PERENT IS A DECIMAL VALUE YOU NEED TO MULTIPLY BY 100 TO GET THE ACTUAL PERCENTAGE. PERCENT CHANGE = AMOUNT OF CHANGE/ ORIGINAL AMOUNT AMOUNT OF CHANGE = ORIGINAL AMOUNT X PERCENT CHANGE ORIGINAL AMOUNT = AMOUNT OF CHANGE / PERCENT CHANGE WORDS THAT INDICATE PERCENT CHANGE PROBLEM: "DISCOUNT, MARKUP, SALE, INCREASE, DECREASE

GRETA AND MAX SELL CABLES. IN A GIVEN MONTH, GRETA SELLS 45 CABLES AND MAX SELLS 51. IF 240 TOTAL CABLES WERE SOLD IN THAT MONTH, WHAT PERCENT WERE NOT SOLD BY GRETA AND MAX?

USE INFO. IN EQUATION TO FIGURE OUT WHAT PERCENTAGE MAX AND GRETA SOLD: PERCENT = PART/WHOLE = (51 +45) / 240 = 96/240 = 0.4 OR 40% BUT THE QUESTIONS ASKS HOW MANY CABLES WEREN'T SOLD BY GRETA AND MAX. IF THEY SOLD 40%, THEN THE OTHER PEOPLE SOLD ? 100% - 40% = 60%

CONVERTING DECIMALS INTO FRACTIONS:

USE THE NUMBERS THAT COME AFTER THE DECIMALS AS THE NUMERATOR IN THE FRACTION. THE DENOMINATOR WILL BE A POWER OF 10 THAT MATCHES THA PLCE VALUE FOR ORIGINAL DECIMAL. EX: DENOMINATOR 0.46 WOULD BE 100 BECAUSE THE LAST NUMBER IS IN THE HUNDREDTHS PLACE. DENOMINATOR FOR 0.657 WOULD BE 1000 BECAUSE THE LAST NUMBER IS IN TH THOUSANDTHS PLACE. ONCE THE FRACTION IS SET UP - SIMPLIFY IT. ON CALCULATOR TO CONVERT FRACTION TO DECIMAL: DIVIDE NUMERATOR BY THE DENOMINATOR.

THERE ARE 90 VOTERS IN A ROOM AND EACH IS EITHER DEMOCRAT OR REPUBLICAN. THE RATIOR OF DEMOCRATS TO REPUBLICANS IS 5:4. HOW MANY REPUBLICANS ARE THERE?

WE KNOW THERE ARE 5 DEMOCRATS FOR EVERY 4 REPUBLICANS IN THE ROOM, WHICH MEANS FOR EVERY 9 PEOPLE 4 ARE REPUBLICAN. 5 + 4 = 9 FRACTION OF REPUBLICANS: 4/9 IF 4/9 OF THE 90 VOTERS ARE REPUBLICANS, THEN: 4/9 X 90 = 40 VOTERS ARE REPUBLICANS.

PROPER FRACTION:

WHEN THE DENOMINATOR IS LARGER

ADDING/SUBTRACTING DECIMALS:

WRITE THE NUMBERS SO THAT THE DECIMAL POITNS ARE ALIGNED. YOU WANT TO SUBTRACT THE ONES PLACE FROM THE ONES PLACE, THE TENTHS PLACE FROM THE TENTHS PLACE, ETC.

ADDING MIXED NUMBERS:

YOU CAN FIRST ADD WHOLE NUMBERS AND THEN THE FRACTIONS.