FRACTIONS

FRACTION RULES

- A POSITIVE NUMBER DIVIDED BY NEGATIVE NUMBER= NEGATIVE NUMBER - A LARGER POSITIVE NUMBER DIVIDED BY A SMALLER POSITIVE NUMBER IS GREATER THAN 1 - FOR ADDITION/ SUBTRACTION PROBLEMS: FIND COMMON DENOMINATOR BY CROSS MULTIPLYING FOR NUMERATOR AND MULTIPLYING ACROSS FOR DENOMINATOR - FOR MULTIPLICATION PROBLEMS: MULTIPLY ACROSS THE NUMERATOR AND DENOMINATOR - FOR DIVISION PROBLEMS: MULTIPLY BY ITS RECIPROCAL (RECIPROCAL OF A/B IS B/A) - EXAMPLE FOR DIVISION FRACTION PROBLEMS: 2/3 ÷ 1/2 2x2/3x1= 4/3

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 1/2 + 2/3

1/2 + 2/3 **CROSS MULTIPLY TO GET SAME DENOMINATOR FOR ADDITION PROBLEMS** 1x3= 3/6 (multiply denominators) 2x2=4/6 (multiply denominators) 3/6+4/6 3/6+4/6 = 7/6(ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 1/2 x 2/3

1/2 x 2/3 **MULTIPLY ACROSS FOR MULTIPLICATION PROBLEMS 1/2 x 2/3= 2/6 2/6= 1/3 (ANSWER)

SIMPLIFY THE FOLLOWING EXPRESSION 12/18

12/18 6/9 2/3 (ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 2/3 - 1/4

2/3 - 1/4 **CROSS MULTIPLY TO GET SAME DENOMINATOR FOR SUBTRACTION PROBLEMS** 2x4= 8/12 (multiply denominators) 3x1= 3/12 (multiply denominators) 8/12-3/12= 5/12 (ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 3/7 + 2/3

3/7 + 2/3 **CROSS MULTIPLY TO GET SAME DENOMINATOR FOR ADDITION PROBLEMS** 9/21 + 14/21= 23/21 (ANSWER)

SIMPLIFY THE FOLLOWING EXPRESSION 30/24

30/24 10/8 5/4 (ANSWER)

SIMPLIFY THE FOLLOWING EXPRESSION 38/6

38/6 19/3 (ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 4/5 + 1/6

4/5 + 1/6 24/30 + 5/30= 29/30 (ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 4/5 + 2/5

4/5 + 2/5= 6/5 (ANSWER)

SIMPLIFY THE FOLLOWING EXPRESSION 48/36

48/36 12/9 4/3 (ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 5/6 - 1/2

5/6 - 1/2 10/12 - 6/12= 4/12 4/12= 1/3 (ANSWER)

PERFORM THE OPERATION. EXPRESS RESULTS IN SIMPLEST FORM. 6/7 x 1/4

6/7 x 1/4 **MULTIPLY ACROSS FOR MULTIPLICATION PROBLEMS 6/7 x 1/4= 6/28 6/28= 3/14 (ANSWER)

OVER THE LAST THREE YEARS, 20% OF THE ADULT RESIDENTS OF MILLTOWN BOUGHT A NEW CAR. OF THE REMAINING ADULTS LIVING IN MILLTOWN, 40% BOUGHT A USED CAR DURING THAT SAME PERIOD. WHAT PERCENTAGE OF ADULT RESIDENTS LIVING IN MILLTOWN BOUGHT NEITHER A NEW CAR NOR A USED CAR OVER THE LAST THREE YEARS?

ANSWER: 40% OF 80= 32 20% OF 100= 20 20+32=52 (NUMBER OF PEOPLE WHO BOUGHT NEW CAR AND USED CAR 100-52=48 (NUMBER OF PEOPLE WHO DIDN'T BUY A NEW CAR OR USED CAR)

CASEY ATE 1/5 OF THE PEANUTS IN A JAR ON MONDAY. 1/4 OF THE REMAINING PEANUTS ON TUESDAY. FINISHED THE PEANUTS IN THE JAR BY EATING AN EQUAL NUMBER OF THEM ON WEDNESDAY, THURSDAY, AND FRIDAY. IF SHE ATE 30 PEANUTS ON FRIDAY, HOW MANY PEANUTS FROM THE JAR DID CASEY EAT FROM MONDAY-FRIDAY?

ANSWER: 150 MONDAY= 1/5 TUESDAY= 1/4 WED/ THURS= FINISHED IN EQUAL NUMBER FRIDAY= 30 60+60+60= 180 (WED/THURS/FRI) MONDAY= 12 TUESDAY=15 180-12-15= 153

SIMPLIFY THE FOLLOWING EXPRESSION 6N/3

ANSWER: 2N

SIMPLIFY THE FOLLOWING EXPRESSION 10-5N/5

ANSWER: 2N-1 10N/5= 2N -5/5= -1

IN PLAINVIEW, ONE THIRD OF HOUSEHOLDS OWN THREE OR MORE TELEVISIONS. IF THERE ARE 5,253 HOUSEHOLDS IN PLAINVIEW, HOW MANY HOUSEHOLDS OWN TWO OR FEWER TELEVISION?

ANSWER: 3,502 5253x1/3= 1751 (NUMBER OF HOUSEHOLDS WITH THREE OR MORE TELEVISIONS) 5253-1751= 3502 (NUMBER OF HOUSEHOLDS WITH TWO OR FEWER TELEVISIONS)

WHEN CUP A IS FILLED TO 2/3 OF ITS CAPACITY, THE CONTENT OF CUP A FILL CUP B TO ITS CAPACITY EXACTLY TWICE. WHAT IS THE RATIO OF THE CAPACITY OF CUP A TO THE CAPACITY OF CUP B?

ANSWER: 3/1 2/3A=2B 2/3=2/1 **CROSS MULTIPLY 6/2= 3= 3/1 (RATIO)

IF 12%(N)=60, THEN 60%(N)=

ANSWER: 300 12/100(N)=6 N=6(100/12) N=500 60/100(500)=300

AMONG COFFEE DRINKERS, 25% DRINK ONLY DECAFFEINATED COFFEE, WHILE ONE THIRD OF THOSE REMAINING SOMETIMES DRINK DECAFFEINATED COFFEE. WHAT PERCENT OF COFFEE DRINKERS NEVER DRINK DECAFFEINATED COFFEE, TO THE NEAREST PERCENT?

ANSWER: 50% ONLY DECAF= 25 PEOPLE 100-25= 75 1/3 OF 75 SOMETIMES DECAF= 25 25(ONLY)+25(SOMETIME)= 50 NEVER DECAF=.50% (100-50)

ABE AND ZOE BOTH WALK AROUND A TRACK. ABE AT A RATE OF 6. MINUTES PER LAP AND ZOE AT A RATE OF 4 MINUTES PER LAP. IF THEY CONTINUE WALKING AROUND AT THESE SAMT RATES, HOW MANY LAPS WILL ABE WALK IN THE TIME IT TAKES ZOE TO WALK 12 LAPS?

ANSWER: 8 ZOE= 4/LAP= 12 LAPS= 48 MINUTES ABE= 6/LAP= 48 MINUTE/6= 8 LAPS

IF N IS AN INTEGER, AND 2<N<7, THEN THE TENTH DIGIT OF THE DECIMAL REPRESENTATION OF 3/N COULD BE SELECT ALL OF THE FOLLOWING. A-4 B-5 C-6 D-7 E-8

ANSWER: B, C, D N= 3= 3/3= 1.0 N= 4= 3/4=0.75 N=5= 3/5= 0.6 N=6= 3/6= 0.5

TWO THIRDS OF THE APPLICANTS FOR A JOB HAVE A COLLEGE DEGREE, AND HALF OF THESE HAVE PREVIOUS EXPERIENCE QUANTITY A: THE NUMBER OF APPLICANTS WITH A COLLEGE DEGREE AND EXPERIENCE QUANTITY B: THE NUMBER OF APPLICANTS WITHOUT A COLLEGE DEGREE

ANSWER: BOTH QUANTITIES ARE EQUAL QUANTITY A: 100x2/3= 66.66 (DEGREE) 66.66/2= 33.33 = 34 **ROUND UP BECAUSE HUMAN** (DEGREE+EXPERIENCE) QUANTITY B: 100-66= 34

IF M/N>1, THEN IT MUST BE THE CASE THAT SELECT ALL THAT APPLY A- M>N B-M<N C-|M|>|N| D-M-N>0 E-MN>0

ANSWER: C, E M>N EX. 10/5=2 > 1 EX. 10/-5= -2 < 1 M<N EX. 5/10= 0.5 <1 |M|>|N| EX. 10/5=2>1 MN>0 (10)(5)=50

THE M MEMBERS OF A CLUB EACH PURCHASED EXACTLY ONE TICKET TO A SHOW. IF THE RETAIL PRICE OF A TICKET IS T DOLLARS, BUT EACH MEMBER RECEIVES A DISCOUNT OF D PERCENT OFF THE RETAIL PRICE ON THE PURCHASE OF HIS OR HER IDEA, WHAT IS THE TOTAL AMOUNT, IN DOLLARS, THAT THE M CLUB MEMBERS SPEND ON TICKETS TO THE SHOW?

ANSWER: MT(100-D)/100

SIMPLIFY THE FOLLOWING EXPRESSION 8N+6P/6N

ANSWER: P/N+4/3 4N+3P/3N P/N+4/3

THE SET S CONSISTS OF ALL FRACTIONS OF THE FORM 1/N FOR INTEGERS N SUCH THAT 1≤N≤4 QUANTITY A: THE SUM OF THE MEMBERS OF S QUANTITY B: 2

ANSWER: QUANTITY A IS GREATER QUANTITY A: 1/1 + 1/2 + 1/3 + 1/4= 2.0833 QUANTITY B: 2

THE DECIMAL 0. AB= 1/N FOR N SUCH THAT 3<N<4 QUANTITY A: A QUANTITY B: B

ANSWER: QUANTITY A IS GREATER. AB=1/3.5= 0.29 AB= 1/N AB= (1/N)/B AB= 0.29/B

EXACTLY 40% OF THE STUDENTS IN A CLASS ARE MEN. QUANTITY A: THE RATIO OF MEN IN THE CLASS TO WOMEN IN THE CLASS QUANTITY B: THE RATIO OF WOMEN IN THE CLASS TO THE TOTAL NUMBER OF STUDENTS IN THE CLASS

ANSWER: QUANTITY A IS GREATER. MEN= 40 QUANTITY A: 40/60= 0.66 QUANTITY B: 60/100= 0.6

QUANTITY A: 1/2 + 2/3 QUANTITY B: 1/2 x 2/3

ANSWER: QUANTITY A IS GREATER. QUANTITY A: 1/2 + 2/3= 3/6 + 4/6= 7/6 QUANTITY B: 1/2 x 2/3= 2/6

BILL PADDLES A CANOE AT THE RATE OF C MILES PER HOUR. HARRY PADDLES A CANOE AT 3/4 BILL'S RATE. THEY EACH PADDLE FOR H HOURS. QUANTITY A: THE DISTANCE BILL PADDLES IN H HOURS QUANTITY B: 125% OF THE DISTANCE HARRY PADDLES IN H HOURS

ANSWER: QUANTITY A IS GREATER. QUANTITY A: 100 QUANTITY B: 100*0.75= 75 125% OF 75= 93.75

A=1/3 B=1/2 QUANTITY A: A/B QUANTITY B: B/A

ANSWER: QUANTITY B IS GREATER. QUANTITY A: 1/3 ÷ 1/2= 2/3 QUANTITY B: 1/2 ÷ 1/3= 3/2

THE SET S CONSISTS OF ALL FRACTIONS OF THE FORM N+1/N FOR INTEGERS N SUCH THAT 1<N<10 QUANTITY A: THE PRODUCT OF THE MEMBERS OF S QUANTITY B: 11/10

ANSWER: TWO QUANTITIES ARE EQUAL QUANTITY A: 1+1/1=2 2+1/2=1.5 3+1/3=1.3 4+1/4=1.25 5+1/5=1.2 6+1/6=1.16 7+1/7=1.14 8+1/8=1.125 9+1/9=1.1 10+1/10=1.1 SUM OF EVERYTHING= 12.875 QUANTITY B: 11

SIMPLIFY THE FOLLOWING EXPRESSION X^2-Y^2/ X+Y

ANSWER= X-Y X^2-Y^2/ X+Y (X+Y)(X-Y)/X+Y X-Y

IF NUMBERS N, M, AND P ARE ORDERED SO THAT N<0<M<1<P, THEN WHICH ONE OF THE FOLLOWING GIVES THE CORRECT ORDER OF 1/N, 1/M, 1/P?

N= -1 M=0.5 P=1 1/N=1/-1= -1 1/M= 1/0.5= 2 1/P= 1/1= 1 1/N < 1/P < 1/M (ANSWER)