Math study tips

What is the fractional equivalent of 6 2/3 %

improper fraction = 20/3 20/3 ÷ 100 = 20/3 × 1/100 = 1/15

quick addtion tips

look for pairs of 10 to speed up addition add left to right instead of right to left

word problems with ratios, proportions, and rates of change

units of an item/units of an item = units of an item/units of an item same numerators and denominators cross multiply 1250 students/50 sections = 1550 students/X sections 50 * 1550 = 77500 divide 77500 by 1250 to solve for X X = 62

After a 15% discount, a television const $102. What was the original price?

x - 0.15 (x) = $102 1x - 0.15 (x) = $102 100-0.15 = 0.85 0.85 (x) = $102 /0.85 /0.85 x= $120

81ft² = yd² (3ft=1yd)

yd²= 1yd²/9ft² x 81ft² = 9yd² square the yards/feet

neighborhood has 5% red mailboxes. Student counts 60 red mailboxes How many mailboxes in the neighborhood?

% * whole = part .05 * X = 60 60/.05 = 1200 total mailboxes Take the number of red mailboxes (60) and devide by

***AFTER a 15% off discount the TV cost $102.00 What was the original cost?

% * whole = part change to decimal 15% = .15 SUBRACT .15 from 100 (since it is OFF not OF) = .85 .85 * whole = 102.00 now we can divide $102.00 by .85 = $120.00

The attendance at a nursing conference was 400 (w) members, 75% of whom voted for an increase in membership dues. What is the number of members who voted for the increase

% X whole = part 0.75 x 400 = 300

The ratio of student who take the bus to school to the total population of a high school is 2:5. What is the % of students who take the bus

% x whole = part % x 5 = 2 2/5 = 40%

Sixteen out of 64 students in a physics class received a grade of A. What is the percent of students who received an a

% x whole = part % x 64 = 16 16/64 = 25%

The number 297 is 24 3/4% of what number

% x whole = part 24.75 % x w = 297 move decimal 0.2475 x w = 297 2970000/2475 = 1,200

A $75 sweater is discounted by $15. Which of the following is the percent of the discount

% x whole = part N% X $75 = $15 15/75 = 20 %

A computer is worth $1,500 at the time of purchase. After five years, the computer is obsolete and has no value. Assuming the value decreases linearly, write the expression that represents the computers value at any time (t)

-300t +1500 1,500/5 = 300 -300(5) = -1,500 which =1,500-1,500= 0

1. Two numbers have the sum of 20. 2.What equation states that the product of one number and the square of the other is 50

1. x + y = 20 2. xy² = 50 =X² (20 - X) = 50 x + y = 20 ; x = 20-y (20-y) y² = 50

106 (101) Base 100

106 + 1 = 107 Base 100, therefore we need 2 more numbers 6 x 1 = 6 therefore 06 106 (101) = 10706

112 (102) Base 100

112 + 2 = 114 12 x 2 = 24 112 (102) = 11424

same as double digit 112 x 118

112 x 118 12 is the number above 11 so 12 x 11 = 132 ( first number 1/ 1 + 2=3/ 2 -last number) 2 x 8 = 16 therefore 112 x 118 = 13216

13(13)

13 + 3 =16 3 x 3=9 =169

Base 10 multiplication

13 x 12 = 156 Add 13 + 2 (last number in 12)= 15 then multiply the 3 x 2 =6 the ones in 13 & 12 =156

subtraction mental math

15 - 6 ask what + 6 = 15 = 9 work backwards

16 (12) =

16 + 2 = 18 carry 10 from 12 6 x 2 = 12 = 192

Multiplying by 11

21432 (11)= 235752 2 2+1=3 gives you the 2nd number 1+4 =5 the 2nd number + the 3rd number gives you the 3rd number in the answer 4+3=7 the 3rd number + the 4th number gives you the 4th number 3+2=5 the 4th number + the 5th number gives you the 5th number 2 is the last number in the number

Left to right addition- mental math addition

23 +13 20 + 10 =30 + 3 = 33 + 3 = 36 add tens and then go to ones keep place as you go. 24 +17 20 + 10 = 30 + 4 =34 + 7 = 41

23 (21) Base 20

23 +1 = 24 DBLB for base of 20 = 48 3 x 1 = 3 23 x 21 = 483

subtraction mental math

24 - 19 19 + what = 24 =5 45 -33= 12 40 - 30 = 10 5-3 =2

3 digit-mental math-addition

243 +125 200 + 100 = 300 + 40 = 340 + 20 = 360 +3 = 363 + 5 + 368

On Monday, 3 students out of a class of 24 were absent from class. What percent of the students were absent from class?

3 divided by 24 3/24 = .125 12.5%

Use the front in method to estimate 67*5=

300

37 x 33 56 x 54 21 x 29 Rule is the first numbers must be equal and the ones must equal 10

4 (next number up from 3 in 37 multiplied to the first number in 33) 37 4 x 3 = 12 (12 is the first number in your answer) Then multiply the last numbers 7 in 37 and 3 in 33 7 x 3 = 21 ( 21 is the last number in your answer) 37 X 33 = 1221 __ 56 x 54 6 x 5 = 30 6 x 4 = 24 therefore 56 x 54 = 3024 ____ 21 x 29 = 3 x 2 = 6 1 x 9 = 9 =609 therefore 21 x 29 = 609

5 (x-2)² = 125

5/5 (x-2)² = 125/5 =25 √ (x-2)² = 25 = x-2 = ± 5 x= -3, 7

Square of 46 between 30-70 (less than 50) mental math

50-46=4 so 46 is 4 away from 50 25-4=21 Square of 4 is 16 answer 46 squared is 2116

Use the front end method to estimate the difference of 642-196=

500

Square of 52 between 30-70 (more than 50) mental math

52-50 = 2 so add 2 to 25 25 + 2 = 27 square of 2 = 04 answer of the square of 52 is 2704

The enrollment at a college went up from 625 students to 710 students over a period of 1 year. What was the percent increase?

710-625 = 85 divide 85 by 625 85/625 = .136 13.6%

to find a WHOLE when given a "% of" and the percent if 73% of X = 471.58

DIVIDE change % to decimal .73 and divide it into 471.58 = 646

L = 2/3k The equation above models the length (L) of the crutch in inches required for a person where K is the height in inches- which of the following is true

Each 3 inches of height (K) adds 2 inches to the length (L)

Roman numerals

I Voted X, Lynn Can Do More 1, 5, 10, 50, 100,500, 1000 Lucky cows drink milk 50, 100,500,1000

It is divisible by five if

It ends in the number 5 or zero Example: 3765 or 3760

It is divisible by 10 if

It ends in zero. No explanation needed.

It's divisible by six if

It is even and a visible by three. Example: 522

It's divisible by nine if

It's digits add up to a multiple of nine. Example 34,164. Adding the digits 3+4+ 1 +6+4 = 18 = 2 x 9= 18

Divisible by Three

It's digits add up to a multiple of three. example: 186. One +8+6 = 15 = 3×5

It's divisible by eight if

It's last three digits form a multiple of eight. Example: 10,496 832. (832÷8 = 104)

It's divisible by four if:

It's last two digits form (not add up to) A number divisible by four. Example: 103,424 24 is divisible by 4

% problems

Keep in mind: OF translates into multiply IS translates into equals AFTER translates into subtraction "What percent of the whole is the part?"

Metric

Kellys Hip Decorator Used Dark Colored Molding @ the Mirror

It's divisible by seven if

Never mind too hard use the calculator

Student A reads 10 pages an hour Student B reads 18 pages an hour Each has a 288 page book to complete. How much sooner will Student B complete the book compared to Student A?

Ratio/proportion problem *time for student A 10pgs/hr = 288 pgs/X hr cross multiply 10 * A = 288 * 1 A = 28.8 hrs Student B 18 * B = 288 * 1 B = 16hrs 28.8 - 16 = 12.8 hrs faster

Multiplying by 12

Same as multiplying by 11 except you have to double the numbers for example 1332 x 12 first number will be the 1 in the beginning of the number Double the 1 and add to 5 1 2+3=5 6+3=9 6+2=8 2+2=4 this is equal to 1332 (12) = 15984

The 18 students who received an A in mathematics class made up 30% of the students in the class. Find the total number of students in the class.

X * 30% = 18 so X = 18/.30 X = 60

Quick tip for percents, bike is 8k, buy today get 1600 off. what percent off?

do it in 10s 16/ 8 = 2 = 20%