Teas Math

1/8

.125 or 12.5% half of 1/4

1/6

.165 or 16.5%

11 squared

11=121

12 squared

144

14 squared

196

Must know squares! 1-10

1=1 2=4 3=9 4=16 5=25 6=36 7=49 8=64 9=81 10=100

Square root of 5

2.2

15 squared

225

3x8

24

6x4

24

8x3

24

25% of what number is 8?

25/100 x X = 8

16 squared

256

3x9

27

9x3

27

7x4

28

6x6

36

Ex: 70 ---- X 7 = x 100

First step is make the problem easier for you! If the top number has a zero/zeros, take away one or two and then take away one or two on the bottom! Ex: 7/10 X 7 = X Then continue to make it easier by simplifying! 7/2 X 7 cause 2 fives go into 10 and 7 fives go into 35! Then solve from there, so much easier! Don't forget needs to be divided! 7 X 7 49 ------ = ---- = 24.5 2

Easy fraction to percentage problem

Get the denominator as close to 100 as possible. Multiply the bottom by a number to get it as close to 100, then multiply the top by that same number. Ex: 8/11 = multiply both by 9 = 72/99 answer is = 72%

Calculating Median/Middle value

If there is an even number of values, average the two in the middle (make sure there in order first) Ex: 3, 4, 5, 6, = (4+5) divided by 2 = 4.5 Odd number: the median is the middle number

Most square roots are

Irrational

Rational number

Is any number that can be written as a fraction = 3/8, 3/4 A terminating decimal = .375, .75 Repeating decimal = .33333333, .54545454 (has a pattern) It can be a square root number, ex: square root of ✔️36 is 6 so that's a rational number, or negative square root of ✔️36 is -6 so it's still rational.

Square root

Is the inverse operation of squaring a number Ex: 10 squared is =100 , square root ✔️100

Finding a total area/square footage of a square/rectangle

Multiply one side by the other Ex: rectangle is 6ft by 8ft = 48ft

Percent increase

New value - old value over old value X 100

Percent decrease

Old value - new value over original value X 100

What does percent mean

Per 100 or over 100

Remember to think logically in percents!

Percents are always per 100! So if they give you a problem like: what percent of 25 is 5? Well obviously 5 goes into 25, 5 times. So if you think money $, $20 out of 100 is 20%!

Adding a bunch of fractions together

Separate the fractions and add them first then combine Ex: 3 1/2 + 5 1/3 + 1 3/4 Take the fraction part first and add them together 1/2 + 1/3 + 3/4 = 19/12 simplify this by making making it 1 7/12 Then add up the whole numbers 3+5+1= 9 9 + 1 7/12= 10 7/12

Perimeter

Sum of all sides Ex: garden is a rectangle that's 25 feet but 30 feet, add it all together. 25+25+30+30=110

Determining the range in a set

The difference between the highest and lowest value in the set

Calculating the mode

The most frequent score Ex: 87, 92, 87, 88, 91. = 87 would be the mode cause it's most frequent

Ratios

Things that are similar (like things) Boys vs girls Blue cars vs red cars Radios don't have units

Calculating Mean/Average

Total the values, then divide by the number of values Ex: mean of 3, 4, 5 = 12/3 = 4

What is the factors of 12? Is the same as saying what is the divisors of 12?

What can go into 12? =1, 2, 3, 4, 6, 12 *make sure you put 1, it's always a divisor, and the actual number 12.

Changing a mixed fraction 2 1/3 to a improper fraction

Whole number multiplied by denominator then added to numerator = 7/3 bottom number stays the same!

1/5

.2 or 20%

2/10

.2 or 20%

1/4

.25 or 25%

2/8

.25 or 25%

1/3

.33 or 33.5%

3/8

.375 or 37.5% half of 3/4

2/5

.4 or 40%

4/10

.4 or 40%

2/4

.50 or 50%

4/8

.50 or 50%

3/5

.6 or 60%

6/10

.6 or 60%

5/8

.625 or 62.5%

2/3

.67 or 67%

3/4

.75 or 75%

6/8

.75 or 75%

4/5

.8 or 80%

8/10

.8 or 80%

7/8

.875 or 87.5%

4/4

1 or 100%

10/10

1. or 100%

5/5

1.0 or 100%

Square root of 3

1.7

Finding total area for a triangle (formula)

1/2 x base x height

How to calculate percents academically

15% of 500 is what? 15 percent is always out of 100, OF is multiplication, IS is equals, WHAT is X! 15/100 x 500 = X Or the question can be worded what is 60% of 5? *this can be tricky, but you always put the percent over 100 Ex: 60/100 = X/5

13 squared

169

Finding an approximate decimal for a cube root: Cube root of 8: Cube root of 27: Cube root of 64: so to find the cube root of 10? Cube root of 15?

2 3 4 You would know it's somewhere between 8 and 27 or 2 & 3 = 2.15 Estimate by multiplying 2.5 x 2.5 x 2.5 = 15.625

5x6

30

Express 30 minutes to 4 hours as a ratio I'm fraction

30/240 (make the hours to minutes) then simplify. Don't forget to get rid of the zeros to make it easier! 3/24= 1/8

8x4

32

5x7

35

9x4

36

20 squared

400

6x7

42

7x6

42

5x9

45

8x6

48

An amount of 50 decreases by 5, what is the percent decrease?

50-45 ------- X 100 = 10% 50 Or if we're Keshwani =) we don't do all that work, we just know that 5 of 50 is 10%

6x9

54

9x6

54

7x8

56

8x7

56

7x9

63

9x7

63

8x8

64

8x9

72

9x8

72

*Tricky with percents* 9 is what percent of 25?

9/25 =X/100

What is the value of X if the average is 6? 5cm, 7cm, 7cm, 6cm, and X?

Add them all up and divide by # of places. 25/5=5

When estimating

Always make sure your estimating low or high! Ex: 6.3 x 7.6, you know 6x7=42 then add .5 of 7 so that's 3.5, =45.5 But I know that's an under estimation cause the answer is 47.88

When multiplying/dividing fractions

Always simplify before! Any number that will go into the both other numbers.

Square root of 2 ✔️

Approx 1.4

Irrational number

Can't be written as a fraction, terminating decimal, repeating decimal A square root number ✔️ or a decimal that never ends = 3.1415927......forever and ever or square root ✔️37= 6.082762.......

What irrational number can be approximated by 3.3166?

DONT multiply the whole decimal cause it will take too long. Take it and round up or down, so take 3.32 and multiply it by 3.32 = 11.0224 So the answer is the irrational number is approximately 11.

Proportions

Dis-similar (unlike things) Miles/gallon Books/dollars Proportions have to have units

Fraction to decimal

Divide the numerator by the denominator

Expressing an improper fraction as a mixed fraction

Divide the numerator by the denominator Top number is the number on left, remainder is numerator and divisor is denominator. Ex: 7/3 = 2 1/3

What is the quotient of

Division! And just multiply it by the reciprocal. Ex: 5/3 divided by 4/15 becomes = 5/3 x 15/4

15% of 500?

Don't make this complicated. What is 10% of 500? Well that's easy, it's 50, so half of that would be 25! So 50+25 is 75% yay

Fraction addition

Ex: 3 + 3/5= 3 3/5 Ex: 8 + 1/5 = 8 1/5

Which fraction is greater and arrange fractions in order

If you know the decimal for the fraction it's the easiest way to decipher which is greater and arrange them in order If you don't know the decimal for the fraction you want to get the LCD fast! Ex: which is greater 4/7 or 5/9? multiply 4/7 by 9/9 and 5/9 by 7/7. But don't waste time doing the bottom numbers! Only do the top, and then you will know which is greater! So simple!

Pi

Is 3.14, a number that goes on forever..........

Cube root

Little 3 ✔️of a number..what number multiplied by 3 is the cube root Ex: Little 3 ✔️8 = ✔️2x2x2 answer: 2 is the cube root of 8!

What is the product of

Multiplication