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