Math Definitions, Formulas and Problems (Arithmetic)
AR 9a. 40% of 15 (rewrite and solve)
0.4 x 15 = 2/5 x 15/1 = 30/5 = 6
Exponent of 0
1
AR 4b. What are the positive divisors of 372?
1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372
AR 9b. 150% of 48 (rewrite and solve)
1.5 x 48 = (1 + 1/2)(48) = 48 + 24 = 72
AR 11. If an athlete weight decreases from 160 lbs to 152 lbs, what is the percent decrease in weight. (rewrite and solve)
160 - 152/160 = 8/160 = 1/20 = .05 = 5%
AR 1a. 15 - (6 - 4)(-2)
19
AR 14b. C is even and d is odd. Even or Odd? 2c+d (rewrite and solve)
2(even) + odd = even + odd = odd
AR 6. Which of the intergers 2, 9, 19, 29, 30 .37. 45. 49, 83, 90, 91 are prime numbers
2, 19, 29, 37, 83
AR 5b. What is the prime divisors of 144?
2, 3
AR 5a. What is the prime divisors of 100?
2, 5
AR 13. 20 dogs and cats in total at the kennel. If the ration is 3 dogs to 2 cats how many cats are at the kennel. (rewrite and solve)
20 = d(3/5) + c(2/5) so 20 = d(.6) + c(.4) so 20 = 20(.6) + 20(.4) = 20 = 12 dogs + 8 cats
AR 10. If a person salary increases form $200 per week to $234 per week, what is the percen increase in the person salary? (rewrite and solve)
234-200/200 = 34/200 = .17 = 17 %
AR 3. Which of the intergers 312, 98, 112, and 144 are divisible by 8?
312, 112 and 144
AR 4a. What is the prime factorization of 372? (rewrite and solve)
372/2 = 186/2 = 93/3 = 31 so 2x2x3x31 = 2^2 X 2 X 31
250% of 16 is
40
AR 1g. (20÷5)^2(-2+6)^3 (rewrite and solve)
4^2x4^3 = 16 x 72 = 1024
15 is 300% of
5
AR 1d. 3^4-(-2)3
89
Ratio
A comparison of two quantities by division
Exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself.
Decimal A
A point used to represent numbers using the base of 10 i.e. 11.11 = 1(10) + 1(1) + 1/10 + 1/100
Decimal B
A point used to represent numbers using the base of 10 i.e. 11.11 = 1(10^1) + 1(1^0) + 1(10^-1) + 1(10^-2)
Square Root
A whole number produced that is rooted when it was squared by the exponent of itself i.e. 7x7 = 49 so 49/7 = 7
Multiplying Fractions
Multiply the numerators Multiply the denominator.
Square Root Rule 3 multiply a
Roots can multiply and divide similarly i.e. √3 √10 = √30
Denominator
The bottom number in a fraction
Absolute Value
The distance a number is from zero on a number line. ALWAYS POSITIVE
Dividing Fractions
To divide fractions, invert the second one and multiply
AR 8f. True or False (-1)^87 = -1
True
AR 8h. True or False 21/28 = 3/4
True
AR 8j. True or False 1/2 > 1/17
True
AR 8l. True or False -√25 < -4
True
Adding Fractions
add the numerator together when you have a common denominator
Proportion
an equation relating two ratios
AR 14a. C is even and d is odd. Even or Odd? c+2d (rewrite and solve)
even + 2(odd) = even + even = even
AR 14c. C is even and d is odd. Even or Odd? cd (rewrite and solve)
even(odd) = even
1AR 4d. C is even and d is odd. Even or Odd? c^d (rewrite and solve)
even^odd = even
Percent - The number is less than the original (number - original)
percent decreased by (x)
Interger
positive and negative numbers that are whole. Includes zero
Real Numbers
the set of all rational and irrational numbers
Numerator
the top number in a fraction
Square Root Rule 3 multiply b
√24 = √4√6 = 2√6
Square Root Rule 4 fraction
√36/√4 = √36/4 = √18/2 = √9 = 3
AR 15. When positive interger n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value for n? (rewrite and solve)
n/3 = n remainder 2 n/5 = 1. It is 3, 5, 7, or 11. 5/2 = 2 r 1 (no) and 7/3 = 2 r 1 (no) 11/3 = 3 r 1, 11/2 = 5 r 1. The answer is 11
Fraction
number with two intergers. With the numerator on top and the denominator on the bottom.
Square Root Rule 1
A number rooted and squared equals the same number i.e. (√3)² = 3
Square Root Rule 2
A number square and rooted equals the same number i.e √(3²) = 3
Percent
A ratio that compares a number to 100
Mixed Numbers
A whole number and a fraction together.
AR 7. What is the prime factorization of 585? (rewrite and solve)
585/5 = 117/9 = 13 or 3x3x5x13 = 3^3x5x13
AR2a. 1/2 - 1/3 + 1/12 (rewrite and solve)
6/12 - 4/12 + 1/12 = 3/12 = 1/4
AR 1c. (60÷12)-(-7+4)
8
The value of a 10% increase of a $1000 investment
$1100 = 1000 X 1.1 = 1100
AR 12. A stock is valued at $40 per share. If the value increase by 20% and then decrease by 25%, what will be the value of the stock per share after decrease. (rewrite and solve)
((40)(1+20/100))(1-25/100) = 48(1 - 25/100) = 48 - 48(1/4) = 48 - 12 = 36
AR 2b. (3/4 + 1/7)(-2/5) (rewrite and solve)
(21/28 + 4/28)(-2/5) = (25/28)(-2/5) = -50/140 = - 5/14
AR 2d (3/-8) ÷ (27/32) (rewrite and solve)
(3/-8) x (32/27) = 96/-216 = 48/108 = 24/54 = -12/27 = -4/9
AR 2c. (7/8 - 4/5)^2 (rewrite and solve)
(35/40 - 32/40)^2 = (3/40)^2 = (3/40)(3/40) = 9/1600
AR 9e. 11 is what percent of 55 (rewrite and solve)
11/55 = 1/5 = .2 = 20%
On 2013 the number of enrolled was 20% less than that in 2012. In 2014 the number of enrolled was 10% greater of children in 2013. By what percentage did the enrollment change from 2012 to 2014
12% = 100 - ((1.00-.20)(1.00x1.20))
AR 9d. 15 is 30% of which number (rewrite and solve)
15 = .3(a) so 15÷(3/10) = 15 x 10/3 = 150/3 = 50
AR 8g. True or False √(-3)^2 < 0
False
Percent - The number is doubled the original
percent increased by 100%
Percent - The number is higher than the original
percent increased is (x)
Percent Change
(Change - Original)/(Original)(1)
AR 14e. C is even and d is odd. Even or Odd? (c+d)^2 (rewrite and solve)
(even + odd)(even + odd) = (odd)(odd) = odd
AR 14f. C is even and d is odd. Even or Odd? c^2 - d^2 (rewrite and solve)
(even)(even) - (odd)(odd) = even - odd = odd
AR 1b. (2 - 17)÷5
-3
AR 1f. (-2)^4 (15-18)^4
1296
AR 8i. True or False -I-23I = 23
False
AR 8k. True or False (59^3)(59^2) = 59^6
False
AR 8c. True or False 7÷0 = 0
False (you can't divide by 0 rule)
Arithmetic
The study of numbers (integers, fractions, decimals) order of operations (PEMDAS), roots, ratio and percentages
AR 8a. True or False -5 <3.1
True
AR 8b. True or False √16 = 4
True
AR 8d. True or False 0 < I-1/7I
True
AR 8e. True or False 0.3 <1/3
True
Fractional Expressions
When the numerator or denominator is not a interger i.e. π or √
AR 1e. (-5)(-3)-15
0
AR 1h. (-85)(0) - (-17)(3) (rewrite and solve)
0 - (-51) = 5
AR 9c. 0.6% of 800 (rewrite and solve)
0.006x800 = 6/1000 x 800 = 4800/1000 = 4.8
Cross Multiplication (Proportion)
Finding X multiply and then divide
