Math Definitions, Formulas and Problems (Arithmetic)

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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


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