What are the sum, difference, product, and quotient of two numbers?
The sum is the result of an addition.
The difference is the result of subtraction.
The product is the result of multiplication.
The quotient is the result of division.
What do we mean by the quotient and the remainder whtn one postive integer is divided by another postive integer?
When 23/5 it comes out to 4 with a remainder of 3.
When 35/5 the quotient is 5 and 0 is the remainder, or there is no remainder.
The remainder muts be and integer that is greater than or equal to 0 and less than the number you are dividing by,
What is the divisor of an integer?
What is a factor of an integer?
The terms divisor and factor mean the exactly the same thing.
A divisor (or factor) of an integer, n, is an integer that leaves no remainder when it is divided into n.
For example, the postive divisors (or factors) of 12 are: 1, 2, 3, 4, 6, and 12.
What is a prime number?
A prime number is a postive integer that has exactly two postive divisors, 1 and itself.
What is a multiple of an integer?
A multiple of an integer, n, is any integer that is the product of n and another integer.
For example: 50 is a multiple of 10 since 50 = 5*10.
What is an even number?
What is an odd number?
An even number is a integer that is a multiple of 2.
An odd number is an integer that is not a multiple of 2.
What is an exponent?
The expression xb, x is the base and b is the exponent.
What are Laws of Exponents?
bmbn = bm+n
bm/bn = bm-n
(bm)n = bmn
am * bm = (ab)m
am/bm = (a/b)m
What is a negative exponent?
For any number, n: x-n means 1/xn
What is a fractional exponent?
If x is positive and n is a positive integer: x1/n means n
What is the square root of a number?
If x is postive, the square root of x, written , is the only postive number.
What are some important properties of square roots?
For any positive numbers x and y:
xy = x * y and a/b = a / b
If the product of two or more numbers is 0, what do you know about the numbers?
If the product is equal to 0, then at least one of the factors is 0.
What is the distributive law?
The distributive law for any numbers a, b, c:
a(b+c) = ab +ac and a(b-c) = ab-ac
also if a 0: (b+c)/ a = b/a + c/a and (b-c)/a = b/a - c/a
What are some important properties of 0?
0 is the only number that is neither postive nor negative
If a is negative and b is postitive, then a<0<b
0 is a multiple of every integer.
In particular, 0 is a multiple of 2, so 0 is even.
For every number a:
a+0=a a-0=a a*0=0 a/0 is undefined
For any number b: b=-b if and only if b=0
If ab=0, then a=0 or b=0
What are some important properties of 1?
For any number a: a*1 amd a/1 = a
For any integer n: 1n = 1
1 is a divisor and factor of every integer
1 is the smallest positive odd integer
1 is not a prime, since primes have exactly two positive divisors and 1 has only one positive divisor , 1
What is a percent?
How do you convert a percent to a fraction or decimal?
How do you convert a fraction or a decimal to a percent?
A percent is a fractios whose denominator is 100.
17% = 17/100
To convert a percent to a fraction or decimal, write it over 100 and if necessary reduce and divide.
To convert a fraction to a decimal or percent, divide the numerator b the denomiator, and then multiply by 100.
1/8 = 1/8 = 0.125 = 12.5%
How do you find the percent of a number?
Write the percent as a decimal and multiply.
To find 35% of 80, write 35% as .35 and multiply: .35*80=28
How do you calculate percent increases and percent decreases?
The percent increase of a quanity is (actual increase/original amount) * 100%
The percent decrease of a quanity is (actual decrease/original amount) * 100%
What is a ratio?
A ratio is a fraction. Ratios can be expressed using the word "to" or suing a colon, ":", but is is best tro write them as a fraction. For example:
3 to 5, 3:5 and 3/5.
What is a proportion?
A proportion is an equation that states that two ratios are equilivant. Since ratiosi are just fractions, any equation, such as 4/5 = 10/15, in which each side is a single fraction is called a proportion.
What does it mean if y is directly proportional to x?
By definition , y is directly proportional to x if the quotient y/x is a constant.
What does it mean if y is inversely proportional to x?
By definition y is inversely proportional to x if the product is xy is a constant.
What formulas should you use in problems involving averages?
The average (arithmetic mean) is a set of n numbers is the sum of those numbers divided by n.