Basics Flashcards
(26 cards)
What are the top & bottom of a fraction called?
Numerator & Denominator
What is the ‘associative property’?
It means the terms can be associated differently without changing the meaning, e.g. (3 x 4) x 5 is the same as 3 x (4 x 5). Addition and multiplication have the associative property.
What the the ‘commutative property’?
The terms can move without changing the result, e.g. 3 x 4 is the same as 4 x 3, but 3 / 4 is not the same as 4 / 3. Addition and multiplication have the commutative property.
What is the ‘distributive property’?
a(b + c) = ab + ac
Apply the distributive property to: 2x - (3x - 5)
2x - (3x - 5) = 2x - 1(3x - 5) = 2x - 3x +5 = -x + 5
Apply the distributive property to: -2x(3x**2 + 5y - 7)
-2x(3x2 + 5y - 7) = (-2x)(3x2) + (-2x)(5y) + (-2x)(-7) = -6x**3 - 10xy + 14x
What is a prime number or a composite number? What are the first 10 primes?
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
What is a factor?
A factor is a number that divides another number and leaves no remainder. e.g. Factors of 12 are 1, 2, 3, 4, and 6.
What are the natural numbers?
Positive whole numbers (i.e. no fractional part) such as those used to count, e.g. 1, 2, 3, 4, etc… The double-struck capital N (“ℕ”) is used to represent the infinite set of all natural numbers.
What are the whole numbers?
The natural numbers plus 0.
What are the integer numbers?
Any number with no decimal or fractional part, including negative numbers, i.e. 5, 0, -7, etc… The double-struck Z (“ℤ”) is used to represent the infinite set of integers.
What are rational numbers?
Any number that can be expressed as a ratio of two integers (which includes all decimal fractions), e.g. 2.345, 1/2, 3.33333.., 5/1, etc.. Integers are also rational numbers. The double-struck Q (“ℚ”) is used to represent the infinite set of rational numbers.
What are the irrational numbers?
Any number that cannot be expressed as the ratio of 2 integers, e.g. sqrt(2), Math.Pi, Math.e, etc…
What are the real numbers?
Real numbers include the rational and irrational numbers, and include any point on an infinite ‘number line’. The double-struck R (“ℝ”) is used to represent the infinite set of real numbers.
What are the transcendental numbers?
Irrational numbers that cannot be represented as an algebraic expression, e.g. sqrt(2) is irrational but not transcendental, whereas Math.Pi and Math.e are.
What is the absolute value of a number and how do you indicate it?
It is the “amount” or “magnitude” of the value regardless of the sign, represented by put the value in “|” symbols. The result is never negative. e.g: “|-9| = 9”, and “|9| = 9”.
What is the opposite of a value?
It’s negative. e.g. the opposite of “-4” = “-(-4)” = “4”.
What does ‘quotient’ mean?
From the Latin ‘quotiens’ meaning ‘how many times’, it is the result of division - often just the integer portion. e.g. 11 / 3 has a quotient of 3 and a remainder of 2.
What is an “improper fraction”?
When the numerator is greater than the denominator, e.g. 12/5. This can be written as a “mixed number”, with an integer and a “proper fraction”, e.g. 2 2/5
What is the “simplified form” of a fraction?
When both parts have no common factors. For example, 24/36 can have both parts factored by 12, giving 2/3
What is a GCF?
Greatest Common Factor. It is used to reduce a fraction to its simplified form.
What is the LCD? Why might you use it?
Least Common Denominator. You use it to get the denominators of fractions to the same value. For example, the LCD of 1/2, 2/3 & 3/4 is 12, so you can convert to 6/12, 8/12, & 9/12.
How do you add or subtract fractions?
Convert all fractions to have a common denominator, then doing basic addition or subtraction on the numerators.
How do you multiply fractions?
Simply multiple the numerators to get the numerator of the result, do the same for denominators, then simplify.
