Arithmetic Reasoning Flash Card Set 987860

Cards 10
Topics Adding & Subtracting Fractions, Adding & Subtracting Radicals, Distributive Property - Multiplication, Factorials, Factors & Multiples, Integers, Percentages, Prime Number, Proportions, Ratios

Study Guide

Adding & Subtracting Fractions

Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.

Adding & Subtracting Radicals

To add or subtract radicals, the degree and radicand must be the same. For example, \(2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}\) but \(2\sqrt{2} + 2\sqrt{3}\) cannot be added because they have different radicands.

Distributive Property - Multiplication

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

Factorials

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Factors & Multiples

A factor is a positive integer that divides evenly into a given number. The factors of 8 are 1, 2, 4, and 8. A multiple is a number that is the product of that number and an integer. The multiples of 8 are 0, 8, 16, 24, ...

Integers

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

Percentages

Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x \({ new - old \over old }\).

Prime Number

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

Proportions

A proportion is a statement that two ratios are equal: a:b = c:d, \({a \over b} = {c \over d}\). To solve proportions with a variable term, cross-multiply: \({a \over 8} = {3 \over 6} \), 6a = 24, a = 4.

Ratios

Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or \({2 \over 3}\) would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles.