Integers Math Quiz

Study Notes

Integers

Integers are whole numbers, including zero, positive and negative numbers.
Examples of integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
Operations with integers include addition, subtraction, multiplication, and division.
Rules for integer operations:
- Adding two positive integers: result is positive.
- Adding two negative integers: result is negative (absolute values added, negative sign kept.)
- Adding a positive and a negative integer: find the difference between their absolute values; the sign of the larger absolute value is kept.
- Subtracting an integer: add the opposite of the integer.
- Multiplying or dividing two integers with the same sign: result is positive.
- Multiplying or dividing two integers with different signs: result is negative.
Properties of integers: closure (addition and multiplication), commutativity (addition and multiplication), associativity (addition and multiplication), distributive property (multiplication over addition).

Fractions

A fraction represents a part of a whole.
A fraction consists of a numerator and a denominator.
The numerator is the top number, indicating the number of parts.
The denominator is the bottom number, indicating the total number of equal parts into which the whole is divided.
Types of fractions:
- Proper fractions: numerator is smaller than denominator (e.g., 2/3).
- Improper fractions: numerator is greater than or equal to denominator (e.g., 5/2).
- Mixed numbers: combination of a whole number and a proper fraction (e.g., 1 2/3).
Equivalent fractions: fractions that represent the same part of a whole (e.g., 1/2 = 2/4 = 3/6)
Operations with fractions: adding, subtracting, multiplying, and dividing. Common denominators are necessary for adding and subtracting.
Converting between fractions, decimals, and percentages is a fundamental skill.

Ratio and Proportion

Ratio compares quantities of the same kind. Expressed as a:b, a/b, or a to b
Ratio can be simplified.
Proportion states that two ratios are equal. Used to solve for unknowns in problems.
Example of a proportion: a/b = c/d
Ratio and proportion problems often involve finding missing values using cross-multiplication.

Decimals

Decimals represent numbers with fractional parts, using a decimal point.
Examples of decimals: 0.5, 2.75, -3.14, 0.125
Converting between fractions and decimals involves understanding the place value system.
Operations with decimals follow the same principles as with integers and fractions, aligning the decimal points correctly when adding, subtracting, multiplying, and dividing.

Percentages

Percentages express a quantity as a fraction of 100.
Conversion between fractions, decimals, and percentages is essential.
Examples of percentages: 50%, 25%, 75%, 10%
Using percentages in problems involving discounts, increases, or finding a percentage of a value. Percentage change calculations are also common.
Percentage calculations are often used to represent proportion or change in numerical quantities.

Surds

Surds are the irrational parts of expressions involving square roots, often represented using the radical symbol √.
Simplification of surds involves rationalizing denominators where necessary.
Examples of surds: √2, √3, √5
Operations with surds include addition, subtraction, multiplication, and division. Careful attention is needed to simplify the resulting surds.
Involving surds may include calculations with square roots and further simplifying expressions.

Description

Test your knowledge of integers, including their properties and operations. This quiz covers topics such as addition, subtraction, multiplication, and division of integers, along with rules and examples. Perfect for reinforcing concepts learned in class.