Math thinking grows the brain. Avoid taking the easy way out when encountering simple math problems in daily life. On paper or in your head, convert measurements, add and subtract large numbers, calculate costs per unit, find averages and percentages and more when opportunities arise. It gets easier, and saves time (and sometimes money) in the long run.

## ESSENTIAL KNOWLEDGE: ARITHMETIC AND MEASUREMENT

**Equation: **A mathematical statement that shows the relationship between two expressions, separated by an equal sign

**Operation:** A mathematical process that takes one or two numbers as inputs and produces a number as an output, such as addition, subtraction, multiplication, or division

**Multiplication:** The process of finding the product of two factors

**Division:** The process of finding an unknown factor

**Whole number:** A number with no fractional part

**Integer: **A whole number, either positive or negative

**Negative number:** A number that is less than zero

**Positive number:** A number that is more than zero

**Absolute value:** A number’s distance from zero, whether negative or positive

**Place value:** The position of a number within a larger number, which is what determines that number’s value. For example, the two in the number .12 is in the hundreds place, while the one is in the tens place.

**Inequality:** A mathematical expression that contains an inequality symbol

**Numerator:** The top number in a fraction that represents the number of parts being considered

**Denominator:** The bottom number in a fraction that represents the total number of equal parts in a whole

**Remainder: **The number left over after division has taken place. This occurs when the numerator cannot be equally divided by the denominator.

**Factor:** A number that divides another number, leaving no remainder. For example, 3 and 4 are factors of 12.

**Greatest common factor:** The largest factor that all the numbers being worked with share. For example, 12 and 16 share a factor of 4.

**Product:** The result of multiplying two numbers

**Multiple:** A number that can be divided by another number without a remainder. For example, 10 and 15 are multiples of 5.

**Least common multiple:** The smallest multiple that is divisible by all the numbers being worked with. For example, 4 is the least common multiple of 2 and 4 is 4 because the multiples of 2 are 2, 4, 6, 8, etc. and the multiples of 4 are 4, 6, 8, 10, etc.

**Lowest terms: **A fraction that has been simplified to its smallest possible form, where the numerator and denominator have no common factors greater than one. For example, 12/16ths in lowest terms is 3/4ths.

**Improper fraction: **A fraction in which the numerator is greater than or equal to the denominator; for example, 11/5

**Mixed fraction:** A fraction that combines a whole number and a proper fraction; for example, 3 1/3

**Like fractions: **Fractions that share the same denominator; for example, 3/4 and 1/4

**Equivalent fractions:** Fractions that represent the same quantity or value, but may have different numerators and denominators; for example, 2/4 and 1/2

**Array:** An arrangement of objects, pictures, or numbers in rows and columns. These can be used to illustrate multiplication and division problems. For example, the math problem 3 x 4 could be shown by creating three rows of four dots.

**Set:** Any collection of elements, whether they are numbers, objects or something else. It contains only one of each type of element, however.

**Sequence: **An enumerated collection of objects in which repetitions are allowed and order matters

**Bar graph:** A chart that uses bars to represent data

**Line graph: **A chart that uses lines, usually on a graph featuring an x-axis and a y-axis, to represent data

**Table:** A chart that organizes numbers into columns. Tables often show the various results of a calculation as it is affected by one or more variables.

**Pie chart:** A chart that organizes percentage values in a single circle that is segmented like a cut pie

**Venn diagram: **A diagram that displays intersecting and various-sized circles to represent the interrelationships between data sets

**One million:** 1,000,000

**One billion: **1,000,000,000

**One trillion:** 1,000,000,000,000

**Roman numerals 1-9:** I, II, III, IV, V, VI, VII, VIII, IX

**Roman numerals 10, 20, 30, 40, 50, 60, 70, 80 and 90: **X, XX, XXX, XL, L, LX, LXX, LXXX, XC

**Roman numerals 100, 200, 300, 400, 500, 600, 700, 800, 900:** C, CC, CCC, CD, D, DC, DCC, DCCC, CM

**Roman numerals 1000, 2000, and 3000:** M, MM, MMM

**Metric system of measurement:** The worldwide standard measurement system, which is based on multiples of 10, and includes meters and grams

**English system of measurement:** A system of measurement used primarily in the United States that includes units such as inches, feet, miles, and pounds

**Kelvin:** A temperature scale used in scientific measurements where 0 degrees represents absolute zero, the lowest possible temperature. 1 degree Kelvin is the same as 1 degree Celsius, but the 0 point (starting point) is different.

**Celsius:** A temperature scale where the freezing point of water is 0 degrees and the boiling point of water is 100 degrees, commonly used in most countries worldwide

**Fahrenheit:** A temperature scale where the freezing point of water is 32 degrees and the boiling point of water is 212 degrees, commonly used in the United States

**Centigrade:** A older name for Celsius

**The number of millimeters in a meter:** 1000

** The number of centimeters in a meter:** 100

** The number of meters in a kilometer:** 1000

** The number of milligrams in a gram:** 1000

** The number of grams in a kilogram:** 1000

** The number of kilograms in a metric ton:** 1000

** The number of inches in a foot: **12

** The number of feet in a yard:** 3

** The number of yards in a mile:** 1760

** The number of ounces in a pound:** 16

** The number of pounds in a ton:** 2000

** The number of teaspoons in a tablespoon:** 3

** The number of fluid ounces in a cup:** 8

** The number of cups in a pint:** 2

** The number of pints in a quart:** 2

** The number of quarts in a gallon:** 4

** The number of milliliters in a liter:** 1000

** The number of days in a year:** 365

**How to convert Celsius to Fahrenheit:** C = (F – 32) X 5/9 and F = (C X 9/5) + 32

**The freezing point in Celsius:** 0 degrees

**The freezing point in Fahrenheit:** 32 degrees

**The boiling point in Celsius:** 100 degrees

**The boiling point in Fahrenheit:** 212 degrees

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