School in a Book: Arithmetic and Measurement

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.


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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