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.

Basic Arithmetic

Equation: Any string of numbers and symbols that makes sense and includes an equal sign

Operation: A rule for taking one or two numbers as inputs and producing a number as an output. Some arithmetic operations are multiplication, division, addition, and subtraction.

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

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

Numerator: The top number in a fraction. This is the number that is to be divided.

Denominator: The bottom number in a fraction. This is the divide-by number.

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 exactly. For example, the factors of 6 are 1, 2, 3 and 6.

Greatest common factor:


Least common multiple:

Lowest terms: A fraction is in lowest terms when it is simplified as much as it can be while still representing the original amount; in other words, when its numerator and denominator have no common factor greater than one. For example, 12/16ths in lowest terms is 3/4ths.

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.

Types of fractions:

Inequality: A mathematical expression that contains an inequality symbol

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

Set: Any collection of elements, whether they are numbers, objects or something else. A set 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

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, IV

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

How to add fractions:

How to subtract fractions:

How to multiply fractions:

How to add decimals:

How to subtract decimals:

How to multiply decimals:

How to divide decimals:

How to add positive and negative numbers:

How to subtract positive and negative numbers:

How to multiply positive and negative numbers:

How to divide positive and negative numbers:

English system of measurement:

Metric system of measurement:

How many inches are in a foot: 12

How many feet are in a yard: 3

How many yards are in a mile: 1760

How many millimeters are in a meter: 1000

How many centimeters are in a meter: 100

How many meters are in a kilometer: 1000

How many ounces are in a pound: 16

How many pounds are in a ton: 2000

How many milligrams are in a gram: 1000

How many grams are in a kilogram: 1000

How many kilograms are in a metric ton: 1000

How many teaspoons are in a tablespoon: 3

How many fluid ounces are in a cup: 8

How many cups are in a pint: 2

How many pints are in a quart: 2

How many quarts are in a gallon: 4

How many milliliters are in a liter: 1000

How many seconds are in a minute: 60

How many minutes are in an hour: 60

How many hours are in a day: 24

How many days are in a year: 365

How to convert centigrade to farenheit: C = (F – 32) X 5/9 and F = (C X 9/5) + 32

Other Arithmetic and Measurement Skills

  • Counting by twos, fives, tens, twelves, fifteens and twenties
  • Adding and subtracting numbers up to 1000 without using a calculator or writing instruments
  • Rounding numbers to the nearest ones, fives, tens, hundreds and thousands
  • Solving basic story problems
  • Using a calculator
  • Using a ruler and drawing compass
  • Calculating map distances
  • Memorizing the 0-12 multiplication table
  • Deciphering information on line graphs, bar graphs, circle graphs and tables
  • Deciphering information on a Vinn diagram


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