Number and Operations

Section 1: Demonstrates Understanding of Rational Numbers
NECAP: M(N&O) – X – 1
Vermont: MX: 1

N&0 – 1 Rational Number: A rational number is any number that can be represented
in the form , where a and b are integers and b ≠ 0. Rational numbers include whole
numbers, integers, fractions that when expressed as decimals terminate or repeat , and
decimals that are terminating or repeating. (See N&O – 11 for a diagram which illustrates
how the set of rational numbers is related to other sets of numbers in the real number
system.)

Example 1.1 – Rational numbers:

The numeral 3 is a rational number since it can be represented as .

N&0 – 2 Whole number: A whole number is any number in the set
{0, 1, 2, 3, 4, 5, ...}. (See N&O – 11 for a diagram which illustrates how the set of whole
numbers is related to other sets of numbers in the real number system .)

N&0 – 3 Fraction: A fraction is a quotient of one number or expression to
another denoted by , when a is the dividend or numerator and b is the divisor
or denominator

A whole number is not typically called a fraction until it is written in fractional form.

	The top number of the fraction is the numerator or dividend.
	The bottom number of the fraction is the denominator or divisor .

Note: Not all fractions are rational numbers (e.g., is a fraction since it is a quotient of one number to another, but is not a rational number since is irrational (See N&0 – 10)).

Fraction Notation in GLEs: The notation at grade 2, for example, is as fol lows : , or where a is whole number greater than 0 and less than or equal to the denominator.   Grade 2 Fractions and and and

Fractions can be expressed as proper fractions, improper fractions, and mixed
numbers.

N&0 – 4 Proper Fraction: A proper fraction is a fraction whose numerator is less in
absolute value than its denominator. All proper fractions lie between –1 and 1 on a
number line (Note: Zero is considered a proper fraction when written in its fractional
form (e.g., ). (See N&O – 23 for a definition of absolute value.)

Example 4.1 – Proper fractions:

N&0 – 5 Improper Fraction: An improper fraction is a fraction whose numerator is
greater than or equal to its denominator in absolute value. (See N&O – 23 for a definition
of absolute value.)

Example 5.1 – Improper fractions:

N&0 – 6 Mixed Number: A mixed number is the sum of an integer and a proper
fraction.
Example 6.1: means .

N&0 – 7 Decimal: A decimal can represent a rational or irrational numbers. A decimal
that either terminates or repeats represents a rational number. A decimal that does not
terminate or repeat represents an irrational number.

N&0 – 8 Percent: Percent is a term meaning per hundred. Percent is denoted with a %
symbol .

Example 8.1:

N&0 – 9 Integer: An integer is any number in the set {…, –3, –2, –1, 0, 1, 2, 3, …}.
(See N&O – 11 for a diagram which illustrates how the set of integers is related to other
sets of numbers in the real number system.)

N&0 – 10 Irrational Number: An irrational number is any real number that is not
rational (i.e., Irrational numbers are real numbers whose decimal representations neither
terminate nor repeat.). (See N&O – 11 for a diagram which illustrates how the set of
irrational numbers is related to other sets of numbers in the real number system.)

Example 10.1 – Irrational numbers: