Rational Numbers

Grade 6 · Math · Study Guide

Understand what rational numbers are, how to compare them, and how to place them on a number line.

A rational number is any number that can be written as a fraction p/q, where p and q are integers and q is not zero. Rational numbers include positive fractions, negative fractions, whole numbers, integers, mixed numbers, and terminating or repeating decimals.

Examples of rational numbers: 1/2, −3/4, 5, −7, 0.75, 2.333…, and 0. Every integer is a rational number because you can write any integer as itself over 1 (e.g., 5 = 5/1).

Negative rational numbers are less than zero. On a number line, negative numbers are to the left of zero. The further left a number is, the smaller it is. For example, −3/4 is greater than −2 because −3/4 is closer to zero.

To compare two fractions, convert them to the same denominator or to decimals. For example, to compare −1/2 and −3/4: convert to decimals (−0.5 and −0.75); since −0.5 > −0.75, we have −1/2 > −3/4.

Absolute value is the distance from a number to zero on the number line, always positive. The absolute value of −4 is 4, written |−4| = 4. Rational numbers are used in cooking, finance, temperatures, and science — making them one of the most practical number types to understand.

Key terms

Rational Number
Any number that can be expressed as a fraction p/q where p and q are integers and q ≠ 0
Integer
The set of whole numbers and their negatives: …−3, −2, −1, 0, 1, 2, 3…
Absolute Value
The distance from a number to zero on the number line; always non-negative
Negative Number
A number less than zero; located to the left of zero on the number line
Opposite
Two numbers the same distance from zero on opposite sides, such as 3 and −3
Number Line
A visual tool showing numbers in order; negative numbers are left of zero, positive numbers are right

Flashcards

Rational number definition
Any number expressible as p/q where p and q are integers and q ≠ 0
Is 0 a rational number?
Yes; 0 = 0/1
Is every integer rational?
Yes; e.g., 6 = 6/1
Absolute value of −15
|−15| = 15
Opposite of −4
4 (same distance, other side of zero)
Compare −1/3 and −2/3
−1/3 > −2/3 because −1/3 is closer to zero
0.6 as a fraction
3/5
Which is less: −5 or −2?
−5 is less; it is further to the left on the number line

Questions

  1. Which of the following is a rational number?

    1. π
    2. √2
    3. −3/5
    4. √7
    Show answer

    Answer: −3/5

    −3/5 is a fraction of two integers, so it is rational; π and √2 are irrational

  2. The absolute value of −9 is ___.

    Show answer

    Answer: 9

    |−9| = 9 — distance from −9 to 0 is 9 units

  3. Every integer is also a rational number.

    Show answer

    Answer: True

    Every integer n can be written as n/1, which fits the definition of a rational number

  4. Which number is greatest?

    1. −1/2
    2. −3/4
    3. −1/4
    4. −5/8
    Show answer

    Answer: −1/4

    Convert to decimals: −0.5, −0.75, −0.25, −0.625; −0.25 is the greatest (closest to zero)

  5. The opposite of −7 is ___.

    Show answer

    Answer: 7

    Opposites are the same distance from zero on opposite sides; the opposite of −7 is 7

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