Integer

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Integer: meaning, method and solved example (6th Grade) – Maths PDF

In short: An integer is any whole number, positive, negative or zero, such as -14, 0 or 27, and has no fraction or decimal part.

6th GradeNumbers and Operations6.NS.C.5

What is Integer?

An integer counts complete steps in either direction from zero. Floors above and below the lobby, degrees above and below freezing, and points gained or lost in a game are natural uses.

Precisely, the whole numbers together with their opposites form this family: 0, \(\pm 1\), \(\pm 2\), \(\pm 3\) and so on without end. Values like \(\frac{1}{2}\) and \(-3.5\) fall between its members and do not belong.

How to spot it

  • A story uses positive and negative whole amounts for gains and losses, altitude, or deposits and withdrawals.
  • A question asks which marks on a number line are whole, negatives included.
  • A thermometer, elevator or bank statement shows values on both sides of zero.
  • You are asked to compare, order or find the opposite of numbers like \(-12\) and 8.

The method

  1. Check that the number has no fraction or decimal part; \(-7\) passes, \(-7.2\) does not.
  2. Place it on a horizontal number line: positives to the right of 0, negatives to the left.
  3. Compare by position: the number farther to the right is greater.
  4. Remember that zero is an integer but is neither positive nor negative.
-6-4-1024negative integerspositive integers-3.5 and 1/2 sit between marks and are not integers
The evenly spaced marks to the left and right of 0.

Integer: solved example

Problem

At 6 a.m. in Duluth the temperature is \(-9\) degrees Fahrenheit. By noon it has risen 15 degrees, and by midnight it has fallen 11 degrees from the noon value. Give each reading as a whole number.

Solution

Noon: \(-9 + 15 = 6\) degrees.

Midnight: \(6 – 11 = -5\) degrees. The readings are \(-9\), 6 and \(-5\).

Try it

Question 1

Which of these are not whole-number values: \(-8\), 0.4, \(\frac{12}{3}\), \(-\frac{5}{2}\)?

Show the answer

0.4 and \(-\frac{5}{2}\) are not. Note that \(\frac{12}{3} = 4\) is an integer.

Question 2

Order from least to greatest: 3, \(-10\), 0, \(-2\).

Show the answer

\(-10, -2, 0, 3\), reading left to right on the number line.

Integer vs. Rational Number

Every integer is a rational number, because \(5 = \frac{5}{1}\), but rational numbers also include fractions and decimals that stop or repeat, like \(\frac{3}{4}\) and \(-0.6\). The integers are only the whole-number marks.

Rational Number

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Whole dictionary: A–Z · 6th Grade · Numbers and Operations

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