Rational — Grade 7 Math, what it means and where it is taught

Any number writable as ab with integers a and b, b ≠ 0.

Taught in Grade 7 Math.

Where it is taught

What it rests on

Work through these first if this one does not settle.

Practise this idea

11 questions in the course bank use Rational, in Real Numbers, Radicals & Rational Exponents, Dividing Polynomials & the Factor Theorem. The first 8 are below; the rest are in those units.

Problem 1

Is 0.75 rational?

  1. Yes
  2. No
Worked answer

Yes

0.75 = 34, so yes.

Problem 2

Classify √9.

  1. Rational
  2. Irrational
Worked answer

Rational

√9 = 3, a whole number, so rational.

Problem 3

Classify √7.

  1. Rational
  2. Irrational
Worked answer

Irrational

7 is not a perfect square

√7 = 2.6457… never repeats, so irrational.

Problem 4

Which of these is irrational?

  1. 0.25
  2. 23
  3. √16
  4. √11
Worked answer

√11

0.25 and 23 are fractions, so rational

√16 = 4, rational

11 is not a perfect square, so √11 is irrational.

Problem 5

Is 227 exactly equal to π?

  1. Yes
  2. No
Worked answer

No

227 = 3.142857… and repeats, so it is rational

π = 3.14159… never repeats

They are close but not equal.

Problem 6

Which describes 0?

  1. Integer and rational
  2. Irrational
  3. Neither
Worked answer

Integer and rational

0 is a whole number and an integer

It is rational because 0 = 01.

Problem 7

Is the sum of two irrational numbers always irrational?

  1. Yes, always
  2. No — it can be rational
Worked answer

No — it can be rational

√2 + (-√2) = 0, which is rational

So the sum is not always irrational

It usually is — but "always" is too strong.

Problem 8

Which sum is irrational?

  1. 3 + √2
  2. √4 + √9
  3. 12 + 13
  4. √16 - 1
Worked answer

3 + √2

√2 is irrational and 3 is rational

So the sum is irrational

All the others reduce to rationals

Elsewhere

Browse all courses