Question

Q5. Create an expression for each type of scenario below.

Rational times Rational

Rational plus Rational

Rational minus Rational

Rational divided by Rational

Rational times Irrational

Rational plus Irrational

Rational minus Irrational

Rational divided by Irrational

Irrational times Irrational

Irrational divided by Irrational

Irrational plus Irrational

Irrational minus Irrational

Answer 1

Here are one-line example expressions for each case, with the evaluated result and whether it’s rational or irrational.

1) Rational × Rational: (3/4) * (2/5) = 3/10 (rational)
2) Rational + Rational: 1/3 + 2/3 = 1 (rational)
3) Rational − Rational: 5 − 7/2 = 3/2 (rational)
4) Rational ÷ Rational: (3/4) ÷ (2/5) = 15/8 (rational)

5) Rational × Irrational: 1/2 * sqrt(2) (irrational, unless the rational factor is 0)
6) Rational + Irrational: 2 + sqrt(3) (irrational)
7) Rational − Irrational: 5 − π (irrational)
8) Rational ÷ Irrational: 4 / sqrt(2) = 2·sqrt(2) (irrational)

9) Irrational × Irrational: sqrt(2) * sqrt(8) = 4 (rational) — note: product can be rational or irrational (e.g., sqrt(2)*π is irrational).
10) Irrational ÷ Irrational: sqrt(2) / sqrt(8) = 1/2 (rational) — note: quotient can be rational or irrational (e.g., π / sqrt(2) is irrational).
11) Irrational + Irrational: sqrt(2) + sqrt(3) (irrational) — note: sum can be rational in special cases (e.g., sqrt(2) + (−sqrt(2)) = 0).
12) Irrational − Irrational: sqrt(3) − sqrt(2) (irrational) — note: difference can be rational in special cases (e.g., sqrt(5) − sqrt(5) = 0).