1-1 Lesson Check

• whole numbers

• natural numbers

• rational numbers

• irrational numbers

Answer explanation

Since this number can be written as a mixed number (1 and 5/9), it can be converted to an improper fraction 14/9. So, it is a rational number.

• Rational Number

• Irrational Number

Answer explanation

The sum of 2 rational numbers is always rational.

• Rational Number

• Irrational Number

Answer explanation

The sum of a rational number and an irrational number is always irrational.

• Rational Number

• Irrational Number

Answer explanation

The product (remember: division is the same as multiplying by the inverse) of an irrational number and a rational number is always irrational.

Which numbers in Set  A = {−7, −4, 2, 14, 21, 34, 42}  are elements of both Set B and Set C, shown below?

 Set B = {even numbers}  

 Set C = {multiples of 7}

• {−4, 2, 14, 21, 42}

• {−7, 14, 21, 42}

• {14, 21, 42}

• {14, 42}

• Rational Number

• Irrational Number

Answer explanation

The sum (remember: subtraction is the same as adding the opposite) of an irrational number and a rational number is always irrational.

• Rational Number

• Irrational Number

Answer explanation

Since any number subtracted by itself is zero and the square root of 36 is 6, then the final answer 6 is rational.

The product of a rational and an irrational number is

(sometimes, always, or never) irrational.

(a)  

Answer explanation

If two irrational numbers are multiplied and have a product that is a non-perfect square, then it is irrational. Sometimes, the product could be a perfect square root, which means then it would be rational.

What is a rational number?

• A rational number  is a number that cannot be written as a fraction.

• A rational number is a number that can be written as a ratio.

• A rational number cannot be a repeating  decimal.

 Which number is irrational?

• 9.6

• √45

• 3/8

• 3.4 x 10⁵

Answer explanation

The square root of a non-perfect square is irrational because it is a non-repeating, and non-terminating decimal.

√45 = irrational