Rational or Irrational Sums and Products

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

True or False

Rational + Irrational = Irrational

• True

• False

Irrational + Irrational = Rational or Irrational

• True

• False

The sum or product of a non-zero rational number and an irrational number is always

• rational.

• irrational.

• a repeating decimal.

• a fraction.

Explain why A+B is irrational. Explain why AxB is rational.

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

• Rational

• Irrational

√2+√4

• rational

• irrational

The product of a non-zero rational number and an irrational number can always be written as 

• a fraction.

• a terminating decimal.

• a non-repeating, non-terminating decimal.

• a repeating decimal

Why is the product of a rational number and an irrational number irrational?

• because the product is always a non-terminating, non-repeating decimal

• because the product is always a fraction

• because the product is always a negative number

• because the product is always a repeating or a terminating decimal