Rational Versus Irrational Sums and Products

• A

• B

• C

• D

• A

• B

• C

• D

• A

• B

• C

• D

• A

• B

• C

• D

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

• rational.

• irrational.

• a repeating decimal.

• a fraction.

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.

•  Sum of rational and irrational, so it is irrational

• Sum of two irrationals, so it is irrational

• Product of two irrationals, so it is irrational 

• Product of two rationals, so it is rational 

When a rational number is multiplied by an irrational number, the product will be a(n) ​ (a)   .

• irrational number

• rational number

• integer

• whole number

• Since both numbers are rational, the product is rational

• Since both numbers are irrational, the product is rational

• Since one number is rational and one number is irrational, the product is irrational

• Since one number is rational and one is irrational, the product is irrational

1.      Select each box in the table where the numbers from corresponding rows and columns will have a rational sum.