Rational and Irrational Sum and Product

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.

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.

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 

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

• rational.

• irrational.

• a repeating decimal.

• a fraction.

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

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

• irrational number

• rational number

• integer

• whole number

7\frac{6}{10}\cdot\ 3\ =\ ?,\ which\ is\ ?

• Sum of rational and irrational, so it is irrational

• Sum of two irrationals, so it is irrational

• Product of rational and irrational, so it is irrational 

• Product of two rationals, so it is rational