Operations on Rational and Irrational Numbers

Which of the following is rational? Which of the following is rational? A. 3 * π B. 2/3 + 9.26 C. √45 + √36 D. 14.3 + 5.78765239....

B. 2/3 + 9.26

Which number expresses 6.72 as a fraction in simplest form? A. 6 3/5 B. 6 7/10 C. 6 18/15 D. 6 3/4

C. 6 18/15

Which statement is true about the sum of two rational numbers? A. It can always be written as a fraction. B. It can never be written as a fraction. C. It can always be written as a repeating decimal. D. It can never be written a terminating decimal.

A. It can always be written as a fraction.

Why is the product of a rational number and an irrational number irrational? A. because the product is always a non-terminating, non-repeating decimal B. because the product is always a fraction C. because the product is always a negative number D. because the product is always a repeating or a terminating decimal

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

The sum of two rational numbers will always be A. an irrational number. B. an integer. C. a rational number. D. a whole number.

The sum of two rational numbers will always be an irrational number. an integer. a rational number. a whole number.

Which of the following will result in a rational answer? A. multiplying π by a fraction B. adding the square root of a non perfect square to a whole number C. adding the square root of a perfect square to π D. multiplying a fraction by a repeating decimal.

[ NOT ] A. multiplying π by a fraction

The area of a rhombus can be evaluated using the formula 1/2 d1d2, where d1 represents the measure of one of its diagonals and d2 represents the measure of its other diagonal. When d1 is a terminating decimal and d2 is a repeating decimal, what can be concluded about the area of the rhombus? A. The area is irrational because both diagonals are irrational. B. The area is rational because the product of an irrational diagonal and rational diagonal will be multiplied by the rational fraction 1/2 C. The area is rational because the formula will multiply both rational diagonals and the fraction 1/2 D. The area is irrational because the formula will multiply two decimals by a fraction.

C. The area is rational because the formula will multiply both rational diagonals and the fraction 1/2

Which number is irrational? A. -4 B. 2/9 C. √11 D. 8.26(REPEATING)

C. √11

The formula for the circumference of a circle is C= πd, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference? A. It is a fraction. B. It is a repeating or terminating decimal. C. It is a rational number. D. It is an irrational number.

D. It is an irrational number.

The product of two rational numbers can always be written as A. an irrational number. B. a whole number. C. an integer. D. a fraction.

D. a fraction.

Sam is determining the area of a triangle. In this triangle, the value for the height is a terminating decimal, and the value for the base is a repeating decimal. What can be concluded about the area of this triangle? A. The area will be irrational because the height is irrational. B. The area is irrational because the numbers in the formula are irrational and the numbers substituted into the formula are rational. C. The area is rational because the numbers in the formula are rational and the numbers substituted into the formula are rational. D. The area will be rational because both the height and the base are irrational.

[ NOT ] B. The area is irrational because the numbers in the formula are irrational and the numbers substituted into the formula are rational.

To find the area of a trapezoid, Dylan uses the formula A = 1/2(b₁+b₂)h The bases have lengths of 3.6 cm and 12 1/3 cm. The height of the trapezoid is √5 cm. The area of the trapezoid is irrational because A. the values of the variables are all irrational numbers. B. the entire answer is being multiplied by a fraction. C. the height is irrational, and it is multiplied by the other rational dimensions. D. the bases have an irrational sum that will be multiplied by the rational height.

[ NOT ] B. the entire answer is being multiplied by a fraction.

The sum or product of a non-zero rational number and an irrational number is always A. rational. B. irrational. C. a repeating decimal. D. a fraction.

irrational.