$$\frac{a \times c}{b \times d}$$

$$\frac{a \times c}{b \times c}$$

Question 1

Which of the following statements about rational numbers is TRUE?

Accepted Answer

A rational number can always be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are integers and $$b 
eq 0.$$

Question 2

Which of the following is the correct reduced form of $$\frac{1890}{2016}$$?

Accepted Answer

$$\frac{15}{16}$$

Question 3

What is the decimal expansion of $$\frac{13}{7}$$, and does it terminate or repeat?

Accepted Answer

It repeats as $$1.857142\ldots$$

Question 4

Which of the following is NOT a rational number?

Accepted Answer

$$\frac{5}{0}$$

Question 5

If $$x = 0.abcabcabc\ldots ($$where $$abc is a $$repeating block of digits), which formula expresses $$x as a $$fraction?

Accepted Answer

$$x = \frac{abc}{999}$$

Question 6

Convert the mixed number $$4\frac{7}{12} to an $$improper fraction.

Accepted Answer

$$\frac{55}{12}$$

Question 7

Which of the following is the reciprocal of $$\frac{11}{3}$$?

Accepted Answer

$$\frac{3}{11}$$

Question 8

What is the result of $$-3\frac{2}{3} 	imes -1\frac{1}{4}$$ expressed as a mixed number?

Accepted Answer

$$4\frac{7}{12}$$

Question 9

Which property of rational numbers guarantees that every rational number has a unique reduced form?

Accepted Answer

The Fundamental Theorem of Arithmetic

Question 10

Add $$\frac{3}{4}$$ and $$\frac{1}{6}$$ and express your answer in reduced form.

Accepted Answer

$$\frac{11}{12}$$

Question 11

Which of the following statements about the density of rational numbers is correct?

Accepted Answer

Between any two rational numbers, there exists another rational number.

Question 12

Find a rational number between $$\frac{1}{3}$$ and $$\frac{1}{2}.$$

Accepted Answer

$$\frac{5}{12}$$

Question 13

A recipe calls for $$\frac{3}{4}$$ cup of sugar to make five dozen cookies. How much sugar is needed to make eight dozen cookies?

Accepted Answer

$$\frac{11}{5}$$ cup

Question 14

Which of the following is the correct way to multiply two rational numbers $$\frac{a}{b}$$ and $$\frac{c}{d}$$?

Accepted Answer

$$\frac{a 	imes c}{b 	imes d}$$

Question 15

What is the result of $$-3\frac{2}{3} \div -1\frac{1}{4}$$ expressed as a mixed number?

Accepted Answer

$$2\frac{14}{15}$$

Question 16

Which of the following is the correct method to convert a terminating decimal to a fraction?

Accepted Answer

Multiply the decimal by $$10^n ($$where $$n is $$the number of decimal places), use the result as the numerator and $$10^n as $$the denominator.

Question 17

Which of the following fractions is equivalent to $$\frac{-2}{5}$$?

Accepted Answer

$$\frac{4}{-10}$$

Question 18

If $$\frac{a}{b} is a $$rational number and $$c 
eq 0$$, which of the following is an equivalent fraction?

Accepted Answer

$$\frac{a 	imes c}{b 	imes c}$$

Question 19

Which of the following best describes a mixed number?

Accepted Answer

The sum of an integer and a rational number.

Question 20

What is the result of $$\frac{2}{7} - \frac{6}{7}$$?

Accepted Answer

$$-4/7$$

Rational Numbers: Properties, Operations, and Applications

Study Guide - Practice Questions