Substitute $$x$$ with $$\frac{2}{3}$$ and check if $$3 \times \frac{2}{3} = 2.$$

Question 1

Which of the following is the correct way to convert the mixed number $$3\ \frac{2}{5} to an $$improper fraction?

Accepted Answer

$$\frac{3 	imes 5 + 2}{5}$$

Question 2

What is the prime factorization of 90?

Accepted Answer

$$2 	imes 3^2$ 	imes 5$$

Question 3

Reduce the fraction $$\frac{24}{36} to $$its lowest terms.

Accepted Answer

$$\frac{2}{3}$$

Question 4

Which of the following statements about prime numbers is TRUE?

Accepted Answer

A prime number has only two factors: 1 and itself.

Question 5

Multiply the fractions $$\frac{3}{4}$$ and $$\frac{2}{5}$$ and reduce the result to lowest terms.

Accepted Answer

$$\frac{3}{10}$$

Question 6

Divide $$\frac{7}{9} by$$ $$\frac{2}{3}$$ and reduce the result to lowest terms.

Accepted Answer

$$\frac{7}{6}$$

Question 7

Add the fractions $$\frac{5}{8}$$ and $$\frac{3}{8}.$$

Accepted Answer

$$\frac{8}{8}$$

Question 8

Subtract $$\frac{7}{12}$$ from $$\frac{11}{12}.$$

Accepted Answer

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

Question 9

Add $$\frac{2}{5}$$ and $$\frac{1}{4}$$, expressing your answer in lowest terms.

Accepted Answer

$$\frac{13}{20}$$

Question 10

Which of the following is the correct way to check if $$x = \frac{2}{3} is a $$solution to the equation $$3x = 2$$?

Accepted Answer

Substitute $$x$$ with $$\frac{2}{3}$$ and check if $$3 	imes \frac{2}{3} = 2.$$

Question 11

Translate the phrase 'one third of a number decreased by 6' into an algebraic expression, letting $$x$$ represent the number.

Accepted Answer

$$\frac{1}{3}x - 6$$

Question 12

A recipe calls for $$\frac{3}{4}$$ cup of sugar. If you want to make half the recipe, how much sugar should you use?

Accepted Answer

$$\frac{3}{8}$$ cup

Question 13

Convert the improper fraction $$\frac{17}{5} to a $$mixed number.

Accepted Answer

$$3\ \frac{2}{5}$$

Question 14

Which of the following is a composite number?

Accepted Answer

15

Question 15

If $$\frac{a}{b} = \frac{c}{d}$$ and $$b, d 
eq 0$$, which of the following is always true?

Accepted Answer

$$ad = bc$$

Question 16

A patient’s temperature is 104°F. Use the formula $$C = \frac{5}{9}(F - 32) to $$find the temperature in Celsius.

Accepted Answer

$$40^\circ C$$

Question 17

Which of the following is the correct result of dividing $$\frac{5}{6} by$$ $$\frac{2}{3}$$?

Accepted Answer

$$\frac{5}{4}$$

Question 18

A chemist mixes $$\frac{1}{2}$$ liter of solution A with $$\frac{2}{3}$$ liter of solution B. What is the total volume of the mixture?

Accepted Answer

$$\frac{7}{6}$$ liters

Question 19

Which of the following is the correct prime factorization of 36?

Accepted Answer

$$2^2$$ 	imes $$3^2$$

Fractions in Algebra: Variables, Real Numbers, and Mathematical Models

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