Question 1

Which of the following best illustrates the commutative property of addition?

Accepted Answer

The commutative property of addition states that changing the order of addends does not change the sum. Option D shows that the order of the addends can be changed without affecting the sum.

Question 2

What should be done in order to isolate the variable x on one side of an equation and the numbers on the other?

Accepted Answer

To isolate the variable x, the opposite of the operation that appears on the same side of the equal sign as x should be carried out. This will move all the numbers to the other side of the equation, leaving x alone on one side.

Question 3

Which of the following best illustrates the associative property of multiplication?

Accepted Answer

The associative property of multiplication states that the way in which factors are grouped does not change the product. Choice D, $(1 \times 2) \times 3 = 1 \times (2 \times 3)$, directly illustrates this property by showing that regardless of how the numbers are grouped, the result remains the same.

Question 4

What is a ratio?

Accepted Answer

A ratio is the comparison between two quantities expressed in terms of their quotient. In other words, a ratio is the quotient of two numbers. For instance, the ratio of the height to the width of a rectangle is defined as the height of the rectangle divided by its width.

Question 5

A fraction whose value is greater than 1 is referred to as

Accepted Answer

An improper fraction is a fraction whose numerator is greater than or equal to its denominator, and its value is greater than 1.

Question 6

What does the term "denominator" refer to?

Accepted Answer

The denominator is the number below the line in a fraction, indicating into how many equal parts the whole is divided.

Question 7

Which of the following statements is necessarily true about a reduced fraction?

Accepted Answer

A reduced fraction is a fraction where the numerator and denominator have no common factors other than 1. This means that the only whole number that divides both the numerator and denominator is 1, which is the definition of answer choice B. Option A is not true as dividing a number by 0 is undefined. Option C and D are not necessarily true as the value of the numerator and denominator can vary and are not related in any specific way in a reduced fraction.

Question 8

To add two fractions with different denominators,what must be determined for the denominators?

Accepted Answer

To add two fractions with different denominators, we need to find the least common multiple of the denominators, which is known as the least common denominator (LCD). Once we have the LCD, we can convert both fractions to equivalent fractions with the same denominator and then add their numerators.

Question 9

When a positive number is multiplied by a negative number,what sign will the value of the product always have?

Accepted Answer

When a positive number is multiplied by a negative number, the sign of the product will always be negative. This is because the two numbers have opposite signs, and when they are multiplied, the negative sign "dominates" the positive sign, resulting in a negative product.

Question 10

What is the product of two reciprocals?

Accepted Answer

The product of two reciprocals is always 1. For example, the reciprocals of 2 and 1/2 are 1/2 and 2, respectively. Their product is 1.

Question 11

What is the correct procedure for dividing fractions?

Accepted Answer

To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction. This can be shown algebraically as (a/b)/(c/d) = (a/b) x (d/c) = ad/bc. Therefore, multiplying one fraction by the reciprocal of the other is the correct procedure.

Question 12

Which of the following illustrates the commutative property of multiplication?

Accepted Answer

The commutative property of multiplication states that changing the order of the factors does not change the product. Option C shows that the factors 1, 2, and 3 can be multiplied in any order, and the product will remain the same (6).

Question 13

What is the purpose of algebra?

Accepted Answer

The purpose of algebra is to identify the unknown value of a variable. Algebra uses letters to represent unknown values and equations to express relationships between the known and unknown values. By manipulating equations, algebra can solve for the unknown value of a variable. Therefore, option D is the best choice.

Question 14

Consider the following expression. 9 - (-3) Which of the following expressions is another way of writing this?

Accepted Answer

Subtracting a negative number is the same as adding its positive counterpart, so 9 - (-3) is equivalent to 9 + 3.

Question 15

Which of the following is a valid use of percentages?

Accepted Answer

Percentages can be used to standardize proportions by converting them to a scale out of 100. This allows for easy comparison and analysis of data.

Question 16

Which of the following expressions demonstrates the correct procedure for multiplying a fraction by a whole number?

Accepted Answer

To multiply a fraction by a whole number, we need to convert the whole number to a fraction by putting it over 1. Then we multiply the numerators and denominators. In this case, we get $10 \times \frac{2}{5}=\frac{10}{1} \times \frac{2}{5}$.

Question 17

Which of the following best defines algebra?

Accepted Answer

Algebra involves using strategic manipulation of equations and relationships to solve for an unknown value. This often includes using numerical manipulation, but the focus is on finding a solution to the equation or relationship rather than simply performing basic arithmetic operations.

Question 18

What does a percentage represent?

Accepted Answer

A percentage represents the number of parts out of every 100 parts. For example, 50% represents 50 out of 100 parts or 0.5 as a decimal.

Question 19

How should a problem that equates two ratios be solved?

Accepted Answer

To equate two ratios, you need to cross-multiply by multiplying the numerator of one ratio by the denominator of the other ratio and vice versa. This will give you an equation that can be solved to find the value of the unknown variable.

Quiz 1: Arithmetic and Algebra