Ultimate Math Test On Expressions and Equations

Math

Grade 6th,
Grade 7th,
Grade 8th

CCSS

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Quizzes Created: 9 | Total Attempts: 29,662

| Attempts: 1,036 | Questions: 26 | Updated: Feb 2, 2026

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1) Three times Cassie’s age increased by nine is twelve

3C+9=12

3(C+9)=12

3C+12=9

12+3C=9

“Cassie’s age increased by nine” means C+9. “Three times” indicates multiplication by three. Since the statement equals twelve, the equation is 3(C+9)=12. Writing 3C+9=12 would incorrectly apply addition after multiplication, changing the meaning.

Explanation

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About This Quiz

Ultimate Math Test On Expressions and Equations - Quiz

.
Welcome to the Expressions and Equations Quiz! This quiz will test your understanding of fundamental concepts in algebraic expressions and equations. Get ready to flex your mathematical muscles as you navigate through a series of thought-provoking questions designed to challenge and expand your knowledge.

In this quiz, you'll encounte... see morea variety of problems that will require you to simplify expressions, solve equations, and manipulate algebraic formulas. Expect to encounter questions covering topics such as combining like terms, factoring polynomials, solving linear and quadratic equations, and understanding the properties of exponents.

Are you ready to put your algebraic expertise to the test? Sharpen your pencils, clear your mind, and dive into the world of expressions and equations with this engaging quiz. Let's see if you have what it takes to conquer the challenges that lie ahead! see less

2) Number in front of a variable

Constant

Exponent

Coefficient

Term

The coefficient is the numerical factor multiplying a variable. It indicates how many times the variable is taken in the expression.

Explanation

The coefficient is the numerical factor multiplying a variable. It indicates how many times the variable is taken in the expression.

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3) A letter that represents a number

Constant

Variable

Coefficient

Term

A variable is a letter used to represent an unknown or changing number. It allows mathematical relationships to be written symbolically.

Explanation

A variable is a letter used to represent an unknown or changing number. It allows mathematical relationships to be written symbolically.

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4) Words for 3x−4

4 less than product of 3 and x

4 less than quotient of 3 and x

Product of 3 and x plus 4

Quotient of x and 3 minus 4

The expression 3x−4 means multiply 3 and x, then subtract 4. In words, this is “4 less than the product of 3 and x.”

Explanation

The expression 3x−4 means multiply 3 and x, then subtract 4. In words, this is “4 less than the product of 3 and x.”

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5) Twice the product of 3 and x

2+(3x)

(2+3)x

2(3x)

2(3+x)

“The product of 3 and x” is 3x. “Twice” means multiply by 2. Therefore, twice the product of 3 and x is 2(3x).

Explanation

“The product of 3 and x” is 3x. “Twice” means multiply by 2. Therefore, twice the product of 3 and x is 2(3x).

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6) Which does NOT mean multiplication

Product

Twice

Times

More than

Words like product, twice, and times indicate multiplication. “More than” usually indicates addition. Therefore, “more than” does not mean multiplication.

Explanation

Words like product, twice, and times indicate multiplication. “More than” usually indicates addition. Therefore, “more than” does not mean multiplication.

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7) 15 more than one third x

(1/3)x+15

15x/3

X/3−15

3x+15

“One third x” is written as (1/3)x. “15 more than” means add 15. Therefore, the expression is (1/3)x+15.

Explanation

“One third x” is written as (1/3)x. “15 more than” means add 15. Therefore, the expression is (1/3)x+15.

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8) 8 less than the sum of a and b

A+b−8

8−a−b

A+b+8

8(a+b)

“The sum of a and b” is a+b. “8 less than” means subtract 8 from that sum. Therefore, the expression is a+b−8.

Explanation

“The sum of a and b” is a+b. “8 less than” means subtract 8 from that sum. Therefore, the expression is a+b−8.

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9) Twenty-two times a number decreased by three

22a−3

3−22a

22(a−3)

A−66

“Twenty-two times a number” gives 22a. “Decreased by three” means subtract 3 after multiplication. Therefore, the correct expression is 22a−3.

Explanation

“Twenty-two times a number” gives 22a. “Decreased by three” means subtract 3 after multiplication. Therefore, the correct expression is 22a−3.

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10) Twenty-two times h plus three

22h+3

3h+22

22(h+3)

H+66

“Twenty-two times h” is written as 22h. “Plus three” means add 3 afterward. Combining both parts gives the expression 22h+3.

Explanation

“Twenty-two times h” is written as 22h. “Plus three” means add 3 afterward. Combining both parts gives the expression 22h+3.

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11) What does 25k mean

25+k

K−25

Product of 25 and k

K÷25

In algebra, writing a number next to a variable indicates multiplication. Therefore, 25k means 25 multiplied by k. It does not represent addition, subtraction, or division.

Explanation

In algebra, writing a number next to a variable indicates multiplication. Therefore, 25k means 25 multiplied by k. It does not represent addition, subtraction, or division.

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12) Difference between expression and equation

Same thing

Equation has = sign

More numbers

Higher value

An equation includes an equal sign showing two expressions are equal. An expression does not include an equal sign. This structural difference defines how equations are solved and expressions are evaluated.

Explanation

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13) Expression for “a number f decreased by 18”

18f

F+18

F−18

18+f

“Decreased by” means subtract. Starting with f and subtracting 18 gives f−18. Adding 18 or multiplying changes the meaning. Therefore, f−18 correctly represents a number f decreased by 18.

Explanation

“Decreased by” means subtract. Starting with f and subtracting 18 gives f−18. Adding 18 or multiplying changes the meaning. Therefore, f−18 correctly represents a number f decreased by 18.

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14) Steve’s starting amount if final balance is $70

Steve deposits $10 for 3 weeks, adding $30 total. His final balance is $70. Subtracting deposits gives x+30=70. Solving the equation results in x=40. This represents the amount Steve had before making any deposits.

Explanation

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15) What is the algebraic expression for four times the sum of nine and a number

4(9+n)

4×9+n

4n+9

9(4+n)

“Four times the sum” means multiply the entire sum by four. The sum of nine and a number is written as 9+n. Multiplying the full sum gives 4(9+n). Writing 4n+9 multiplies only the variable, not the entire sum, so it is incorrect.

Explanation

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16) Ratio of m and n

M/n

N/m

M+n

A ratio compares two quantities using division. “The ratio of m and n” is written as m/n. Reversing the order changes the ratio and is incorrect.

Explanation

A ratio compares two quantities using division. “The ratio of m and n” is written as m/n. Reversing the order changes the ratio and is incorrect.

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17) =+, −, ×, ÷ are all operations

True

False

Sometimes

Never

Addition, subtraction, multiplication, and division are the four fundamental operations in mathematics. Each symbol listed represents one of these operations. Since all listed symbols perform operations on numbers or quantities, the statement is true.

Explanation

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18) Four less than a number

4−x

X−4

X+4

4+x

“Four less than a number” means subtracting 4 from the number. If the number is x, the expression is x−4.

Explanation

“Four less than a number” means subtracting 4 from the number. If the number is x, the expression is x−4.

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19) Brett’s starting floor if final floor is 11

Let the starting floor be x. Net movement is +10−7+4−6=+1. Since Brett ends on floor 11, x+1=11. Solving gives x=10. Therefore, Brett started on the 10th floor before riding the elevator.

Explanation

Let the starting floor be x. Net movement is +10−7+4−6=+1. Since Brett ends on floor 11, x+1=11. Solving gives x=10. Therefore, Brett started on the 10th floor before riding the elevator.

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20) Sum of three and twenty-two divided by a

(3+22)/a

A/(3+22)

3+22/a

A+25

“The sum of three and twenty-two” is 3+22. “Divided by a” means divide the entire sum by a. Therefore, the correct expression is (3+22)/a.

Explanation

“The sum of three and twenty-two” is 3+22. “Divided by a” means divide the entire sum by a. Therefore, the correct expression is (3+22)/a.

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21) “a decreased by 17” translates to

A−17

17−a

A+17

17+a

“Decreased by” indicates subtraction. Starting with a and subtracting 17 gives a−17. Reversing the subtraction would change the meaning, so a−17 is correct.

Explanation

“Decreased by” indicates subtraction. Starting with a and subtracting 17 gives a−17. Reversing the subtraction would change the meaning, so a−17 is correct.

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22) Quotient of 55 and z

55/z

Z/55

55z

Z−55

“The quotient of 55 and z” means divide 55 by z. Quotient always indicates division, so the correct expression is 55/z.

Explanation

“The quotient of 55 and z” means divide 55 by z. Quotient always indicates division, so the correct expression is 55/z.

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23) Mark’s pencils if Sara and Kim have 15 and Sara has 9

$34

Sara and Kim together have 15 pencils. Sara has 9, so Kim has 6. Mark and Kim together have 10 pencils. Subtracting Kim’s 6 pencils from 10 gives Mark’s total. Therefore, Mark has 4 pencils.

Explanation

Sara and Kim together have 15 pencils. Sara has 9, so Kim has 6. Mark and Kim together have 10 pencils. Subtracting Kim’s 6 pencils from 10 gives Mark’s total. Therefore, Mark has 4 pencils.

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24) Coefficient of y in 22y/9

1/9

22/9

The expression 22y/9 can be rewritten as (22/9)y. The coefficient is the number multiplying y, which is 22/9.

Explanation

The expression 22y/9 can be rewritten as (22/9)y. The coefficient is the number multiplying y, which is 22/9.

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25) If m=17, the sum of 5 and m is

Substitute m=17 into the expression 5+m. This gives 5+17=22. Substitution is used when a variable’s value is known. Therefore, the sum of 5 and m is 22.

Explanation

Substitute m=17 into the expression 5+m. This gives 5+17=22. Substitution is used when a variable’s value is known. Therefore, the sum of 5 and m is 22.

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