Algebra Word Expressions Practice Questions

Review these concepts at Algebra Word Expressions Study Guide.

Algebra Word Expressions Practice Questions

Practice

Practice 1

Write each phrase as a numerical expression.

1. five increased by two
2. the quotient of sixteen and four
3. four less than the sum of two and nine
4. negative twelve times three fewer than fifteen
5. the difference between the total of one and seven and the product of six and three

Practice 2

Write each phrase as an algebraic expression. Use x to represent one number and y to represent a second number.

1. negative nine times a number
2. a number combined with six
3. eight take away a number
4. a number shared by ten
5. two plus one-half of a number
6. the total of a number and negative one times another number
7. the quotient of seven and a number minus a second number
8. eighteen less than a number multiplied by another number
9. the difference between the square of a number and ten times another number
10. the total of six times a number and the difference between another number and nine

Solutions

Practice 1

1. The keyword increased signals addition. Five increased by two is 5 + 2.
2. The keyword quotient signals division. The quotient of sixteen and four is 16 ÷ 4.
3. The keywords less than signal subtraction and the keyword sum signals addition. The sum of two and nine is 2 + 9, and four less than that sum is (2 + 9) – 4.
4. The keywords fewer than signal subtraction and the keyword times signals multiplication. Three fewer than fifteen is 15 – 3. Negative twelve times that quantity is –12(15 – 3).
5. The keyword difference signals subtraction, but before we can subtract, we have to translate the total of one and seven and the product of six and three into numbers and operations. The keyword total signals addition. The total of one and seven is (1 + 7). The keyword product signals multiplication. The product of six and three is (6)(3). Now we are ready to write the difference between the two quantities. The difference between the total of one and seven and the product of six and three is (1 + 7) – (6)(3).

Practice 2

1. The keyword times signals multiplication. Negative nine times a number is –9x.
2. The keyword combined signals addition. A number combined with six is x + 6.
3. The keyword phrase take away signals subtraction. Eight take away a number is 8 – x.
4. The keyword shared signals division. A number shared by ten is
5. The keyword plus signals addition. The keyword of signals multiplication. One-half of a number is times a number, or that number divided by two. Two plus one-half of a number is
6. The keyword total signals addition and the keyword times signals multiplication. The total of a number and negative one times another number is x + –1y, which simplifies to x –y.
7. The keyword quotient signals division and the keyword minus signals subtraction. The quotient of seven and a number minus a second number is .
8. The keyword phrase less than signals subtraction and the keyword multiplied signals multiplication. A number multiplied by another number is xy. Eighteen less than a number multiplied by another numberis xy – 18.
9. The keyword difference signals subtraction and the keyword times signals multiplication. The square of a number is a number times itself, or x².Ten times another numberis 10y. The difference between the square of a number and ten times another number is x² – 10y.
10. The keyword total signals addition, the keyword times signals multiplication, and the keyword difference signals subtraction. The difference between another number and nine is y – 9. The total of six times a number and that difference is 6x + (y – 9).