Worksheet: Writing Algebraic Expressions

In this worksheet, we will practice reading and writing algebraic expressions and applying this to real-life situations.

Q1:

Write an expression for 12 more than the product of a number π‘₯ and 4.

  • A4(12+π‘₯)
  • B12π‘₯βˆ’4
  • C12βˆ’4π‘₯
  • D4π‘₯
  • E4π‘₯+12

Q2:

Write an expression for a number 𝑧 decreased by 75.

  • Aπ‘§βˆ’75
  • B75βˆ’π‘§
  • C𝑧+75
  • Dπ‘§βˆ’75𝑧
  • E75π‘§βˆ’75

Q3:

Write an expression for the product of 6 and π‘₯.

  • A6π‘₯
  • B6βˆ’6π‘₯
  • C6+6π‘₯
  • D6π‘₯
  • E6π‘₯βˆ’π‘₯

Q4:

Express the following in algebraic form: The square of a number π‘˜ which is then multiplied by 19.

  • A19π‘˜οŠ¨
  • B19π‘˜
  • C19+π‘˜οŠ¨
  • Dπ‘˜19
  • Eπ‘˜19

Q5:

Write β€œeleven more than sixteen times the number of women” as an algebraic expression, where 𝑀 is the number of women.

  • A11𝑀+16
  • B16π‘€βˆ’11
  • C16𝑀+11
  • D11π‘€βˆ’16
  • E𝑀+27

Q6:

Write an expression for the number that is 3 less than a quarter of 𝑦.

  • A𝑦4βˆ’3
  • B3𝑦4βˆ’3
  • C3βˆ’π‘¦4
  • D𝑦4+3
  • E𝑦4

Q7:

Write an expression for the sum of a number π‘₯ and 4, all divided by 6.

  • A4π‘₯+46
  • Bπ‘₯+64
  • C4π‘₯6
  • Dπ‘₯6+4
  • Eπ‘₯+46

Q8:

Write the expression that means β€œdivide β„Ž by 66 and add 34Β to the quotient.”

  • Aβ„Ž34βˆ’66
  • Bβ„Ž34+66
  • Cβ„Ž66+34
  • Dβ„Ž66βˆ’34

Q9:

Express the following as an algebraic expression: The quotient of a number 𝑀 and 5, increased by 2.

  • A𝑀5+2
  • B2𝑀+5
  • C𝑀2+5
  • D𝑀2βˆ’5
  • E𝑀5βˆ’2

Q10:

Write an expression for the product of the cube of π‘₯ and the difference between a number 𝑦 and 9, all divided by 2.

  • A3π‘₯(π‘¦βˆ’9)2
  • Bπ‘₯π‘¦βˆ’11
  • Cπ‘₯2(π‘¦βˆ’9)
  • Dπ‘₯(π‘¦βˆ’9)2
  • Eπ‘₯(π‘¦βˆ’9)

Q11:

Write an expression for double the square of π‘₯, which is then divided by 9 less than the cube of 𝑦.

  • A4π‘₯π‘¦βˆ’9
  • Bπ‘¦βˆ’92π‘₯
  • C2π‘₯π‘¦βˆ’9
  • D9βˆ’2π‘₯π‘¦βˆ’9
  • E2π‘₯π‘¦βˆ’9

Q12:

The product of 𝑦 and π‘₯ is 14. Write an expression for the value of 𝑦.

  • A14βˆ’π‘₯
  • Bπ‘₯βˆ’14
  • C14π‘₯
  • D14π‘₯
  • Eπ‘₯14

Q13:

If the length of a rectangle is 9+π‘₯, and its width is π‘₯, describe the relationship that exists between them.

  • AThe width is nine times the length.
  • BThe length is nine times the width.
  • CThe length is nine less than nine times the width.
  • DThe length is nine less than the width.
  • EThe length is nine more than the width.

Q14:

Write the following algebraic expression as a verbal expression: 2π‘š.

  • Atwo times π‘š
  • Btwo more than π‘š
  • Cthe square of π‘š
  • Dtwenty-π‘š

Q15:

Express one-sixth of 𝑦 in algebraic form.

  • A6𝑦
  • B16𝑦
  • C𝑦+6
  • Dπ‘¦βˆ’6
  • E6𝑦+1

Q16:

Given that Daniel is 7𝑐 years old now, write an expression for his age 5 years ago.

  • A7𝑐+5
  • B7π‘βˆ’35
  • C7𝑐+35
  • D7π‘βˆ’5
  • E35𝑐

Q17:

Write an expression for the square of a number π‘₯.

  • Aπ‘₯2
  • B2π‘₯
  • C4π‘₯
  • D2π‘₯
  • Eπ‘₯

Q18:

Express the following sentence as an algebraic expression: Amelia is five years younger than Isabella.

  • Aπ‘₯+5
  • B5βˆ’π‘₯
  • C5π‘₯
  • Dπ‘₯5
  • Eπ‘₯βˆ’5

Q19:

Given that a person’s age now is π‘₯, write an expression for twice their age 10 yr ago.

  • A2π‘₯βˆ’10
  • B2π‘₯βˆ’20
  • C2π‘₯+20
  • D2π‘₯+10
  • Eπ‘₯βˆ’10

Q20:

Write an algebraic equation to show that π‘š divided by 8 is βˆ’45.

  • Aπ‘š45=8
  • B8π‘š=45
  • Cπ‘š8=βˆ’45
  • Dβˆ’45π‘š=8
  • E8π‘š=βˆ’45

Q21:

Write an expression that represents one seventh of 𝑦.

  • A𝑦7
  • B7𝑦
  • Cπ‘¦βˆ’7
  • D𝑦+7
  • E7βˆ’π‘¦

Q22:

Write an expression for the number which is 40 divided by the difference between π‘₯ and 5.

  • A405π‘₯
  • B40π‘₯βˆ’5
  • Cπ‘₯βˆ’540
  • Dπ‘₯40βˆ’5
  • E40π‘₯βˆ’5

Q23:

I am π‘₯ years old. How old will I be in 10 years’ time?

  • Aπ‘₯10 years old
  • B(π‘₯βˆ’10) years old
  • C10π‘₯ years old
  • Dπ‘₯ years old
  • E(π‘₯+10) years old

Q24:

Translate the following verbal expression into an algebraic one, and then simplify it: The product of seven and a number is multiplied by ten.

  • A(7π‘₯)β‹…10, 70π‘₯
  • B(π‘₯+7)β‹…10, 7π‘₯+70
  • C(π‘₯+7)β‹…10, 17+π‘₯
  • D(7π‘₯)β‹…10, 17π‘₯
  • E(7π‘₯)β‹…10, 70π‘₯+10

Q25:

Translate the following verbal expression into an algebraic one, and then simplify it: The sum of 9 times a number and thirteen is added to fourteen times the same number.

  • A(9π‘₯+13)+14, 27+9π‘₯
  • B(9π‘₯+13)+14π‘₯, 13+23π‘₯
  • C(9π‘₯+14)+13π‘₯, 14+22π‘₯
  • D(9π‘₯+14)+13, 22+14π‘₯
  • E(13π‘₯+9)+14π‘₯, 9+27π‘₯

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