Lesson Worksheet: Writing Algebraic Expressions Mathematics • 6th Grade

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

Q1:

Write an expression for a number 𝑧 decreased by 75.

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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)

Q6:

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

Q7:

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

Q8:

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.

Q9:

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

Q10:

Express one-sixth of 𝑦 in algebraic form.

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

Q11:

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

Q12:

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

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

Q13:

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

Q14:

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

Q15:

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

Q16:

Write an expression that represents one seventh of 𝑦.

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

Q17:

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

Q18:

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

Q19:

Translate the following verbal expression into an algebraic one, and then simplify it: The sum of 9 times a number and 13 is added to 14 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‘₯

Q20:

Translate the following verbal expression into an algebraic one, and then simplify it: The sum of six and a number is added to twenty-three.

  • A(6+π‘₯)+23π‘₯, 24π‘₯+6
  • B6(π‘₯+1)+23π‘₯, 29π‘₯+6
  • C6(π‘₯+1)+23, 6π‘₯+29
  • D6(1+π‘₯)+23, π‘₯+17
  • E(6+π‘₯)+23, π‘₯+29

Q21:

The natural number that follows 𝑛+6 is .

  • Aπ‘›βˆ’6
  • B𝑛+7
  • C𝑛
  • Dπ‘›βˆ’7
  • E𝑛+5

Q22:

Write the expression that means two times the square of π‘₯.

  • Aπ‘₯2
  • Bπ‘₯+4
  • C2π‘₯
  • D(2π‘₯)
  • Eπ‘₯+2

Q23:

Which of the following verbal expressions matches the algebraic expression 16π‘ŽοŠ¨?

  • Asquare of one-sixth of π‘Ž
  • Bone-sixth of π‘Ž squared
  • Cone-sixth of two times number π‘Ž
  • Dsquare of six π‘Ž
  • Esix of π‘Ž squared

Q24:

Which of the following verbal expressions matches the algebraic expression ο€Ό15π‘οˆοŠͺ?

  • A𝑏 divided by 15, all to the power of 4
  • B15 decreased by 𝑏 to the power of 4
  • C15 divided by 𝑏, all to the power of 4
  • D15 divided by 𝑏 times 4
  • E𝑏 divided by 15 times 4

Q25:

Given that a person’s age now is π‘₯, write an expression for the square of their age in 4 years.

  • A(π‘₯+4)
  • B4π‘₯
  • Cπ‘₯+16
  • D16π‘₯
  • Eπ‘₯+4

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.