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Worksheet: Writing Algebraic Expressions

Q1:

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

  • A 1 2 βˆ’ 4 π‘₯
  • B 4 π‘₯
  • C 1 2 π‘₯ βˆ’ 4
  • D 4 π‘₯ + 1 2
  • E 4 ( 1 2 + π‘₯ )

Q2:

For a marathon, an athlete practiced on a track that is π‘š miles long. She ran for 5 laps each on Monday and on Wednesday and 4 laps on Friday. On Sunday, she ran for 18 miles. Write an expression in the simplest form that represents the total distance the athlete ran during her practice.

  • A 1 3 π‘š + 1 8
  • B 9 π‘š + 1 8
  • C 2 0 π‘š + 1 8
  • D 1 4 π‘š + 1 8
  • E 9 π‘š βˆ’ 1 8

Q3:

A shop sells chocolates for 26 LE a kilogram and boxes for 6 LE. A boy bought π‘₯ kg of chocolate and a box. Write an expression for the amount he paid.

  • A ( 2 6 π‘₯ βˆ’ 6 ) L E
  • B ( 6 π‘₯ + 2 6 ) L E
  • C ( 6 π‘₯ βˆ’ 2 6 ) L E
  • D ( 2 6 π‘₯ + 6 ) L E
  • E ( 3 2 π‘₯ ) L E

Q4:

Mason spent π‘š minutes practicing the piano on Monday. On Tuesday, he practiced for 20 minutes more than he did on Monday. On Wednesday, he practiced for 35 minutes less than he did on Tuesday. On Thursday, he practiced for three times as long as he did on Monday. On Friday, he practiced for 25 minutes less than he did on Thursday. Write, in the simplest form, an expression that represents the number of minutes he spent practicing on these five days.

  • A 5 π‘š βˆ’ 2 0
  • B 8 π‘š βˆ’ 4 0
  • C 5 π‘š βˆ’ 4 0
  • D 9 π‘š βˆ’ 2 0
  • E 1 0 π‘š βˆ’ 2 0

Q5:

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

  • A 2 π‘₯ 2
  • B 2 π‘₯
  • C π‘₯ 2
  • D π‘₯ 2
  • E 4 π‘₯

Q6:

Mr. David purchased supplies for $45 to renovate his apartment’s floor. He paid one person $8 per hour to sand the wooden floor, and then he paid another person $14 per hour to apply the finish to the wood. If both people worked for β„Ž hours, write an expression that can be used to represent the total cost of renovating the apartment floor, and then simplify it.

  • A 4 5 + 8 β„Ž + 1 4 , 5 9 + 8 β„Ž
  • B 4 5 βˆ’ 8 β„Ž + 1 4 β„Ž , 4 5 + 6 β„Ž
  • C 4 5 + 8 β„Ž βˆ’ 1 4 , 3 1 + 8 β„Ž
  • D 4 5 + 8 β„Ž + 1 4 β„Ž , 4 5 + 2 2 β„Ž
  • E 4 5 + 8 β„Ž βˆ’ 1 4 β„Ž , 4 5 βˆ’ 6 β„Ž

Q7:

Write β€œeleven more than sixteen times as many women” as an algebraic expression.

  • A 1 6 𝑀 βˆ’ 1 1
  • B 1 1 𝑀 βˆ’ 1 6
  • C 1 1 𝑀 + 1 6
  • D 1 6 𝑀 + 1 1
  • E 𝑀 + 2 7

Q8:

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

  • A 4 π‘₯ 𝑦 βˆ’ 9 2 3
  • B 2 π‘₯ 𝑦 βˆ’ 9 2
  • C 𝑦 βˆ’ 9 2 π‘₯ 3 2
  • D 2 π‘₯ 𝑦 βˆ’ 9 2 3
  • E 9 βˆ’ 2 π‘₯ 𝑦 βˆ’ 9 2 3

Q9:

At a grocery store, Shirley bought bags of cat food for $16.00 each and the same number of bags of dog food for $8.25 each. Write, in its simplest form, an expression for the total amount she spent.

  • A
  • B
  • C
  • D
  • E

Q10:

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

  • A
  • B
  • C
  • D
  • E

Q11:

You have $100 in the bank. Each day, you deposit $10 into your account. Write an expression for your balance after 𝑑 days.

  • A 1 0 𝑑 βˆ’ 1 0 0
  • B 1 0 𝑑
  • C 1 0 0 𝑑 + 1 0
  • D 1 0 𝑑 + 1 0 0
  • E 1 1 0 𝑑

Q12:

In preparation for a tournament, Daniel exercised β„Ž hours on Friday. On Saturday, he exercised 2 hours less than he did on Friday. On Sunday, he exercised 1 2 of an hour more than he did on Saturday. Write, in the simplest form, an expression to represent the number of hours Daniel exercised over the weekend.

  • A 3 β„Ž + 7 2
  • B 7 2 β„Ž βˆ’ 3
  • C 7 2 β„Ž + 3
  • D 3 β„Ž βˆ’ 7 2
  • E 2 β„Ž + 7 2

Q13:

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

  • A π‘₯ 2 ( 𝑦 βˆ’ 9 ) 3
  • B π‘₯ ( 𝑦 βˆ’ 9 ) 3
  • C π‘₯ 𝑦 βˆ’ 1 1 3
  • D π‘₯ ( 𝑦 βˆ’ 9 ) 2 3
  • E 3 π‘₯ ( 𝑦 βˆ’ 9 ) 2

Q14:

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

  • A 6 π‘₯ βˆ’ π‘₯
  • B 6 π‘₯
  • C 6 + 6 π‘₯
  • D 6 π‘₯
  • E 6 βˆ’ 6 π‘₯

Q15:

At noon, a barista notices that she has $20 in her tip jar. In the afternoon, her average tip is $0.50 per customer. Write an expression to describe how much money she will have in her tip jar at the end of her shift if she serves 𝑛 more customers.

  • A $ ( 2 0 𝑛 )
  • B $ ( 0 . 5 𝑛 βˆ’ 2 0 )
  • C $ ( 2 0 𝑛 βˆ’ 0 . 5 )
  • D $ ( 0 . 5 𝑛 + 2 0 )
  • E $ ( 2 0 𝑛 + 0 . 5 )

Q16:

Admission to a museum costs $5 per person. A family has a coupon for a discount of $8. There are 𝑝 people in the family. Write an expression that represents how much the family pays.

  • A 5 𝑝 βˆ’ 4 0
  • B 5 𝑝
  • C 5 𝑝 8
  • D 5 𝑝 βˆ’ 8
  • E 8 + 5 𝑝

Q17:

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

  • A 𝑀 2 + 5
  • B 𝑀 5 βˆ’ 2
  • C 𝑀 2 βˆ’ 5
  • D 𝑀 5 + 2
  • E 2 𝑀 + 5

Q18:

Express the following as an algebraic expression: The quotient of a number 𝑀 and βˆ’ 7 , increased by 8.

  • A 𝑀 8 + 7
  • B 𝑀 βˆ’ 7 βˆ’ 8
  • C 𝑀 8 βˆ’ 7
  • D 𝑀 βˆ’ 7 + 8
  • E 8 𝑀 + 7

Q19:

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

  • A β„Ž 3 4 + 6 6
  • B β„Ž 6 6 βˆ’ 3 4
  • C β„Ž 3 4 βˆ’ 6 6
  • D β„Ž 6 6 + 3 4

Q20:

Write an expression for a number 𝑧 decreased by 75.

  • A 7 5 βˆ’ 𝑧
  • B 𝑧 + 7 5
  • C 7 5 𝑧 βˆ’ 7 5
  • D 𝑧 βˆ’ 7 5
  • E 𝑧 βˆ’ 7 5 𝑧

Q21:

The height of the Empire State Building is 164 meters more than 3 times the height of the Statue of Liberty. Let β„Ž be the height of the Statue of Liberty. Write an expression that represents the height of the Empire State Building in terms of β„Ž .

  • A 1 6 4 βˆ’ 3 β„Ž
  • B 3 β„Ž βˆ’ 1 6 4
  • C 1 6 4 β„Ž + 3
  • D 3 β„Ž + 1 6 4
  • E 3 ( β„Ž + 1 6 4 )

Q22:

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

  • A π‘₯ 6 + 4
  • B 4 π‘₯ 6
  • C π‘₯ + 6 4
  • D π‘₯ + 4 6
  • E 4 π‘₯ + 4 6

Q23:

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

  • A 3 βˆ’ 𝑦 4
  • B 𝑦 4
  • C 3 𝑦 4 βˆ’ 3
  • D 𝑦 4 βˆ’ 3
  • E 𝑦 4 + 3

Q24:

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

  • A 1 9 + π‘˜ 2
  • B 1 9 π‘˜
  • C π‘˜ 1 9
  • D 1 9 π‘˜ 2
  • E π‘˜ 1 9 2

Q25:

Express one-sixth of 𝑦 in algebraic form.

  • A 𝑦 + 6
  • B 6 𝑦
  • C 𝑦 βˆ’ 6
  • D 1 6 𝑦
  • E 6 𝑦 + 1