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Lesson Worksheet: Addition and Subtraction of Algebraic Expressions Mathematics • 7th Grade

In this worksheet, we will practice adding and subtracting algebraic expressions by adding and subtracting like terms.

Q1:

Simplify (2𝑠+1)+(3𝑠+2).

  • A5𝑠+3
  • B4𝑠+7𝑠+3
  • C6𝑠+3
  • D5𝑠+2
  • E5𝑠3

Q2:

Using the vertical method, subtract the following algebraic expressions: 2𝑥+5𝑦+7,3𝑥2𝑦1.

  • A𝑥+7𝑦+8
  • B𝑥+7𝑦+8
  • C𝑥+3𝑦+6
  • D5𝑥+3𝑦+6
  • E𝑥7𝑦8

Q3:

Find 𝐴𝐵 given 𝐴=8𝑥+2 and 𝐵=5𝑥1.

  • A3𝑥+3
  • B13𝑥+3
  • C3𝑥+1
  • D13𝑥+1
  • E3𝑥+3

Q4:

Subtract 6𝑥3𝑦+3𝑧 from 8𝑥5𝑦2𝑧.

  • A2𝑥+2𝑦+5𝑧
  • B2𝑥8𝑦5𝑧
  • C2𝑥2𝑦+𝑧
  • D2𝑥2𝑦5𝑧

Q5:

Michael had 3𝑥+6 coins and gave 2𝑥+3 coins to James. How many coins does Michael have left?

  • A3𝑥
  • B3𝑥+62𝑥+3
  • C𝑥+3
  • D5𝑥+9
  • E𝑥+6

Q6:

Find the perimeter of the right triangle shown in the diagram.

  • A𝑥4
  • B6𝑥+10
  • C32(𝑥+3)
  • D3𝑥(𝑥+3)

Q7:

Charlotte has 2𝑥+7dollars. She gives 3𝑦2dollars to Benjamin and then receives 𝑥𝑦dollars from Jacob. Write a simplified expression for the remaining amount of money, in dollars, that Charlotte has.

  • A3𝑥+4𝑦+9dollars
  • B3𝑥4𝑦+9dollars
  • C3𝑥4𝑦+9dollars
  • D𝑥4𝑦9dollars
  • E3𝑥+2𝑦+5dollars

Q8:

Consider three rectangles whose areas are represented by the expressions below.

All three rectangles are put together such that none of them overlap. Write an expression to represent the area of the new combined shape.

  • A11𝑥6𝑦𝑧
  • B19𝑥12𝑦𝑧
  • C11𝑥6𝑦𝑧
  • D11𝑥+6𝑦𝑧
  • E11𝑥+6𝑦𝑧

If shape 𝐴 is removed, and instead it sticks to a fourth rectangle, 𝐷, such that the shapes 𝐴 and 𝐷 do not overlap, the combined area of 𝐴 and 𝐷 is 16𝑦𝑧5.

Write an expression to represent the area of rectangle 𝐷.

  • A13𝑥23𝑦𝑧+5
  • B13𝑥23𝑦𝑧5
  • C13𝑥+23𝑦𝑧5
  • D18𝑥+23𝑦𝑧
  • E13𝑥+23𝑦𝑧5

Q9:

If a rectangular prism has a volume of 40𝑥𝑦𝑧, a length of 𝑥, and a width of 10𝑦, find its height.

  • A4𝑥
  • B40𝑧
  • C4𝑦
  • D40𝑦
  • E4𝑧

Find the surface area of the rectangular prism in its simplest form.

  • A20𝑥𝑦+80𝑦𝑧+8𝑥𝑧
  • B20𝑥𝑦+8𝑦𝑧+80𝑥𝑧
  • C8𝑥𝑦20𝑦𝑧+80𝑥𝑧
  • D80𝑥𝑦+20𝑦𝑧8𝑥𝑧
  • E8𝑥𝑦8𝑦𝑧8𝑥𝑧

Q10:

Find the surface area of a rectangular prism with side lengths 𝑥, 11𝑦, and 15𝑧.

  • A30𝑥𝑦+330𝑦𝑧+22𝑥𝑧
  • B330𝑥𝑦22𝑦𝑧+30𝑥𝑧
  • C22𝑥𝑦+30𝑦𝑧+330𝑥𝑧
  • D22𝑥𝑦+330𝑦𝑧+30𝑥𝑧
  • E30𝑥𝑦+22𝑦𝑧330𝑥𝑧

This lesson includes 40 additional questions and 270 additional question variations for subscribers.

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