Algebraic Notation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Algebra's Shorthand

Mathematics · Algebra · ages 11-12
Name ______________________   Date ____________

  1. Which expression means "the sum of 7 and a number"?

    • 7n
    • 7 + n
    • n - 7
    • 7 / n

  2. Which expression means "8 times a number"?

    • 8n
    • 8 + n
    • n / 8
    • n - 8

  3. What does ab mean?

    • a + b
    • a × b
    • a - b

  4. a² means a × 2.

    Circle one:   True   False

  5. Which expression means "y divided by 4"?

    • y²
    • 4y
    • y/4

  6. In the expression 1/2 x, what does the 1/2 do?

    • It adds one half to x
    • It divides x by one half
    • It does nothing
    • It takes one half of x

  7. Which expression means "4 times the sum of 3 and a number"?

    • 4 × 3 + n
    • 3 + 4n
    • 4(3 + n)
    • 43 + n

  8. The expression 4m is the same as:

    • m × m × m × m
    • 4 + m
    • m + m + m + m
    • m / 4

  9. Ben was asked to write "the product of x and y". He wrote x + y. What is his mistake?

    • He should have written xy
    • He should have written x - y
    • He should have written x/y

  10. In the expression 3(a + 2), if a = 5, what is its value?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Algebra's Shorthand W1-mt_KwdjWEmMNo-s1

  1. 7 + n · The word "sum" means the answer after adding. So the sum of 7 and a number is 7 + n.
  2. 8n · In algebra, "times" means multiply, and we show multiplication by writing the number right next to the letter. So 8 times a number is 8n.
  3. a × b · When two letters sit next to each other with no sign between them, it means multiply.
  4. False · a² means a × a, not a × 2. The small raised 2 tells you to multiply a by itself.
  5. y/4 · Dividing by 4 is written as a fraction: y/4.
  6. It takes one half of x · A fraction can be a coefficient. A number or fraction written next to a letter means multiplication, so 1/2 x means one half of x.
  7. 4(3 + n) · The words "the sum of" group 3 and the number together. Brackets show that the 4 multiplies the whole sum.
  8. m + m + m + m · 4m means 4 times m, which is m added 4 times: m + m + m + m.
  9. He should have written xy · "Product" means multiply, and letters written together mean multiply, so it should be xy, not x + y.
  10. 21 · Work out the bracket first: 5 + 2 = 7. Then multiply by 3: 3 × 7 = 21.
Worksheet · LightMySky