Expressions & Order of Operations — Challenge

A letter stands for a number you have not been told yet, and the order of operations settles what a written expression means.

What these problems cover

These questions use 1 idea from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

What is the value of 5+3× 2?

  1. 11
  2. 13
  3. 16
  4. 10
  5. 30
Worked answer

11

Multiplication is done before addition, whatever the order on the page.

3× 2 = 6, then 5+6 = 11.

Adding first would give 8× 2 = 16, which is the common error.

Problem 2

Simplify 7x-3x.

  1. 4x
  2. 10x
  3. 4
  4. 21x
  5. 4x2
Worked answer

4x

Both terms are multiples of x, so they can be combined by subtracting the numbers in front.

7-3 = 4, so the answer is 4x.

The x does not disappear, which rules out 4, and it is not squared, which rules out 4x2.

Problem 3

What is the value of 2a+b when a=4 and b=5?

  1. 11
  2. 13
  3. 18
  4. 45
  5. 9
Worked answer

13

Substitute both values: 2· 4+5.

8+5 = 13.

Adding a and b first would give 2· 9 = 18, which is 2(a+b) and a different expression.

Problem 4

Which expression means the product of 6 and n?

  1. 6n
  2. 6+n
  3. n-6
  4. n6
  5. n6
Worked answer

6n

Product means the result of multiplying.

Writing a number next to a letter means multiplication, so the product of 6 and n is 6n.

Problem 5

Simplify 3(x+2).

  1. 3x+6
  2. 3x+2
  3. x+6
  4. 3x
  5. 5x
Worked answer

3x+6

The 3 outside multiplies everything inside the bracket.

3· x = 3x and 3· 2 = 6, giving 3x+6.

Multiplying only the x leaves 3x+2, which is the usual slip.

Problem 6

What is the value of 20÷ 4+1?

  1. 4
  2. 5
  3. 6
  4. 21
  5. 25
Worked answer

6

Division comes before addition.

20÷ 4 = 5, then 5+1 = 6.

Adding first would give 20÷ 5 = 4.

Problem 7

What is the value of 42?

  1. 8
  2. 16
  3. 12
  4. 64
  5. 42
Worked answer

16

The exponent 2 means the base is used twice as a factor.

4× 4 = 16. Doubling would give 8, and 43 would give 64.

Problem 8

Which expression is equivalent to x+x+x?

  1. x3
  2. 3x
  3. x+3
  4. 3
  5. 2x
Worked answer

3x

Three copies of x added together is three lots of x.

That is 3x. Three copies multiplied together would be x3, which is different.

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