Integers · Order of operations · 8.5

Substitute a value.

To evaluate an expression like 4a + 2 at a = −3, substitute the value in parentheses and apply the order of operations: 4 × (−3) + 2 = −10.

01 / THE IDEA

See it work.

Watch the method

Substitute a value

4a + 2 at a = −3: 4 × (−3) + 2 = −10.

1 / 2
4×(−3)+24 \times (-3) + 2
1

Multiply

4 × (-3) = -12

−12+2-12 + 2
2

Add

-12 + 2 = -10

−10-10
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a whole number — negatives allowed, e.g. -7.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Plug in carefully

Replace the letter with the value in parentheses so signs and powers attach correctly, then evaluate.

Why it works

Wrap the value in brackets before you compute.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate 4 × (4) + 2

1

Multiply

4 × 4 = 16 16 + 2

2

Add

16 + 2 = 18 18

EX 2medium

Evaluate 2 × (-4) + -5

1

Multiply

2 × (-4) = -8 -8 + -5

2

Add

-8 + (-5) = -13 -13

EX 3hard

Evaluate (-1) × (-1) - 3

1

Multiply

-1 × (-1) = 1 1 - 3

2

Subtract

1 - 3 = -2 -2

04 / COMMON TRAPS

Where students slip.

Trap

Substituting without parentheses.

Fix

Use brackets so −3 stays attached to its sign.

Trap

Evaluating left to right.

Fix

Multiply before adding.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Evaluate 4 × (4) + 2

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
C2

Evaluate (5) × (-4) - 6

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
C3

Evaluate 5 × (1) + -4

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
C4

Evaluate (-2) × (6) - -5

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
Apply

Apply (4)

A1

Evaluate 2 × (-4) + -5

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
A2

Evaluate 4 × (5) + -6

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
A3

Evaluate (-5) × (2) - -2

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
A4

Evaluate (-6) × (3) - 5

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
Extension

Extension (4)

E1

Evaluate (-1) × (-1) - 3

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
E2

Evaluate 4 × (2) + -2

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
E3

Evaluate (2) × (6) - -5

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.
E4

Evaluate (6) × (2) - -6

Need a hint?
  • Put the value in parentheses.
  • Then apply the order of operations.