Integers · Order of operations · 8.6

Two variables.

With two or more letters, substitute each value in parentheses, then evaluate. For ab − c at a = −2, b = 4, c = 3: (−2)(4) − 3 = −11.

01 / THE IDEA

See it work.

Watch the method

Two variables

ab − c at a = −2, b = 4, c = 3: (−2)(4) − 3 = −11.

1 / 2
−2×4−3-2 \times 4 - 3
1

Multiply

-2 × 4 = -8

−8−3-8 - 3
2

Subtract

-8 - 3 = -11

−11-11
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.

All the values at once

Replace each variable with its value in parentheses, then work through the order of operations.

Why it works

Drop each number into its slot, then compute.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate 5 × (5) + 1

1

Multiply

5 × 5 = 25 25 + 1

2

Add

25 + 1 = 26 26

EX 2medium

Evaluate 4 × (3) + -3

1

Multiply

4 × 3 = 12 12 + -3

2

Add

12 + (-3) = 9 9

EX 3hard

Evaluate 3 × (5) + -6

1

Multiply

3 × 5 = 15 15 + -6

2

Add

15 + (-6) = 9 9

04 / COMMON TRAPS

Where students slip.

Trap

Mismatching values and letters.

Fix

Substitute each letter with its own value.

Trap

Skipping the parentheses.

Fix

Brackets keep the signs attached.

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 5 × (5) + 1

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
C2

Evaluate 3 × (-3) + -2

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
C3

Evaluate (-3) × (6) - 4

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
C4

Evaluate (4) × (-5) - 2

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
Apply

Apply (4)

A1

Evaluate 4 × (3) + -3

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
A2

Evaluate 4 × (-2) + -2

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
A3

Evaluate (1) × (1) - 1

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
A4

Evaluate (2) × (-4) - 4

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
Extension

Extension (4)

E1

Evaluate 3 × (5) + -6

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
E2

Evaluate (1) × (-5) - -3

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
E3

Evaluate 2 × (-5) + -1

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.
E4

Evaluate 3 × (6) + -2

Need a hint?
  • Substitute each value in brackets.
  • Then evaluate by precedence.