← ACARA Digital Technologies Years 7–8

Order of operations with brackets

Brackets run first, so a + b is added before dividing by 2. Then * and /, then + and -. Operators on the same level go left to right. Without brackets, only b is divided by 2.

Part of: ACARA Digital Technologies Years 7–8 — Programming with Control Structures and Functions (JavaScript) — Module 18

Understanding Order of operations with brackets in ACARA Digital Technologies Years 7–8

What it does: 3 * 4 is inside the innermost brackets so it runs first (12), then 2 + 12 = 14, then 14 * 5 = 70. b / 2 is worked out first and then a is added, so this is not the average of a and b. Same-level operators go left to right: 20 - 5 is 15, then 15 - 3 is 12. Not 5 - 3 first. Brackets run first, so a + b is worked out before the division by 2 happens.

Common mistakes: Without brackets, only english is divided by 2 because / runs before +. It should be (maths + english) / 2 so the marks are added first. Division happens before addition, so only c is divided by 3. Brackets are needed around a + b + c so the sum is divided: (a + b + c) / 3.

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This module's key terms are also in a printable crossword (Modules 562–580) and word search (Modules 522–580).

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Learning

Duo

What does console.log(2 + 3 * 4) print?

2014

Matches

let avg = math + english / 2;

↓

There are no brackets, so only english is divided by 2 and then math is added. It should be (math + english) / 2.

Applying

Meanings

Term

(a + b) / 2

Meaning

Brackets run first, so a + b is added before dividing by 2. Then * and /, then + and -. Operators on the same level go left to right. Without brackets, only b is divided by 2.

Practice

let a = 80;

Testing

Gaps

let average = (a b) / 2;

Check Answer

Spots

2let english = 90;

3let avg = maths + english / 2;

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Quick Questions

1. What does console.log(2 + 3 * 4) print?

A. 20

B. 14 ✓

* runs before +, so 3 * 4 is 12 first, then 2 + 12 is 14.

2. Which line correctly works out the average of a and b?

A. let avg = (a + b) / 2; ✓

B. let avg = a + b / 2;

Brackets make a + b run first. Without them, only b is divided by 2, then a is added.

3. If a = 6 and b = 10, what does a + b / 2 give?

A. 8

B. 11 ✓

Division runs first: 10 / 2 is 5, then 6 + 5 is 11. The average (8) needs brackets: (a + b) / 2.

4. What does console.log((2 + 3) * 4) print?

A. 20 ✓

B. 14

The brackets run first: 2 + 3 is 5, then 5 * 4 is 20.

5. What does 2 * (3 + (4 - 1)) give?

A. 12 ✓

B. 10

Work from the innermost brackets out: 4 - 1 is 3, then 3 + 3 is 6, then 2 * 6 is 12.

Match the Pairs

let avg = (a + b) / 2; → Adds a and b first because of the brackets, then divides the total by 2 to get the average.

let result = 20 - 6 - 4; → Works left to right because - is on the same level, so it does 20 - 6 = 14 and then 14 - 4 = 10.

Nested brackets: JavaScript works out the innermost brackets first, then works outwards. → let total = (2 + (3 * 4)) * 5;

Without brackets, * and / run before + and -, so only the last number is divided. → let avg = a + b / 2;

let avg = math + english / 2; → There are no brackets, so only english is divided by 2 and then math is added. It should be (math + english) / 2.

let answer = 10 + 2 * 3; // should be 36 → The * runs before the +, so the answer is 16, not 36. It needs brackets: (10 + 2) * 3.

Key Term

(a + b) / 2

Brackets run first, so a + b is added before dividing by 2. Then * and /, then + and -. Operators on the same level go left to right. Without brackets, only b is divided by 2.

Fill in the Blanks

1. let a = 6; let b = 10; let average = (a + b) / 2;

Hint: Type the operator that joins the two values together inside the brackets before the division happens.

2. console.log((4 + 6) / 2); // 5

Hint: Type the operator that divides the bracketed total to give the answer in the comment.

3. let result = 2 * ((3 + 5) - 1); // 14

Hint: Work from the inner brackets outwards. Type the number that makes the result match the comment.

4. let x = 20 / 5 * 2; // 8

Hint: Same-level operators run left to right. Type the operator on the same level as division that gives the comment's answer.

5. let mark = (90 + 72 + 84) / 3; // 82

Hint: Type the number of values being averaged, which is what the bracketed total is divided by.

Spot the Error

Question 1

A let maths = 80;

B let english = 90;

C let avg = maths + english / 2;

D console.log(avg);

Line C — Without brackets, only english is divided by 2 because / runs before +. It should be (maths + english) / 2 so the marks are added first.

Question 2

A let a = 6;

B let b = 9, c = 12;

C let avg = a + b + c / 3;

D console.log(avg);

Line C — Division happens before addition, so only c is divided by 3. Brackets are needed around a + b + c so the sum is divided: (a + b + c) / 3.

Question 3

A let c = 20;

B let f = c * 9 / (5 + 32);

C console.log(f);

Line B — The brackets make JavaScript add 5 + 32 first, then divide by 37. The formula needs c * 9 / 5 + 32, with no brackets, so the multiply and divide run before the add.

Question 4

A let price = 12;

B let total = price + 3 * 4;

C console.log(total);

Line B — Without brackets, 3 * 4 is worked out first, giving 24 instead of 60. Brackets are needed so price + 3 is added before multiplying: (price + 3) * 4.

Question 5

A let x = (2 + (3 * 4) * 2;

B console.log(x);

C console.log(x - 10);

Line A — The brackets are not paired. The outer opening bracket is never closed. It should be (2 + (3 * 4)) * 2, so the inner brackets run first, then the outer ones.

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