Order of Operations With Integers-BIDMAS Worksheets (with ... - Free Printable

Let's solve each of the problems on the worksheet using the BIDMAS rule (Brackets, Indices, Division/Multiplication, Addition/Subtraction), which is the order of operations. We'll go step by step for each problem.

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e) $ 6 \times 3 - (-2)^3 $

Step 1: Evaluate the exponent:
$ (-2)^3 = (-2) \times (-2) \times (-2) = -8 $

Step 2: Multiply:
$ 6 \times 3 = 18 $

Step 3: Subtract:
$ 18 - (-8) = 18 + 8 = 26 $

✔ Answer: 26

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g) $ 1 + (-9)^2 - 10 $

Step 1: Evaluate the exponent:
$ (-9)^2 = (-9) \times (-9) = 81 $

Step 2: Add and subtract from left to right:
$ 1 + 81 = 82 $
$ 82 - 10 = 72 $

✔ Answer: 72

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i) $ 5 \times (-2 \times 5)^2 $

Step 1: Evaluate inside the brackets first:
$ -2 \times 5 = -10 $

Step 2: Square it:
$ (-10)^2 = 100 $

Step 3: Multiply:
$ 5 \times 100 = 500 $

✔ Answer: 500

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k) $ -4^2 - 5 \times (-2) $

⚠️ Important Note: The expression is $ -4^2 $, not $ (-4)^2 $.
In standard order of operations, exponentiation comes before the negative sign unless parentheses are used.

So:
- $ 4^2 = 16 $
- Then apply the negative: $ -4^2 = -16 $

Now:
Step 1: $ -4^2 = -16 $
Step 2: $ 5 \times (-2) = -10 $
Step 3: $ -16 - (-10) = -16 + 10 = -6 $

✔ Answer: -6

> 🚨 If it were $ (-4)^2 $, that would be $ +16 $, but here it's not in parentheses, so it's $ -16 $.

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i) $ \frac{-40 + 3 \times (3 + 7)}{5 \times (2^1 - 1^2)} $

Let’s break this down carefully.

#### Numerator: $ -40 + 3 \times (3 + 7) $
- Brackets: $ 3 + 7 = 10 $
- Multiplication: $ 3 \times 10 = 30 $
- Addition: $ -40 + 30 = -10 $

#### Denominator: $ 5 \times (2^1 - 1^2) $
- Exponents: $ 2^1 = 2 $, $ 1^2 = 1 $
- Brackets: $ 2 - 1 = 1 $
- Multiply: $ 5 \times 1 = 5 $

Now divide:
$ \frac{-10}{5} = -2 $

✔ Answer: -2

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k) $ \frac{3 - 3 \times (2 - 7)^2}{2^0 + 4^1 + 3^1} $

Wait — there’s a typo in labeling. This is labeled k), but we already had a k) above. But let’s proceed.

#### Numerator: $ 3 - 3 \times (2 - 7)^2 $
- Brackets: $ 2 - 7 = -5 $
- Exponent: $ (-5)^2 = 25 $
- Multiply: $ 3 \times 25 = 75 $
- Subtract: $ 3 - 75 = -72 $

#### Denominator: $ 2^0 + 4^1 + 3^1 $
- $ 2^0 = 1 $
- $ 4^1 = 4 $
- $ 3^1 = 3 $
- Sum: $ 1 + 4 + 3 = 8 $

Now divide:
$ \frac{-72}{8} = -9 $

✔ Answer: -9

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m) $ \frac{2^7 \div 8^2 + 2^2 \times 4 + 8^0}{28 \div 7 + 5^2 - 5^1 - (12 - 7)^2} $

This one is complex. Let's do numerator and denominator separately.

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#### Numerator: $ 2^7 \div 8^2 + 2^2 \times 4 + 8^0 $

First, evaluate all powers:

- $ 2^7 = 128 $
- $ 8^2 = 64 $
- $ 2^2 = 4 $
- $ 8^0 = 1 $

Now substitute:
$ 128 \div 64 + 4 \times 4 + 1 $

Now do division and multiplication:
- $ 128 \div 64 = 2 $
- $ 4 \times 4 = 16 $

Now add:
$ 2 + 16 + 1 = 19 $

✔ Numerator = 19

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#### Denominator: $ 28 \div 7 + 5^2 - 5^1 - (12 - 7)^2 $

Evaluate step by step:

- $ 28 \div 7 = 4 $
- $ 5^2 = 25 $
- $ 5^1 = 5 $
- $ (12 - 7)^2 = 5^2 = 25 $

Now substitute:
$ 4 + 25 - 5 - 25 $

Do left to right:
- $ 4 + 25 = 29 $
- $ 29 - 5 = 24 $
- $ 24 - 25 = -1 $

✔ Denominator = -1

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Now divide:
$ \frac{19}{-1} = -19 $

✔ Answer: -19

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| e) | 26 |
| g) | 72 |
| i) | 500 |
| k) | -6 |
| i) | -2 |
| k) | -9 |
| m) | -19 |

> ⚠️ Note: There seems to be a duplication of labels (two "k"s). Based on context, the second k) refers to the fraction with $ (2 - 7)^2 $, and m) is the last one.

Let me know if you'd like these formatted as a clean worksheet or explained further!