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7 The real numbers
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Stage 4

7.06 Mixed operations with integers

Lesson
Worksheet
Practice
Lesson

Mixed operations with integers

We know how to follow the  order of operations  when evaluating expressions involving more than one operation.

The order of operations is as follows:

  1. Evaluate whatever is contained in brackets.

  2. Evaluate any powers.

  3. Evaluate any multiplication or division, reading from left to right.

  4. Evaluate any addition or subtraction, reading from left to right.

If we have negative integers in our expression, we still follow the exact same rules; we just need to be careful when evaluating the terms involving negatives.

Examples

Example 1

Evaluate 5+9\times(-6).

Worked Solution
Create a strategy

We first need to evaluate the multiplication, and then the addition.

Apply the idea
\displaystyle 5+9\times(-6)\displaystyle =\displaystyle 5+(-54)Evaluate the multiplication
\displaystyle =\displaystyle -49Evaluate

Example 2

Evaluate (7-8)\times(-5).

Worked Solution
Create a strategy

We first need to evaluate the operation in the brackets, and then the multiplication.

Apply the idea
\displaystyle (7-8)\times(-5)\displaystyle =\displaystyle (-1)\times(-5)Evaluate 7-8
\displaystyle =\displaystyle 5Evaluate

Example 3

Evaluate 21\div(-7)\times2.

Worked Solution
Create a strategy

Evaluate the multiplication and division from left to right.

Apply the idea
\displaystyle 21\div(-7)\times2\displaystyle =\displaystyle -3\times2Evaluate 21\div(-7)
\displaystyle =\displaystyle -6Evaluate
Idea summary

The order of operations is as follows:

  1. Evaluate whatever is contained in brackets.

  2. Evaluate any powers.

  3. Evaluate any multiplication or division, reading from left to right.

  4. Evaluate any addition or subtraction, reading from left to right.

Outcomes

MA4-4NA

compares, orders and calculates with integers, applying a range of strategies to aid computation

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