Worksheet 3.0 (page 1 of 3)
Simplifying integer expressions
Simplifying integer expressions requires the knowledge of integer arithmetic and
order of operation. Here are two examples:
Example 1
Simplify 4 – 7 + 8 – 6
This question can be completed by adding in the appropriate number of positive
and negative units. Please note that –7 is being interpreted as its equivalent
expression + –7, as they both result in the same answer. However, it is possible
to use either interpretation.
Make as many lots of zero units as possible.
Remove the zero units.
Leaves –1.
Therefore 4 – 7 + 8 – 6 = –1.
Example 2
Simplify 3 – 5  2 + 3  –4
Multiplication is calculated before addition and subtraction, therefore 5  2 and
3  –4 are calculated first.
5  2 = 10
3  –4 = –12
CSF Sample Units: Years 8 to 10 Maths – Introducing integers
Worksheet 3.0 (page 2 of 3)
Now the expression can be rewritten as 3 – 10 + –12 (remember, taking out 10
positive units is the same as putting in 10 negative units).
Making and removing lots of zero units:
Leaves –19.
Therefore 3 – 5  2 + 3  –4 = –19.
1
Simplify each of the following expressions using your units.
a) 3 – 5 + 4
b) 7 + –2 – 1
c) –4 + 10 – 7
d) –5 + 3 – 5
e) 10 – 8 + 3 – 2
f) 5 – 4 + 7 – 8
g) –2 + 3 – 4 + 5 – 6 + 7
h) 6 – 10 + 3 – 5 + 4 – 2
CSF Sample Units: Years 8 to 10 Maths – Introducing integers
Worksheet 3.0 (page 3 of 3)
2
3
4
Simplify each of the following expressions.
a) 2 + 3  –5
b) 5 – 2  –6
c) –2  6 + 10
d) –3  –5 – 7
e) 4  –5 – 8
f) 11 – 4  –2
g) 3 + –4  2 – 1
h) 6 – 3  2 + 9
Simplify each of the following expressions.
a) 3  4 – 2  –5
b) –2  4 + 1  –6
c) –5  –2 – 3  8
d) 6  3 – –2  7
e) 7 – –3  10 + 3  2
f) 8 + 4  –5 – 7  –3 + 6
Make up two expressions of your own to be simplified. Share these with
other students in your class for calculation.
CSF Sample Units: Years 8 to 10 Maths – Introducing integers