Basic Calculation Skills

ADDITION EXAMPLES

735 + 280 = 1015         827 + 564 = 1391         800 + 500 = 1300     20 + 60 = 80     7 + 4 = 11   1391

Add in columns

Add numbers matching place values in columns. If the answer to any column is 10 or bigger, carry the 10s to the next column.

    7 2   Units: 3 + 1 + 2 = 6   2 5 1   Tens: 6 + 5 + 7 = 18 (8 carry 1) + ¹4 6 3   Hundreds: 4 + 1 + 2 = 7   7 8 6    

Subtract in columns

Here are two methods for subtracting numbers using place-value columns.

DECOMPOSITION (TRADING)

Trade 10 from the next place value.

  9 ^{6 1}5 – 6  4  8   3  2  7

72 ÷ 4     OR          OR    

Remainders

Remainders can be written in different ways.

Imagine sharing 7 cupcakes between 2 people.

Each person would receive three cakes with one leftover.

 7 ÷ 2 = 3 r 1 Or each person gets three and a half cakes.

7 ÷ 2 = 3 or 3.5

You can change the order when multiplying and dividing.

Sometimes rearranging the problem can make working easier.

24 × 37 ÷ 8 = 24 ÷ 8 × 37   = 3 × 37   = 117

Integers are numbers which are not a fraction.

Rules

Below is a summary of the meaning of pairs of signs.

Two like signs become +
– (–9) = + 9
+ (+9) = + 9

Two different signs become –
+ (–9) = – 9
– (+9) = – 9

EXAMPLE

Evaluate these three calculations.

20 + (–7)
20 – (–7)
20 – (+7)

SOLUTION

20 + (–7) = 20 – 7   = 13 20 – (–7) = 20 + 7   = 27 20 – (+7) = 20 – 7   = 13

Opposite numbers have the same size but are on opposite sides of zero. 

So 3 and –3 are opposites.

The sum of a number and its opposite is always zero.

Since –3 and +3 are opposites:
+3 + (–3) = 0
–3 + (+3) = 0

Rules for multiplying or dividing

Two LIKE signs give a positive answer:
( + ) × ( + ) = ( + )
( − ) × ( − ) = ( + )
( + ) ÷ ( + ) = ( + )
( − ) ÷ ( − ) = ( + ) Two DIFFERENT signs give a negative answer:
( + ) × ( − ) = ( − )
( − ) × ( + ) = ( − )
( + ) ÷ ( − ) = ( − )
( − ) ÷ ( + ) = ( − )

Examples

−12 × −2 = 24

9 × −7 = −63

−6 ÷ −2 = 3

−44 ÷ 11 = −4

Note: Positive numbers are written without their + sign.

Powers are a special form of expressing multiplication.

(–3)² = –3 × –3 = 9

(–2)³ = –2 × –2 × –2 = –8

B I D M A S

Brackets, Indices, Divison, Multiplication, Addition, Subtraction

The four operations are related to each other. Operations are inverses of each other if one undoes the effect of the other. 

• Adding is the inverse of subtracting.
• Multiplying is the inverse of dividing.
• Taking a square root is the inverse of squaring a number.
• Taking the cube root is the inverse of cubing a number.

You can use inverse operations to check answers to calculations.

When a calculation involves more than one operation, you have to reverse the order of the inverse operations to check the answer. 

Fraction lines also act as grouping symbols. The line shows the numerator as one group and the denominator as another.

EXAMPLE

Evaluate .

SOLUTION

= =1   The fraction bar works like grouping symbols: calculate the top and bottom separately, and then divide.

Square root signs are similar to brackets. Do any calculations within square root signs before taking the square root.

EXAMPLE

Find .

SOLUTION

Do the subtraction within the square root sign first.

 =  = 6

Note:  ≠  –    ( –  = 10 – 8 = 2)