# Basic Calculation Skills

- Created by: Lucia_Sophia
- Created on: 22-11-19 10:44

## Addition Strategies

##### 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**) + ** ^{1}**4 6 3 Hundreds: 4 +

**1**+ 2 = 7 7

**8**6

## Subtraction Strategies

## 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

## Multiplication Strategies

## Division Strategies

72 ÷ 4 OR OR

## Remainders

## 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

## Mixed Multiplication and Division

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

## Adding and Subtracting Integers

*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

*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

## Multiplying and Dividing Integers

## 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 and Directed Numbers

*Powers are a special form of expressing multiplication.*

(–3)^{2} = –3 × –3 = 9

(–2)^{3} = –2 × –2 × –2 = –8

## Order Of Operations

**B I D M A S**

**B**rackets, **I**ndices, **D**ivison, **M**ultiplication, **A**ddition, **S**ubtraction

## Inverse Operations

*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

*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.

## Operations With Square Roots

*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)

## Comments

No comments have yet been made