Download Chapter 2 – Operations on Decimal Numbers

Chapter 2 – Operations on Decimal Numbers
Sum – the answer to an addition question.
Difference – the answer to a subtraction question.
Product – the answer to a multiplication question.
Quotient – the answer to a division question.
When solving problems it is very useful to estimate mentally first so you have an idea what your
answer should be close to.
Ex: 26 + 12
This is close to 30 + 10 = 40. The answer should be close to 40.
Ex: 98.75 – 33.5
This is close to 100 – 30 = 70. The answer should be around 70.
Ex: 45.7 x 12.8
This is close to 50 x 10 =500. The answer should be around 500
Ex: 278.4 ÷ 8.3
This is close to 270 ÷ 9 = 30. The answer should be around 30.
Graphics in this chapter’s notes came from http://www.coolmath.com/
2.1 - Adding and Subtracting Decimal Numbers
•
Always line numbers up according to place value. If this is done, the decimal will also
line up. Place 0’s on either right or left so that there are the same number of digits
stacked.
Practice
12.6 + 7.8
2.56 + 16.88
19.4 – 6.3
47.3 – 8.14
Graphics in this chapter’s notes came from http://www.coolmath.com/
2.2 – Multiplying Decimal Numbers
When multiplying decimal numbers you can ignore the decimals until the end. You DO NOT
need to line up the numbers according to place value.
In the following example you will:
•
•
•
•
First multiply the 8 by 5, then 3, then 2.
In the next row place a zero down first then multiply the 7 by 5, then 3, then 2.
Then you will add the two numbers.
The last part is placing the decimal in the correct place.
0
Practice
24.5 x 1.6
35.6 x 8.23
Graphics in this chapter’s notes came from http://www.coolmath.com/
2.3 – Dividing Numbers with Decimals
The best way to learn long division is by doing it. Here is an example, then all you need to do is
practice!
Moving the decimal when the divisor has a decimal:
Graphics in this chapter’s notes came from http://www.coolmath.com/
When and where to place the ‘0’
Add/Subtract:
You MUST line up the decimals. If the numbers do not have the same number of digits when
you stack them, then you can place a ‘0’ on either the right or left side of the existing number
Example
Question
45.3 + 5.29
Step 1 – Stack numbers and
line up the decimals
45.3
+ 5.29
0 added in on the left
Step 2 – add the 0’s to either the left or
right of existing numbers
45.30
+ 05.29
0 added in on the right
Placing the 0’s in the question keeps the
numbers stacked properly and DOES
NOT CHANGE THE NUMBER
Multiplication:
There is no need to place an additional 0 in the question. However, 0’s need to be added in to the
answer when multiplying with 2 and 3 digit numbers.
Example:
Question
4.53 x 5.2
Step 1 – Stack numbers.
Do not line up the
decimals.
4.53
x 5.2
906
+ 22650
23556
Step 2 – Add decimal into answer
4.53 (2 numbers after decimal) plus
x 5.2 (1 number after decimal)
906
+ 22650
23.556 (place decimal 3 spots to the left)
0 placed in second
answer row
Division:
There is no need to place an additional 0 in the question. However, you must keep adding 0’s to
the dividend when the answer after subtraction is not zero.
Graphics in this chapter’s notes came from http://www.coolmath.com/
Chapter 2.4 – Order of Operations
When solving multi step problems, there is a specific order that must be followed to find the
correct answer.
B – brackets – Whatever is within a bracket (also called ‘parentheses’) is solved before anything
else.
E – exponents – Numbers that have exponents with them will always be solved second.
Exponents look like this: 32, 105, 83.
32 = 3x3 = 9
43 = 4x4x4 = 64
D/M – division/multiplication – Next we solve either division or multiplication questions
working from the left to the right, whichever comes first.
A/S – addition /subtraction – Lastly we solve either addition or subtraction questions working
from the left to the right, whichever comes first.
•
To remember this order people often refer to these steps as BEDMAS (or PEDMAS if
you like P for parentheses better than B for brackets).
4 + 3 x (6 – 2)
(5 + 3 x 2) – 6 ÷ 2
4+3x4
(5 + 6) – 6 ÷ 2
4 + 12
11 – 6 ÷ 2
16
11 – 3
8
Practice
(14 - 2 ) + 20 ÷ 5
10 x 3 x ( 10 + 5 )
(10 + 3 ) + 8 ÷ 4
2 x 13 x ( 3 - 8 )
Graphics in this chapter’s notes came from http://www.coolmath.com/