The result of adding numbers is called the sum. The plus sign (+) tells you that you have to add. Numbers can be added in any order, as the sum will be the same no matter which number will be added first. For example, 5 + 3 = 3 + 5. This called the commutative property of addition.
Numbers can also be grouped in any way, and the sum will be the same. This is called the associative property of addition. For example, (2 + 4) + 3 = 2 + (4 + 3). The sum is 9 in both cases.
Additionally, if you were asked to add 245 + 713, then you could do this in two ways. These are called the extended form and the shortened form.
Extended Form Shortened Form
2 hundreds + 4 tens + 5 ones 245
9 hundreds + 5 tens + 8 ones 958
An arithmetic progression is a sequence of numbers which grows at the same rate. For example:
2, 5, 8, 11, 14, 17, 20, 23.........
Each new number in the sequence is 3 more than the previous term.
Work out the next 5 numbers in this sequence.
Answer
26, 29, 32, 35, 38
Perimeter
The perimeter of a shape is the distance all the way around its edge.
Index Cards
Two standard sizes for index cards are are 5cm by 10 cm, and 10cm by 15cm. Find the perimeter of each type of card.
Perimeter (5cm by 10cm) = 5 + 10 + 5 + 10 = 30cm
Perimeter (10cm by 15cm) = 10 + 15 + 10 + 15) = 50cm
See more perimeter problems in the Handouts section below.
The Fibonacci sequence was developed by the Italian mathematician Leonardo of Pisa (Fibonacci). The sequence is generated by add the two previous numbers in the sequence together, starting with 0 and 1. So the sequence goes:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.......
These are the first 13 terms of the sequence.
Work out the next 5 terms.
Answer
233, 377, 610, 987, 1597
Industrial technology
Eight individually powered machines in a small production shop have motors using 560, 275, 975, 445, 569, 664, 183, and 420 watts each. What is the total wattage used when a) The total shop is in operation? b) The three largest motors are running? c) The three smallest motors are running?
Solution
a) 560+275+975+445+569+664+183+420 = 4091 Watts
b) 975+664+569 = 2208 Watts
c) 183+275+420 = 878 Watts
See more Trade Based Problems in the Handouts section below