number systems integers positive & negative numbers
DESCRIPTION
Integers Integers are positive and negative whole numbers, including zero. … -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, … Can you think of situations where negative numbers are used? Banking & FinanceTemperature GolfLifts We define the set of integers using; Z was first used by a group of European mathematicians trying to organise numbers into groups. Zahlen is German for zero.TRANSCRIPT
Number SystemsIntegers
Positive & Negative Numbers
History of Integers The Babylonians were the first civilization to come up with the concept of
zero, to signify that something was missing
The idea of negative numbers and zero in mathematics can be traced back to India about 620 BCE and a man named Brahmagupta. He used them to calculate the debts and fortunes of the nobility We still use the rules he created today.
This idea spread into Arabia in the 10th Century and from there eventually made its way into European mathematics in the 15th century.
Integers
Integers are positive and negative whole numbers, including zero.
… -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, … Can you think of situations where negative numbers are
used? Banking & Finance Temperature Golf Lifts
We define the set of integers using;Z was first used by a group of European mathematicians trying to organise numbers
into groups. Zahlen is German for zero.
Positive Numbers Positive number
A number greater than zero. 0 1 2 3 4 5 6
If there is no sign written in front of a number then you can assume it is positive.• So 1 = +1 2 = + 2 e.t.c
Negative Numbers Negative number
A number less than zero The sign to the left of the number tells you if it is positive or
negative.
0 1 2 3 4 5 6-1-2-3-4-5-6
Opposite Numbers or Zero Pairs Opposite Numbers
Numbers that are the same distance from zero in the opposite direction
0 1 2 3 4 5 6-1-2-3-4-5-6
and
One Way to Add Integers Is With a Number Line
0 1 2 3 4 5 6-1-2-3-4-5-6
• When the number is positive, count to the right.
• When the number is negative, count to the left.
+-
Adding & Subtracting Integers
0 1 2 3 4 5 6-1-2-3-4-5-6
+
-
+3 - 5 = -2
Adding & Subtracting Integers
0 1 2 3 4 5 6-1-2-3-4-5-6
+
-
+6 - 4 = +2
Adding & Subtracting Integers
0 1 2 3 4 5 6-1-2-3-4-5-6+
-
+3 - 7 = -4
Adding & Subtracting Integers
0 1 2 3 4 5 6-1-2-3-4-5-6-
+
-3 + 7 =+4
Multiplying Integers What we know already
or that a positive number multiplied by a positive number = a positive number
What about
Well you could think about this as
So we can say that a negative number multiplied by a positive number = a negative number.
The Double Negative RuleI didn’t not eat a massive amount of chocolate on
Halloween Night!What happens in English when we have two negatives
together in a sentence? The sentence becomes positive
The same thing happens in maths, for example
So we can say that a negative number multiplied by a negative number = a positive number.
Multiplying Integers
What we know already(zero pairs)
So what about well if we consider thisand use the distributive rule
Written out fully this becomes
(Rule on previous slide)
So we can say that a negative number multiplied by a negative number = a positive number.
Dividing IntegersThe same rules we have for multiplication applies for division.
A positive number divided by a positive number = a positive number. A negative number divided by a positive number = a negative number. A negative number divided by a negative number = a positive number.
Questions
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