number systems integers positive & negative numbers

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Number Systems Integers Positive & Negative Numbers

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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.

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Page 1: Number Systems Integers Positive & Negative Numbers

Number SystemsIntegers

Positive & Negative Numbers

Page 2: Number Systems Integers 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.

Page 3: Number Systems Integers Positive & Negative Numbers

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.

Page 4: Number Systems Integers Positive & Negative Numbers

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

Page 5: Number Systems Integers Positive & Negative Numbers

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

Page 6: Number Systems Integers Positive & Negative Numbers

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

Page 7: Number Systems Integers Positive & Negative Numbers

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.

+-

Page 8: Number Systems Integers Positive & Negative Numbers

Adding & Subtracting Integers

0 1 2 3 4 5 6-1-2-3-4-5-6

+

-

+3 - 5 = -2

Page 9: Number Systems Integers Positive & Negative Numbers

Adding & Subtracting Integers

0 1 2 3 4 5 6-1-2-3-4-5-6

+

-

+6 - 4 = +2

Page 10: Number Systems Integers Positive & Negative Numbers

Adding & Subtracting Integers

0 1 2 3 4 5 6-1-2-3-4-5-6+

-

+3 - 7 = -4

Page 11: Number Systems Integers Positive & Negative Numbers

Adding & Subtracting Integers

0 1 2 3 4 5 6-1-2-3-4-5-6-

+

-3 + 7 =+4

Page 12: Number Systems Integers Positive & Negative Numbers

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.

Page 13: Number Systems Integers Positive & Negative Numbers

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.

Page 14: Number Systems Integers Positive & Negative Numbers

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.

Page 15: Number Systems Integers Positive & Negative Numbers

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.

Page 16: Number Systems Integers Positive & Negative Numbers

Questions

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