Lesson 1: Integers (I)

Vocabulary on Integers

” Lesson 1: Integers” (Notes)

Word Problems on Integers

I Have to Know by the End of this Lesson

1. Revising concepts

Last year you learnt the essential notions about integers but you probably need some help to remember. Here you are some links on the main concepts

Integers on number lines

Absolute value and opposite integers

Compare and order integers

Integer inequalities with absolute values

 Here you are a funny video “Integers Rap”. Coluld you write a comment giving the translation of the lyrics into Spanish?

2. Operations with integers

ADDITION AND SUBTRACTION

To add up two integers we do the following:

• If both of them have the same sign, we add up their absolute values and we write their sign
• If they have different sign, we subtract their absolute values and we write by the result the sign of the integer that has the bigger absolute value.

Subtracting a number is adding up its opposite. We add up the minuend to the opposite of the subtrahend.

Rule		Example
Two like signs become a positive sign	+(+)	(+3)+(+2) = 3 + 2 = 5
	-(-)	(+6)-(-3) = 6 + 3 = 9
Two unlike signs become a negative sign	+(-)	(+7)+(-2) = 7 – 2 = 5
	-(+)	(+8)-(+2) = 8 – 2 = 6

Here you are a video on subtracting integers

The following  exercises are elemental. Click on the following links if you want to refresh your knowledge:

All addition

All subtraction

Addition and subtraction

 MULTIPLICATION AND DIVISION

To work out the product, or quotient, of two integers:

1^st Multiply, or divide,  their absolute values

2^nd Write + sign if they have like signs or write – sign if they have unlike signs.

Now remember the rule of the signs

When You Multiply …

			Example
×	two positives you get a positive:		(+3 ) · (+2) = +6
×	a positive and a negative you get a negative:		(-3) · (+ 2) = -6
×	a negative and a positive you get a negative:		(+3) · (-2) = -6
×	two negatives you get a positive:		(-3) · (-2) = +6

The same rules are valid for division

			Example
:	two positives you get a positive:		(+12 ) : (+2) = +6
:	a positive and a negative you get a negative:		(-12) : (+ 2) = -6
:	a negative and a positive you get a negative:		(+12) : (-2) = -6
:	two negatives you get a positive:		(-12) : (-2) = +6

Practise multiplication and division on these links

Multiplying signed integers

Dividing signed integers

Practise  these operations with numbers in brackets on the following links:

http://descartes.cnice.mec.es/materiales_didacticos/ing_enteros1/suma.htm   addition

http://descartes.cnice.mec.es/materiales_didacticos/ing_enteros1/resta.htm    subtraction

http://descartes.cnice.mec.es/materiales_didacticos/ing_enteros2/multipli.htm   multiplication

http://descartes.cnice.mec.es/materiales_didacticos/ing_enteros2/division.htm   division