chapter 4 math notes

7/31/2019 Chapter 4 Math Notes

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Chapter 4- (algebra)- Math notes A pronumeral is a letter used in place of a number

BASIC PURPOSE ALGEBRA- Solve mathematical problems involving an

unknown

Patterns and Rules

No. of

flowerbeds

(x)

1 2 3 4 5 6

No. of

sleepers (y)

6 11 16 21 26 31

Rule: y= 5x + 1

If numbers in the first row are consecutive (1,2,3 etc.) look at the 2nd row find the

difference between each number multiply the top number by that number and then

add or subtract whatever is necessary to get to the number at the bottom.

Substitution

When a pronumeral is replaced by a number.

Division shown as fraction

multiplication sign not shown- this means multiplication

2m= 2 x m

Grouping Symbols

Grouping symbols include (parentheses, brackets, braces)

3 (a + 5) equal to 3 x (a + 5)

Grouping symbols first evaluated.

If substituting positive and negative numbers just remember the rules for directed

numbers.

Like terms

terms which have the same pronumeral (example: 2e + 3e= 5e)

Called simplifying an expression. Cannot add or subtract unlike terms. Left as they are. (answer must still be


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written either way)

Multiplying pronumerals

Order doesn't matter

Multiplication sign usually left out

multiple of the same pronumerals will result in powers (example: 3e x 3e= 9e2

Pronumerals usually written alphabetical order (though it does not matter)

Numbers in front of letters. Numbers first.

Dividing pronumerals

Rewrite as a fraction if not already done so

Remember to simplify by cancelling- same pronumerals cancel out.

Expanding expressions with grouping symbols

This is expanding expressions with grouping symbols 3 x (2 + 1) in expansion is 3 x 2 + 3 x 1

Then you evaluate

Factorising

Factorising is the opposite of expanding.

To factorise

1. Find HCF

2. Put that outside- add brackets and then evaluate how to get from there to there

Algebraic fractions

Addition and subtraction same as always except with pronumerals

Multiplication and division same as always except simplifying with pronumerals as

well.

Indices/ index/ power

In multiplication a number of pronumerals of same value multiplied together result in apower.

B2 = B x B

In multiplication when multiplying pronumerals with powers you must add the powers

In division you must subtract the powers

In addition and subtraction you cannot add or subtract pronumerals with different

powers as they are not like terms.


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Raising a power to another power

You can tell if it is suggesting to raise a power to another power if it is in brackets

and there is a power inside and outside the brackets.

To raise a power to another power you must raise everything inside to that power. Ifthere is another power inside that would multiply with the other power to give you

the new power. Then you evaluate.

SUMMARY

A pronumeral is a letter that is used in place of a number

Replacing a pronumeral with a number is called substitution

When dividing pronumerals, the division sign is rarely used. Normally we

rewrite the expression as a fraction and simplify it by cancelling.

When multiplying pronumerals, leave out the x sign. The term 3y means 3 x y. Parentheses are grouping symbols. For example, 3 (x + 4) means 3 x (x + 4) or

3 x X + 3 x 4

When simplifying an expression, terms may be collected only if they are like.

Expanding an expression involves removing grouping symbols.

The distributive law fives the rule for expanding expressions.

Factorising an expression means breaking it down into smaller factors,or

putting grouping symbols back into the expression .

When adding or subtracting algebraic fractions, you first must find the

denominators. When multiplying algebraic fractions, multiply the numerators together and the

denominators together. Try to simplify by cancelling the numerator and

denominator by any common factors.

When dividing algebraic fractions change the division sign to multiplication

sign and write the following fraction as its reciprocal.

chapter 4 math notes

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