Algebra: Chapter 3-1 and 3-2, pages 114 and 119.
The Addition and Multiplication Properties of Equality (I call these 1 STEP EQUATIONS)
You can add, subtract, multiply or divide the same number to both sides of an equation and get an equivalent equation. We call these the addition and multiplication property of equality.
If `a=b`, then `a+c=b+c` and if `a=b`, then `ac=bc`
Subtraction and division are opposites of addition and multiplication, so we have no problems there. There are lots of examples at my favorite site, Purplemath, give these a look! Remember to show ALL the STEPS and that you can do these either vertically or horizontally. DON’T TAKE SHORTCUTS!
Examples:
(Addition)
`-6 = y-8`, we add 8, the opposite of -8
`-6+8=y-8+8`, we use the addition property to add 8 to both sides of the equation and finally,
`2=y`
(and Multiplication)
`y/9=14`, we will multiply both sides by `9/1` or just `9`
`9* (y/9)=9*14`, remembering that `9/9 =1`, we have
`y=126`
Whatever you do to an equation, do the S A M E thing to B O T H sides of that equation! If its `x+7`, then subtract 7 from both sides. If its `x-6`, then add 6 to both sides. If its `5x`, then divide both sides by `5` and if its `x/3`, then multiply both sides by `3`! Always do the opposite operation in these 1 step equations.
Two of tonight’s homework problems (lesson 1) solved by MrE are here! Just click it!
Two of tonight’s homework problems (lesson 2) solved by MrE are here! Just click it!
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Algebra 1a: Chapter 2, Lesson 1, page 54.
Integers and Rational Numbers
Integers consist of the whole numbers and their opposites. On the number line, the positive integers are to the right of `0` and the negative integers are to the left of `0`. Zero is neither positive or negative.
A mathematical sentence that contains an inequality symbol is called an inequality.
The symbol `>` means greater than.
The symbol `<` means less than.
On the number line, numbers increase as we move from left to right.
The absolute value of a number is its distance from `0` on the number line. We use the symbol `|n|` to represent “the absolute value of n”.
Algebra 1a: Chapter 2, Lesson 2, page 59.
Rational Numbers
“Any number that can be expressed as the ratio of two integers, `a/b`, is called a rational number.
There is a point on the number line for every rational number. The number is called the coordinate of the point and the point is the graph of the number. When we draw a point for a number on a number line, we say that we have graphed the number.“