Friday, January 29, 2010
Gator Math
"An inequality is similar to an equation. There are two expressions separated by a symbol that indicates how one expression is related to the other. In an equation such as 7x = 49, the = sign indicates that the expressions are equivalent. In an inequality, such as 7x > 49, the > sign indicates that the left side is larger than the right side.
To solve the inequality 7x > 49, we follow the same rules that we did for equations. In this case, divide both sides by 7 so that x > 7. This means that x is a value and it is always larger than 7, and never equal to or less than 7.
The "less than" symbol (<) may also be seen in inequalities. " To remember this, we have the "Alligator rule". The alligator wants to eat the bigger number, therefore his mouth is open to the 10 and not the 5: 5 10
If the number on the left were smaller, the alligator head would face the other way, as in this picture.
3 2
Another symbol is the "not equal" sign , when you see this symbol you know that either it is greater than (>) or less than (<) but it is not equal. For instance if you were to have a b, so it would have to be either a (<) b or a (>) b.
Square Roots
You may see a pattern. The number on the left side of the = sign, mulitplied by itself, gives us the number under the square root sign.
The Power of 2!!
2^1:
Fractions and their Functions
Subtracting fractions
Mulitplying fractions
Monday, January 25, 2010
Manuel's Apples
This problem can be solved using what we call "Algebra". "Algebra is a branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set."
To better understand this concept, let us explore the previous story problem.
Step 1: To solve this problem, we could say that because Manuel gets 1 apple for every day we must figure out how many apples he has after 3 weeks. There are 7 days in one week, so for three weeks we could use the equation 7days=1week, so for 3 weeks, it would be 7 times 3. This can be written algebraically as: 7days=1week, ____days=3w, so 7*3=21, therefore 21 days=3weeks.
Step 2: Because he gets 1 green apple each day, 1green apple=1day, therefore 21greenapples=21days.
21days=
Step 3: Manuel gets one red apple every three days. Over the 21 day period, he will get one red apple every three days. This can be written algebraically as: 21days=3r. We use the variable "r" to represent the red apples.
21 days=3r or 21days=Step 4: By using this equation, we can divide: 21days/3r=7. Therefore, after 21 days, Manuel will have 7 red apples.
21 days=
Now we can safely say that after 3 weeks, Manuel will have 21 green apples and 7 red apples.
3 weeks=