Probability-A number between 0 and 1 that describes the likelihood that an event will occur. For example, if a bag contains a red marble, a white marble, and a blue marble, then the probability of drawing a red marble is 1/3.
Theoretical Probability- A probability found by analyzing a situation mathematically. If all the outcomes are equally likely, you can first list all the possible outcomes, and then find the ratio of the number of outcomes you are interested in to the total number of outcomes. For example, there are 36 possible equally likely outcomes (number pairs) when two dice are rolled. Of these outcomes, 6 have a sum of 7, so the probability of rolling a sum of seven is 6/36m or 1/6.
Experimental Probability- A probability that is found by experimenting. They are used to predict what might happen over the long run. For example in class we found the experimental probability of a marshmallow landing on its side by tossing the marshmallow and keeping track of the outcomes. The experimental probablilty would be the ratio of the number of times the marshmallow landed on its side to the total number of trials.
Integers
Integers are the counting numbers, their opposites, and zero. Here is a set of integers: ...,-3,-2,-1,0,1,2,3...
The absolute value of a number is its distance from zero on a number line. It can be thought of as the value of a number when its sign is ignored. For example, -3 and 3 both have an absolute value of 3.
Addition- the sum of two positive integers is a positive integer. The sum of two negative integers is a negative integer. The sum of a positive integer and a negative integer will have the sign of the number that has a greater absolute value.
ex. 6 + 4 = 10
- 6 + -4= -10
-6 + 4 = -2
6 + -2 = 4
Subtraction- When we subtract integers, we are really adding the inverse(opposite) of the number that follows the operation sign. So change the operation to addition, and change the second number to its inverse. Then, follow the rules for adding. If a number does not have a sign, it is a positive number.
ex. 15 - 6 = 15 + -6 = 9
-7 - 4 = -7 + -4 = -11
29 - (-7) = 29 + 7 = 36
-12 - (-4) = -12 + 4 = -8
Multiplication- The product of two positve integers is positive. The product of two negative integers is positive. The product of a negative and a positive is negative.
ex. 7 x 8 = 56
-7 x -8 = 56
-7 x 8 = -56
8 x -7 = -56
Division- A positive divided by a positive is positive. A negative divided by a negative is positive. A positive divided by a negative is negative. A negative divided by a positive is negative.
positive/positive=positive
negative/negative=positive
positive/negative=negative
negative/positive=negative
ex. 72/8 = 9
-78/-8 = 9
-72/8 = -9
72/-8 = -9
Measurement
Area- the amount of space enclosed by the sides of a figure. Area is measured in square units
Rectangle- A=L x W Area equals lenght times width
Parallelogram- A= B x H Area equals base times height
Triangle- A= B x H
2
Area equals base times height divided by two
Circle- A= pi x r2 Area equals pi times the radius squared
Perimeter- The measure of the distance around a figure.
Rectangle and Parallelogram- P= S+S+S+S or P= (L+W) x 2
Triangle- P= S+S+S
Circle- C= d x pi Circumference equals diameter times pi
Adding and Subtracting Decimals
When adding and subtracting decimals, line up the decimals points. Move the decimal straight down into the answer. Add or subtract the numbers as you would for whole numbers. Add zeros as place holders when necessary.
Ex. 40.5 + 7.132 + 6=
40.500
7.132
6.000
53.632
Ex. 24.94-3.074=
24.940
- 3.074
21.866
Multiplying Decimals
Multiply decimals as if they were whole numbers. Then count the number of digits to the right of the decimal in each factor. Finally, move the decimal point that many places to the left in the product.
Ex. 245.76 x 4.5=
245.76
x 4.5
122880
983040
1,105.920
Dividing Decimals
If the divisor is not a whole number, move the decimal point to the right(mulitply by a power of 10) to make it a whole number. Move the decimal point in the dividend to the right the same number of places. Then divide as if they were whole numbers. Finally, move the decimal point straight up from its new location into the quotient.
Decimal Place Value
(Use the place value chart and the notes in the vocab. section of your binder)
TENS/ONES/ .TENTHS/HUNDREDTHS/THOUSANDTHS/TEN-THOUSANDTHS/HUNDRED-THOUSANDTHS
54.78632
Fifty-four and seventy-eight thousand,six hundred thirty-two hundred-thousandths
6.004
Six and four thousandths
354.8
Three hundred fifty-four and eight tenths
Homework Help
How many thirds are in 3 1/3?
There are 3/3 in every whole. So three wholes are in 9/3 and 1 more third makes 10/3. There are 10 thirds in 3 1/3.
Comparing Fractions
You can make equivalent fractions to help you compare fractions.
ex. 2 > 1
3 2
2 =4 1 = 3
3 6 2 6
4 is greater than 3
6 6
so, 2 is greater than 1
3 2
Also, your fraction strips are a helpful tool. Use them!
Comparing Fractions and Decimals
To compare fractions and decimals you can change them both to fractions or both to decimals. ex. 3/5 > .3
.3=3/10
3/5 =6/10
Therefore 3/5 is greater than .3
or
3/5=6/10 which is .6
.6 is greater than .3
Use your fraction strips if you need them. Think things through!
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