Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Positional notation wikipedia, lookup

Location arithmetic wikipedia, lookup

Elementary mathematics wikipedia, lookup

Approximations of π wikipedia, lookup

Arithmetic wikipedia, lookup

Transcript
```7th grade STAAR Review Skills to remember
Fractions, Decimals, and Percents
3

Fraction to decimal:


Decimal to percent: .875 = 87.5% move the decimal two places to the right
Percent to decimal: 67% = .67 move the decimal two places to the left. The
decimal is at the end of a number if it is not there.
25 1
Decimal to fraction: .25 =
=
put the number over a 10, 100 or 1,000
100 4
depending on the place value of the last digit. Reduce

10
= .3
Divide (top dog in the house)
Ordering Fractions, Decimals, and Percents
Put the following numbers in order from least to greatest: Try it before you look at
 .3, 87.5%, .67, - ¼
Steps: Change them all to fractions, decimals, or percent’s. Decimals and percent’s
are the easiest.
.3 = 30%
.67 = 67%
-¼ = - .25= - 25%
87.5% stays the same
Negatives come first because they are the smallest numbers.
Decimals (adding, subtracting, multiplication, and division)
1. Line up decimal points (add zero’s if needed)
3. Bring decimal down
4.5
+8.9
13.4
8.9
- 4.5
4.4
Multiplication of decimals
1. Longer number on top.
2. Multiply as if the decimal isn’t there.
3. The number of digits behind the decimal in the problem, is how many should be in
Ex.
2.1
X .6
1.26
Move the decimal twice from the right. Your answer should have two digits behind
the decimal because there are 2 digits behind the decimals in the problem.
Division of decimals
1. If there is a decimal on the outside of the , move it so that it is behind the
number, then move it that many times in the inside also
2. Bring the decimal inside the house to the top.
3. Long divide as normal.
Ex. 28.4 ÷ 2 = 14.2
Ex. 18.4 ÷ 2.4 = 7.66666
Try them and see if you get the same answers!
Fractions (adding, subtracting, multiplying, and dividing)
1. Need a common denominator
2. Add or subtract the numerators only
1
2
7
9
8
3
1
9
7
9
2
18
Ex. + =
Ex. - =
Try them and see if you get the same answers!
Multiplying
1. Multiply straight across the top and bottom
2. Reduce
1
2
2
9
3
27
Ex. . X =
Division
1. Keep, change, flip
2. Keep the first number, change division to multiplication, flip the second fraction
3. Multiply straight across and reduce
Ex.
1
9
÷
2
3
=
1
9
X
3
2
=
3
18
Integers – Remember the song!!
Different signs subtract
Keep the sign of the higher number
Then it will be exact
Ex. - 8 + - 8 = -16 (same signs)
Ex. 18 + - 5 = 13 ( different signs)
Subtraction
Change the minus to a plus
Change the sign of the next
Then all you do is add them up
As if it were a plus
Ex. 18 – (-5) = 18 + 5= 23 (same signs, add)
Ex. - 6 –(3) = -6 + - 3 = - 9 ( same signs, add)
Ex. 7 – 8 = 7+ -8 = -1 (different signs, subtract)
Multiplication/division
Same signs, always positive
Different signs, negative
Ex. 18/-2 = -9
Ex. -18/-2 = 9
Ex 2 X -3 = -6
Ex. -2 X -3 = 6
Solving for X
1. X + 3 = 7
-3 -3
X=4
4.
𝑋
= 10
5
X = 50
2. X - 9 = 62
+9 + 9
X = 71
3.
2x= 10
Divide by 2
X=5
(multiply each side by 5 )
You are trying to get the variable by itself by doing the opposite operation.
2x + 9 = 21
Subtract 9 from both sides and then divide by 2. Always perform subtraction and addition
first. Then multiply and divide to solve for X.
2x + 9 = 21
-9
-9
2x = 12
2
2
X= 6
Unit Rate- The price per one item
If three loaves of bread cost \$7.71, what is the cost of two loaves of bread?
First, find the cost of 1 loaf of bread by dividing the cost (\$7.71) by how much you have.
This will give you the price of one (2.57). Once you know the price of one, you can multiply
by two and figure out the price for two loaves of bread. Two loaves would cost \$5.14.
You can also set up a proportion like this:
3 𝑙𝑜𝑎𝑣𝑒𝑠
\$7.71
=
2 𝑙𝑜𝑎𝑣𝑒𝑠
\$𝑋
Cross multiply and divide by the last number to solve for X.
Exponents:
42 = 4 X 4 which is 16
2³ = 2 X 2 X 2 which is 8
Square roots
√25 = 5 because 5 X 5 equals 25.
√32 = 5.7 because it is going to be in between 5 and 6.
√25 = 5
Order of Operations
Parenthesis
Exponents
Multiplication
Division
Subtraction
Geometry
Translations= slide
√36 = 6
Reflection = flip (normally across the x or y axis)
Dilation= to make larger or smaller
Finding Scale Factor: New
Old
Using Scale Factor: Multiply the sides by the scale factor
Scale factor= how many times bigger or smaller a shape is in comparison to another.
3
7.5
4
The scale factor going from the smaller triangle to the larger triangle is 2.5. If you multiply
the sides of the smaller triangle by 2.5, you will get the lengths of the larger triangle. Try it!
Finding missing sides with similar figures:
5
15
7
X
Set up a proportion and solve for X.
5
=
7
15
𝑥
X = 21
OR
Figure out the scale factor and multiply to find the missing side.
Scale factor is 3 because if you multiply the sides of the smaller trapezoid by 3, then you get
the lengths of the larger trapezoid.
Probability
Theoretical probability –
favorable outcomes
Possible outcomes
Experimental probability -
number of times event occurs
Number of trials
Independent probability- the outcome doesn’t affect one another, you replace the items
1. Probability of rolling a 2 on a dice, and spinning a red on a spinner that has 4
sections (red, blue, green and yellow)
1 1
1
1
1
X =
dice
spinner
6 4
24
6
4
2. Probability that you will pull out a yellow and then a blue marble if there are
5 blue and 3 yellow. You replace after each draw
3
8
5
15
3
8
64
8
X =
yellow
5
blue
8
Dependent probability – the outcome does affect the other, you DO NOT replace the items in
the bag
1. Probability that you will pull out a yellow and then a blue if there are 5 blue and
3 yellow. You do not replace the marble after each draw.
3
8
5
15
3
5
7
56
8
7
X =
yellow
blue
Percent proportions
Part
Whole
=
𝑋
100%
Cross multiply and divide by the last number to solve!
Ex. A government agency has a car pool of 120 vehicles. Every week about 15% of the
vehicles are pulled out of service for repair and inspection. How many vehicles per week is
this? Try it! The answer is 18.
Ex. The department of transportation inspected 200 rural bridges last year. Of that amount,
6 were determined to be unsafe. What percent of bridges were considered safe? The
Percent of change
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑛𝑑 𝑛𝑒𝑤
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙
𝑋
= 100%
Cross multiply and divide by the last number to solve!
Ex. A picture originally priced at 300 sold for 400. The answer is 33.3333% Try and solve it
yourself!
Proportional Relationships.
Let, n, represent the position of a number in
the following arithmetic sequence.
4, 9, 14, 19, 24...
Which expression can be used to find any
term in the sequence?
A n2
B 5n - 1
C 4n + 9
D 9n + 4
N is the position of the number in the sequence. So 1st position, 2nd position and so on.
When you are deciding which rule goes with the sequence of numbers, you need to plug in
1, 2, 3, and so on into the letter N. The answer is B.
Measurement
Perimeter- Add all the sides to find the perimeter! This will not be on the formula chart.
Rectangle is on the formula chart…
Circumference - is the perimeter of a circle. Formula - 2 𝜋 𝑟 𝑜𝑟 𝑑 𝜋
Area- the space inside of a 2-D shape measured in square feet) The formulas are on your
math chart. Remember on the area of a circle (𝐴 = 𝜋𝑟 2 ), you must square the radius
first!!!!!! Square means to multiply the number by itself for example
Radius- is from the middle of the circle to any point on the outside
Diameter- a straight line passing through the center of the circle.
Area of a triangle A= (1/2)bh **(1/2) means to divide by 2
Volume



Volume- the space inside of a 3-D object.
REMEMBER: B MEANS AREA OF THE BASE
Prism/pyramid- Pyramid comes to one point, prism does not.
Also, remember :(1/3) MEANS TO DIVIDE BY 3 AND (4/3) MEANS TO multiply
BY 4 AND DIVIDE BY 3.
Prism
Pyramid:
Measures of Central Tendency and Variablility




Mean: the average. Add up all the numbers and divide by how many there
are.
Median: the middle number. Put the numbers in order and cross them off
until you get to the middle. If there are two, add them up and divide by two.
Mode: most often
Range- subtract the highest from the lowest (Measure of Variablility)
TYPES OF GRAPHS
STEM AND LEAF
LINE PLOT
BAR GRAPH
LINE GRAPH
CIRCLE OR PIE GRAPH – GREAT FOR SHOWING PERCENTAGES!!
To find percent of graph used, look at data and
write it as a fraction and then convert to a
percent. For example \$43 million from
chocolate sales. Total sales \$105 million. 43/105
= .409 = 40.9% round to 41%
VENN DIAGRAM – COMPARE DATA
How many people liked pizza?
How many people liked tacos only?
How many people like all three??
How many people didn’t like any of
the choices?
```
Related documents