7th Grade Math Study Guide 2017-2018
scalene triangle
a triangle with no congruent sides
distributive property of multiplication
a(b + c) = ab + ac 27 x 6 = (20x6 ) + (7 x 6) = 120 + 42 = 162
distributive property of addition
a(b+c)=ab+ac
right angle
an angle that measures 90 degrees
acute angle
an angle that measures less than 90 degrees
Spreadsheets
an interactive application for organization, analysis and storage of data in tabular form. A grid that organizes data
Bar graphs
A bar graph or bar chart is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.
Line graphs
A line graph is commonly used to display change over time as a series of data points connected by straight line segments on two axes. The line graph therefore helps to determine the relationship between two sets of values, with one data set always being dependent on the other set.
coordinate pairs- do they satisfy an equation?
A pair of numbers used to locate a point on a graph(x,y) i.e.- does (2,-4) lie on a line y=4x+12?
Ratios and proportions
A ratio is a way to compare two quantities by using division as in miles per hour where we compare miles and hours. A proportion on the other hand is an equation that says that two ratios are equivalent. ... If one number in a proportion is unknown you can find that number by solving the proportion. Example- 12 cookies cost 4 dollars, how much does 1 cookie cost? 12/4=1/x =3
Order of Operations
A set of rules for evaluating an expression involving more than one operation (PEMDAS)
rotational symmetry
A shape has Rotational Symmetry when it still looks the same after a rotation (of less than one full turn). This image can be rotated to three different positions and each look the same.
figure of transformation
A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation. Types of transformations in math. Translation. Reflection.
reflection
A transformation that "flips" a figure over a mirror or reflection line.
translation
A transformation that "slides" each point of a figure the same distance in the same direction.
isosceles triangle
A triangle that has 2 equal sides.
equilateral triangle
A triangle with three congruent sides
Area or triangle
A=1/2bxh
Area and perimeter of rectangles
A=LxW P=2(L)+2(w)
Area and circumference of a circle
A=πr^2 (squared) C=2πr
Adding and subtracting integers
Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. Subtracting a negative number from a negative number - a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers. For example, say we have the problem -2 - -4. Remember- Keep Change Opposite.
obtuse angle
An angle that measures more than 90 degrees but less than 180 degrees
Probability
The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
Converting decimals to a percent
To convert a decimal to a percent, multiply the decimal by 100, then add on the % symbol. An easy way to multiply a decimal by 100 is to move the decimal point two places to the right.
supplementary angles
Two angles whose sum is 180 degrees
complementary angles
Two angles whose sum is 90 degrees
Add, subtract, multiply, and divide decimals, fractions, mixed numbers, and integers
View this video- https://www.youtube.com/watch?v=4c_mB2MF_8c
quadrilaterals
4 sided polygon
Number Sense: Comparing and Ordering
Comparing Fractions, Decimals, and Percents You can compare fractions, decimals and percents using greater than, less than or equal to. Convert fractions, decimals, and percents to the same form to compare the values. If you are comparing a fraction and a percent, write both of them either as fractions or percents to figure out which is greater. Use this information to write a set of numbers or quantities in order from least to greatest or from greatest to least. Compare 45% and 45. First, write 45% and 45 in the same form. Let's change 45 to a percent. Find the equivalent fraction of 45 as a fraction out of 100. Multiply both numerator and denominator by 20. 4×205×20=80100 Next, convert the fraction to a percent. 80100=80% Now, we can compare 45% and 80%. 45%<80% 45% is less than 80%. Let's compare percents and decimals. Compare 18% and 0.9. First, write 18% and 0.9 in the same form. Let's change 0.9 to a percent. Move the decimal point two places to the right and add the percent sign. 0.9=90% Now, compare 18% and 90%. 18%<90% 18% is less than 90%. Write 0.56, 34%, 910, and 12 in order from least to greatest. First, rewrite them in the same form. Let's convert all of them to percents. 34% is already in percent form. Convert 0.56 to a percent. Move the decimal point two places to the right and add the percent sign. 0.56=56% Next, find the equivalent fractions of 910 and 12 as fractions over 100 and convert them to percents. Multiply the numerator and denominator of 910 by 10. Multiply the numerator and denominator of 12 by 50. 9×1010×101×502×50==90100=90%50100=50% Then, compare the percents. 56%,34%,90%,50% Finally, write them in the order from least to greatest. 34%,50%,56%,90% or34%,12,0.56,910
Determine if a number is prime, composite and its divisibility.
Composite number- A whole number that can be divided exactly by numbers other than 1 or itself. Example: 9 can be divided exactly by 3 (as well as 1 and 9), so 9 is a composite number. But 7 cannot be divided exactly (except by 1 and 7), so is NOT a composite number (it is a prime number).
Compare and order Decimals
Decimals- When comparing decimals, start in the tenths place. The decimal with the biggest value there is greater. If they are the same, move to the hundredths place and compare these values. ... If it helps, add zeros to the right so both decimals have the same number of digits
Determine if a number is prime, composite and its divisibility.
Divisibility rules- Divisibility by 2: The number should end in an even number. Divisibility by 3: The sum of digits of the number must be divisible by 3. Divisibility by 4: The number formed by the tens and units digit of the number must be divisible by 4. Divisibility by 5: The number should have 0 or 5 as the units digit. Divisibility by 6: The number should be divisible by both 2 and 3. Divisibility by 9: The sum of digits of the number must be divisible by 9.
Compare and order fractions
Fractions- Use the LCD to write equivalent fractions with a common denominator. 2. Compare the numerators: The larger fraction is the one with the greater numerator. Let's look at some more examples of comparing fractions with unlike denominators
Multiplying and dividing integers
If you multiply or divide two positive integers, your answer will be positive. If you multiply or divide a positive integer and a negative integer, your answer will always be a negative.
Compare and order integers and absolute values
Integers and absolute values- Recall that integers are a set of numbers that include the positive whole numbers (1, 2, 3, 4, 5, ...), their opposites (-1, -2, -3, -4, -5, ...) and zero. Sometimes you will want to compare different integers or put them in order from smallest to largest. A number line can help you to do this.
Compare and order the following
Mixed numbers- How to Compare Fractions To compare fractions with unlike denominators convert them to equivalent fractions with the same denominator. If you have mixed numbers convert them to improper fractions Find the lowest common denominator (LCD) for the fractions Convert each fraction into its equivalent with the LCD in the denominator Compare fractions: If denominators are the same you can compare the numerators. The fraction with the bigger numerator is the larger fraction.
Determine if a number is prime, composite and its divisibility.
Prime number- A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
solve and graph equations on a number line
Step 1: Put the equation in Slope Intercept Form. Step 2: Graph the y-intercept point (the number in the b position) on the y-axis. ... Step 3: From the point plotted on the y-axis, use the slope to find your second point. ... Step 4: Draw your line using the two points you plotted (y-intercept (b) first, slope (m) second.
Converting decimals to fractions
Step 1: Write down the decimal divided by 1, like this: decimal 1. Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify (or reduce) the fraction.
Evaluate expressions for given values
example- evaluate 4x+3=16, when x=3
percent of a number
https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent-problems/v/taking-a-percentage-example When asked to find a certain percent of a number, you must first change the percent to a decimal or fraction, and then MULTIPLY that by the number. Find 40% of 45. "of" means multiply
slope of a line
rise over run y2-y1/x2-x1 y=mx+b
rotation
the action of rotating around an axis or center.
symmetry
the quality of being made up of exactly similar parts facing each other or around an axis.
convert sentences into algebraic expressions
watch video- https://www.youtube.com/watch?v=4TP0dZrbso0
solve inequalities with coefficients
watch video- https://www.youtube.com/watch?v=RHwmsKUZo2I The only difference between a linear equation in one variable and a linear inequality in one variable is the verb. Instead of an "="sign, there is an inequality symbol: <(less than) >(greater than)≤ (less than or equal to) ≥ (greater than or equal to) Only one new idea is needed to solve linear inequalities: if you multiply or divide by a negative number, then the direction of the inequality symbol must be changed.
solve equations with coefficients
watch video- https://www.youtube.com/watch?v=U7agVFULbx8
graph line when given coordinate points or equation of a line
watch video-https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func/alg-writing-slope-intercept-equations/v/equation-of-a-line-2 Find the Equation of a Line Given That You Know Two Points it Passes Through. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line.
solve and graph inequalities on a number line
watch video-https://www.youtube.com/watch?v=-kPnGB36zcU Solve -3(x - 2) = 12: x - 2 = - 4 x = - 2 Graph x = - 2, using a filled circle because the original inequality was ≤: Graph of x = - 2 Plug values into the equation -3(x - 2)≤12: Pick a point on the left of -2 (-3, for example):-3(- 3 - 2)≤12 ? 15≤12 ? No. Pick a point on the right of -2 (0, for example):-3(0 - 2)≤12 ? 6≤12 ? Yes. Draw a dark line from -2 extending to the right, with an arrow at the end: Graph of -3(x - 2)≤12, or of x≥ - 2 Thus, x≥ - 2.