Area
The area of a figure is the number of square units that will cover the figure.
Square/Rectangle/Parallelogram:
To find the area of a square, rectangle, or parallelogram, multiply the base times the height. Express the answer in square units:
ht
The area is 9 square units, or 9 u2. If you were measuring in inches, it would be 9 in2.
**Be careful to write as 9 in2, NOT 92 in. 92 in. = 81 inches**
“Night or day, day or night… area equals base times height”
Circle:
To find the area of a circle, use the formula:
A = π r2
Using π ≈ 3.14, and r = radius
(In some circle problems, you will be given the radius as a fraction. In that case, use as π
8m
3.14 (82) = 3.14 • 64 = 200.96
A = 200.96m2
Thursday WarmUps
7th Grade
Tips & Reminders
Area
Triangle:
To find the area of a triangle, multiply base times height and then divide by 2. You may see this formula written two ways:
A = (or) A =
“Area of triangles are easy to do…base times height and divide by 2”
ht ht
Ex: base = 12 m ht = 6 m
(12 • 6) ÷ 2 = 36 m2
or
12 • 6 = 36m2 (or) 36m2
Perimeter
Perimeter is the distance around a figure:
“Add up all lengths as you go around…perimeter is what you’ve found!”
2 cm + 3 cm + 3 cm = 8 cm
P = 8cm
Perimeter
You can find the perimeter of a right triangle if you have only two sides, using the Pythagorean Theorem.
a c 3 in x
b 4 in
Pythagorean Theorem = a2 + b2 = c2
32 + 42 = c2 9 + 16 = x2
25 = x2 x = 5
Perimeter = 3 + 4 + 5 = 12 in
Circumference/Diameter/ Radius
Circumference: The distance around a circle. To find the circumference, use one of the following formulas, depending on what information is already given to you.
C = d • π, where d = diameter
C = 2r • π, where r = radius
** 2π r ≠ π r2 **
C = 2(8) • 3.14
8m C = 50.24 m
12 in C = 12 • 3.14
C = 37.68 in
Diameter: Radius:
A line segment The distance from
connecting two the center ofthe points on the circle circle to a point
and passing through onthe circle.
the center. Diameter
is equal to 2 times
radius and is the
longest chord in the
circle.
Integers
Absolute Value:
-the distance of a number from zero on a number line
-the following symbol is used when finding the absolute value: | |
Ex: |6| = 6, because it is 6
places from zero.
|-6| = 6, because it is also 6
places from zero
Combining Integers (Adding & Subtracting):
-If the signs are the same, add the absolute value of the integers and keep the common sign.
Ex: -3 + -5 = -8
4 + 2 = 6
-If the signs are different, subtract the absolute values and take the sign of the integer with the larger absolute value.
Ex: -3 + 5 = 2
5 – 3 = 2, and the larger number, 5, is positive, so the answer is positive 2
-8 + 5 = -3
8 – 5 is 3, and the larger number, 8, is negative, so the answer is negative 3
Percent
Percent of a Number:
What is 40% of 36? Use proportions to solve, keeping in mind: is part = %
of whole 100
Substitute in what you already know:
x = 40
36 100
100x = 36(40) 100x = 1440
100x = 1440 x = 14.4
100 100
(OR)
Set up an equation:
What is 40% of 36?
n =40% of 36
n = 0.40 • 36
n = 14.4
Percent
Find the percent one number is of another:
60 = ? % of 80?
is part = %
of whole 100
Substitute in what you already know:
60 = x
80 100
80x = 60(100) 80x = 6000
80x = 6000 x = 75
80 80
= 75%
(OR)
Set up an equation:
60 = n% of 80
60 = n • 80
60 = 80n n = 0.75 = 75%
80 80
Equivalent Fractions
Multiply/divide the numerator and denominator by the same number to find equivalent fractions:
= = ==
=
Ordering Fractions
Either get common denominators or convert to decimals, then put in order as requested.
Compare Fractions with Like Denominators
If fractions have the same denominator, compare the numerators.
, because 4 is greater than 2
, because 1 is less than 5
Comparing Fractions with Unlike Denominators
One method is to get a common denominator by multiplying each fraction by the denominator of the opposite fraction, and then comparing numerators:
and
= =
< , so <
Another method is to get equivalent fractions using the LCM as the new denominator:
and
The LCM of 10 and 8 is 40.
= =
, so <
Another method is to convert each fraction to a decimal, by dividing the numerator by the denominator, and then compare the decimals. Remember to take the decimal out the same number of places:
and
= 0.67 = 0.75
0.67 < 0.75, so <