Thursday Warm Ups
7th Grade
Tips & Reminders
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:
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=
ht
Perimeter
Area
bh
2
(or)
A=
1
bh
2
a
c
The area is 9 square units,
or 9 u2. If you were
measuring in inches, it
would be 9 in2.
ht
ht
2
NOT 9 in. 9 in. = 81 inches**
Ex: base = 12 m ht = 6 m
(12 • 6) ÷ 2 = 36 m2
or
Circle:
4 in
Pythagorean Theorem
25
=x
2
x
= a2 + b 2 = c 2
9 + 16 = x2
x=5
Perimeter = 3 + 4 + 5 = 12 in
Circumference/Diameter/
Radius
**Be careful to write as 9 in2,
“Night or day, day or night…
area equals base times height”
3 in
b
3 2 + 4 2 = c2
“Area of triangles are easy to
do…base times height and divide by
2”
2
You can find the perimeter of a right
triangle if you have only two sides,
using the Pythagorean Theorem.
12 • 6 = 36m2 (or) 1 (12  6)  36m2
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 **
2
To find the area of a circle, use the
formula:
8m
C = 2(8) • 3.14
C = 50.24 m
Perimeter
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 22 as π
7
Perimeter is the distance around a
figure:
“Add up all lengths as you go
around…perimeter is what you’ve
found!”
8m
3.14 (82) = 3.14 • 64 = 200.96
2 cm + 3 cm + 3 cm = 8 cm
2
A = 200.96m
P = 8cm
12 in
C = 12 • 3.14
C = 37.68 in
Diameter:
A line segment
connecting two
points on the circle
and passing through
the center . Diameter
is equal to 2 times
radius and is the
longest chord in the
circle.
Radius:
The distance from
the center of the
circle to a point
on 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.
Percent
Percent of a Number:
Find the percent one number is
of another:
What is 40% of 36? Use
proportions to solve, keeping in
mind:
is part
= %
of whole
100
60 = ? % of 80?
Substitute in what you already
know:
x = 40
36 100
|-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
100x = 36(40)
100x = 1440
100x = 1440
100
100
x = 14.4
is part
= %
of whole
100
Substitute in what you already
know:
60 = x
80
100
80x = 60(100)
80x = 6000
80x = 6000
80
80
x = 75
75
= 75%
100
(OR)
(OR)
Set up an equation:
What is 40% of 36?
n = 40% of 36
n
= 0.40
•
n = 14.4
36
Set up an equation:
60 = n% of 80
60 = n
•
60 = 80n
80 80
n = 0.75 = 75%
80
Equivalent Fractions
Multiply/divide the numerator and
denominator by the same number
to find equivalent fractions:
3 3 2 6
=
=
4 42 8
3 33 9
=
=
4 4  3 12
72  9
8
=
81  9
9
Ordering Fractions
Either get common denominators
or convert to decimals, then put in
order as requested.
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:
2
3
and
3
4
Compare Fractions with
Like Denominators
If fractions have the same
denominator, compare the
numerators.
4 2
> , because 4 is greater than 2
7 7
1 5
< , because 1 is less than 5
9 9
24
3 4
=
8
12
9
,
12
<
33 9
=
4  3 12
8
12
2
3
so
3
4
<
Another method is to get equivalent
fractions using the LCM as the new
denominator:
2
3
and
10
8
The LCM of 10 and 8 is 40.
24
10  4
=
8
40
8
40
<
15
,
40
35
85
=
2
10
so
15
40
<
3
8
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:
2
3
and
3
4
2
= 0.67
3
0.67 < 0.75, so
3
= 0.75
4
2
3
<
3
4