Wednesday
WarmUps
7th Grade
Tips & Reminders
Basic Algebra
To solve basic algebra equations, you
want to isolate the variable. To
isolate the variable, do the inverse
operation to both sides of the
equation. What is done to one side of
the equation must be done to the other
to keep the equation “in balance”.
Inverse operations: Operations that
“undo” each other. Addition and
subtraction are inverse operations.
Multiplication and division are
inverse operations.
Multiplication:
Multiply/Divide Integers
When multiplying and dividing
integers:
If the signs are the same,
the answer will be positive
4 • 5 = 20 or 4 (5) = 20
same signs = positive product
ex:
6 • -4 = 24 or -6 (-4) = 24
same signs = positive product
21  3 = 7
5n = 20
or
18  3 = 6 or
-
-
 18
6
3
Check you answer:
5 (4) = 20
m
= 4 (20)
20
Check your answer:
80
=4
20
ex: 4 • 6 = 24 or 4( 6) = 24
different signs =
negative product
-
m = 80
= 46.% = 45%
0 . 3 0 5 = 30.5%
-
-
 32
 8
4
different signs =
negative quotient
32  4 = -8 or
-
-
Percent to Decimal:
Move the decimal two places to
the left. If one is not present, add
it to the end, then move it.
Drop the percent symbol.
54% =
If the signs different, the
answer will be negative
(20)
0 . 4 6
same signs = positive quotient
same signs = positive quotient
Get the m by itself by
multiplying each side by 20.
Move the decimal two places
to the right. Add the percent symbol.
If there are no digits past the decimal
point, you don’t have to use it.
21
7
3
n = 4
m
=4
20
Decimal to percent:
-
Get the n by itself by dividing
each side by 5.
5n = 20
5
5
Division:
Converting Decimals and
Percents
5 4 . = 0.54
25.8% = 2 5 . 8 = 0.258
Converting
Decimals to Fractions
Decimals are fractions with a
special set of denominators
(tenths, hundredths,
thousandths, etc) and a special
written form. To write a
decimal as a fraction, say it
aloud. You’ll notice it sounds
like a fraction:
Decimal:
Word name:
0.9
nine tenths
Fraction:
9
10
Decimal:
Word name:
Fraction:
0.47
forty-seven
hundredths
47
100
Decimal:
3.7
Word name: three and seven
tenths
Converting
Fractions to Percents
To convert a fraction to a
percent, a proportion can be
used.
Write
3
as a percent:
8
3
x

8 100
5
as a decimal
8
A decimal is a fractional part of
10, 100, 1000, etc. Write a
proportion, making an equivalent
fraction with the denominator a
number that the denominator of
the given fraction can be divided
evenly into.
5
x

8 1000
To solve the proportion, cross
multiply:
=
When converting a fraction to a
decimal, proportions can also
be used.
Write
Since a percent is a fraction
with a denominator of 100, you
are really looking for an
equivalent fraction with a
denominator of 100:
3
x

8 100
Converting
Fractions to Decimals
8x = 3(100)
8x = 300
8
8
To solve the proportion, cross
multiply:
5
x

8 1000
=
8x = 5000
8
8
x = 37.5 = 37.5%
625
= 0.625
1000
x = 625;
(or)
Fraction:
7
3
10
Decimal:
5.25
Word name: five and twenty
five hundredths
(or)
You can also divide the
numerator by the denominator.
Annex zeros if needed.
4
0
.
2
5
1
.
0
0
-
Fraction:
5
25
1
= 5
100
4
You can also divide the numerator by
the denominator. Annex zeros if
needed.
1
1
4
8x = 5(1000)
4
4
0
.
2
5
1
.
0
0
-
8
8
-
2
0
2
0
-
0
2
0
0
0
0.25 = 25%
2
1
4
= 0.25
Terminating, Repeating,
and Continuing Decimals
Terminating: A decimal that
ends on its own. Ex: 0.75
Repeating: A decimal in which
one or more digits repeat
infinitely.
Dividing Decimals by
Decimals
4 . 2 2 8 . 5 6
Change the divisor to a whole
number by moving the decimal
point to the right. Move the
decimal point in the dividend the
same number of spaces to the
right. Annex zeros if necessary.
Ex: 0.757575……. = 0.75
4 2. 2
Continuing: A decimal that
neither terminates, nor is
repeating. This is also called a
“non-terminating, nonrepeating” decimal.
8
5 . 6
Divide as you would with whole
numbers. Remember to bring up
the decimal point into the
quotient.
Ex: 0.548759314…
6 . 8
Other examples of irrational
numbers are:
π = 3.14……
3 = 1.732….
Dividing Decimals by
Whole Numbers:
43.26  6
6
0
7 . 2
1
4
3 . 2
6
- 4
-
2
1
2
1
2
0
6
- 0
6
0
Bring up the decimal point into
the quotient. Divide as you would
with whole numbers.
Annex zeros if necessary.
4 2 2 8 5 . 6
- 2 5 2
3 3
6
- 3 3
6
0