Math 1314 College Algebra Arithmetic Review Day 1

1. Arithmetic Review for Math 1314:
Signed-Number Rules, Division & Zero, Fraction Rules,
Fractions & Decimals, Rounding, Percent

2. Adding/Subtracting Signed Numbers
Like Signs: Add & keep the sign.
Different Signs: Subtract & take the sign of the larger number.
Examples:
2+3=5
– 2 – 3 = –5
– 3 + 2 = –1
–2+3=1

3. Multiplying/Dividing Signed Numbers
Like Signs: The answer is positive.
Different Signs: The answer is negative.
Examples:
6÷3=2
(–2)(–3) = 6
–2  3 = –6
−6
= –2
3

4. Zero Divided by a Nonzero Number
0÷K=0
or
0
K
=0
(as long as K is not equal to 0)
Remember: Zero on top of the fraction is OK 
0
K
=0
A Number Divided by Zero
N ÷ 0 is undefined
(we cannot divide by 0)
Remember: Zero on the bottom of the fraction NO 
N
0
is undefined

5. Adding/Subtracting Fractions
Find the Lowest Common Denominator (LCD).
Convert each fraction into an equivalent fraction with the LCD.
Add/Subtract the numerators and put the result over the LCD.
Reduce the answer, if possible.
Example:
1 2 5
13 22 5
3 4 5
4
2
− + − = −
+
− = − + − = − = −
2 3 6
23 32 6
6 6 6
6
3

6. Multiplying Fractions
Method 1: Multiply across and then reduce.
Method 2: Cancel like factors and then multiply across.
(You may only cancel a factor from a numerator and denominator,
not from two numerators or two denominators.)
Examples:
5 3
15
1

=
=
6 20
120
8
𝑜𝑟
5 3
5 1 3 1
1

=

=
6 20
6 2 20 4
8

7. Dividing Fractions
Multiply by the Reciprocal: Flip over the second fraction and multiply.
Examples:
1
3
1
4
1
4 1
1
÷ =
 =

=
12
4
12 3
12 3
3
9
7
7
7 8
7 8
8
= 7 ÷ =  =  =
=8
7
8
1 7
1 7
1
8

8. Converting a Fraction to a Decimal
Divide the numerator by the denominator.
Examples:
3
8
2
3
= 3 ÷ 8 = 0.375
= 2 ÷ 3 = 0.6666 … = 0. 6
(Use a bar to indicate repeating digits)
Converting a Decimal to a Fraction
Write the number (without the decimal point) over a power of 10, where the number of
zeros in the denominator is the same as the number of digits to the right of the decimal.
Then reduce the fraction.
Examples: 0.25 =
25
100
=
1
4
1.6 =
16
10
=
8
5
𝑜𝑟
3
1
5

9. Rounding
Do not round off answers unless otherwise instructed.
Rounding to the nearest tenth means round to 1 decimal place.
Rounding to the nearest hundredth means round to 2 decimal places.
Rounding to the nearest thousandth means round to 3 decimal places.
If the digit to the right is 5 or higher, round up.
If the digit to the right is 4 or less, don’t round up.
Examples: Round 26.82735 to the nearest hundredth  26.83
Round 8.749893 to the nearest tenth  8.7

10. Converting a Percent to a Decimal
Drop the % sign and move the decimal two places to the left.
Example: 38% = 0.38
Converting a Decimal to a Percent
Move the decimal two places to the right and put on a % sign.
Example: 0.072 = 7.2%

11. Converting a Percent to a Fraction
Drop the % sign and put the number over 100. Reduce the fraction.
Example: 15% =
15
100
=
3
20
Converting a Fraction to a Percent
Method 1: Convert the fraction to a decimal and then to a percent.
Method 2: Multiply the fraction by
Examples:
100
%
1
and simplify the answer.
9
= 0.045 = 4.5%
200
9
9
100
900
=

%=
%
200
200
1
200
9
2
1
2
= % = 4 % 𝑜𝑟 4.5%

12. 1. 12 – 39 =
2. – 13 – 40 =
3. –5(–13) =
4.
5.
6.
7.
8.
−56
=
8
1
3
−4=
6
4
9
− 3  22 =
17
2
÷3=
18
5
Write 8 as
a decimal and as a percent.
9. Round 2.36397 to the nearest tenth.
Answers on next slide.

13. ANSWERS
1. 12 – 39 = – 27
2. – 13 – 40 = – 53
3. –5(–13) = 65
4.
5.
6.
7.
8.
−56
=–7
8
1
3
7
− =−
6
4
12
4
9
6
−  =−
3 22
11
17
2
17
5
÷ =
𝑜𝑟 1
18
3
12
12
5
Write as a decimal
8
and as a percent. 0.625, 62.5%
9. Round 2.36397 to the nearest tenth. 2.4

14. “Problems are to the mind
what exercise is to the muscles;
they toughen and make strong.”
~Norman Vincent Peale