math 1314 college algebra arithmetic review

WELCOME TO COLLEGE ALGEBRA!Arithmetic Review for Math 1314:Signed-Number Rules, Division & Zero, Fraction Rules,

Fractions & Decimals, Rounding, Percent

SIGNED-NUMBER RULESAdding/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

SIGNED-NUMBER RULESMultiplying/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

= –2

DIVISION & ZEROZero Divided by a Nonzero Number

0 ÷ K = 0 or (as long as K is not equal to 0)

Remember: Zero on top of the fraction is OK

A Number Divided by Zero

N ÷ 0 is undefined (we cannot divide by 0)

Remember: Zero on the bottom of the fraction NO

FRACTION RULESAdding/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:

FRACTION RULESMultiplying 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:

FRACTION RULESDividing Fractions

Multiply by the Reciprocal: Flip over the second fraction and multiply.

Examples:

FRACTIONS & DECIMALSConverting a Fraction to a Decimal

Divide the numerator by the denominator.

Examples:

(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:

ROUNDINGRounding

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

PERCENTConverting 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%

PERCENTConverting a Percent to a Fraction

Drop the % sign and put the number over 100. Reduce the fraction.

Example:

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 and simplify the answer.

Examples:

PRACTICE PROBLEMS1. 12 – 39 =

2. – 13 – 40 =

3. –5(–13) =

4. =

5. =

6. =

7. =

8. Write as a decimal and as a percent.

9. Round 2.36397 to the nearest tenth. Answers on next slide.

PRACTICE PROBLEMS - ANSWERS1. 12 – 39 = – 27

2. – 13 – 40 = – 53

3. –5(–13) = 65

4. = – 7

5. =

6. =

7. =

8. Write as a decimal and as a percent. 0.625, 62.5%

9. Round 2.36397 to the nearest tenth. 2.4

COLLEGE ALGEBRA FOR A BETTER BRAIN

“Problems are to the mind

what exercise is to the muscles;

they toughen and make strong.”~Norman Vincent Peale