Math 1314 College Algebra Arithmetic Review
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Transcript of Math 1314 College Algebra Arithmetic Review
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WELCOME TO COLLEGE ALGEBRA!Arithmetic Review for Math 1314:Signed-Number Rules, Division & Zero, Fraction Rules,
Fractions & Decimals, Rounding, Percent
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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
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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
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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
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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:
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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:
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FRACTION RULESDividing Fractions
Multiply by the Reciprocal: Flip over the second fraction and multiply.
Examples:
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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:
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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
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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%
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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:
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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.
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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
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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