IF AN ODD NUMBER OF NEGATIVES IS USED, MULTIPLY OR DIVIDE AS USUAL,...

2. If an odd number of negatives is used, multiply or divide as usual, and the answer is negative.a. –15 5 = –3 b.(–2 ×–4) ×–5 = –40This is helpful to remember when working with powers of a negative number. If the power is even,the answer is positive. If the power is odd, the answer is negative.FractionsA fraction is a ratio of two numbers, where the top number is the numeratorand the bottom number is thedenominator.

R

^EDUCING

F

^RACTIONS

To reduce fractions to their lowest terms, or simplest form, find the GCF of both numerator and denominator.Divide each part of the fraction by this common factor and the result is a reduced fraction. When a fractionis in reduced form, the two remaining numbers in the fraction are relatively prime.

32x

6

a. b.

4xy

⁸

y

9

²

3

When performing operations with fractions, the important thing to remember is when you need a com-mon denominator and when one is not necessary.

A

DDING AND

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UBTRACTING

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RACTIONS

It is very important to remember to find the least common denominator (LCD) when adding or subtract-ing fractions. After this is done, you will be only adding or subtracting the numerators and keeping the com-mon denominator as the bottom number in your answer.

3

2

y

xy

⁴

5

²

3

LCD15LCDxy

3

x

2

3

y

x

xy

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xy

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5

3

²

3

⁵

5

15

¹⁰

15

¹⁶

15

–

A R I T H M E T I C

–

M

^ULTIPLYING

F

^RACTIONS

It is not necessary to get a common denominator when multiplying fractions. To perform this operation, youcan simply multiply across the numerators and then the denominators. If possible, you can also cross-can-cel common factors if they are present, as in example b.

1

12

3

²

3

²

9

25

⁵

3

¹²

25

5

⁴

⁵

3

¹

⁴

5

D

^IVIDING

F

^RACTIONS

A common denominator is also not needed when dividing fractions, and the procedure is similar to multi-plying. Since dividing by a fraction is the same as multiplying by its reciprocal, leave the first fraction alone,change the division to multiplication, and change the number being divided by to its reciprocal.

4

3x

5

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3

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5

¹

4

³

1

³

5

y

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y

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1

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4

DecimalsThe following chart reviews the place value names used with decimals. Here are the decimal place names forthe number 6384.2957.

6 3 8 4 . 2 9 5 7

DOTHENUCISMRALPIt is also helpful to know of the fractional equivalents to some commonly used decimals and percents,especially because you will not be able to use a calculator.0.110%

10

¹

0.333

¹

₃

%

¹

3

0.440%

²

5

3 3 0

0.550%

¹

2

0.666

²

₃

%

²

3

0.7575%

³

4

A

DDING AND

S

UBTRACTING

D

ECIMALS

The important thing to remember about adding and subtracting decimals is that the decimal places must belined up.a. 3.6 b. 5.984+5.61 –2.34