Comparing Fractions in VS .NET

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Comparing Fractions
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If the denominators of two fractions are equal, then the fraction with the larger numerator is bigger If the numerators of the two fractions are equal, then the fraction with the smaller denominator is bigger When comparing fractions that have different numerators and denominators, cross-multiply the numerator of each fraction by the denominator of the other fraction Write the product of each multiplication next to the numerator you utilized to get it Compare the products on each side of the fractions to determine which of the two fractions is the greater 4,000 1 Example: Compare ______ and __ 3 60,000
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CHAP 7: MATHEMATICS
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Cross-multiply: 4,000 1 (12,000) ______ and __ (60,000) 3 60,000 12,000 is less than 60,000 4,000 1 therefore: ______ is less than __ 3 60,000
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Adding and Subtracting Fractions
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Fractions having the same denominators require only the adding or subtracting of the numerators 3 2 5 Example: __ + __ = __ = 1 5 5 5 3 2 1 __ __ = __ Example: 5 5 5 Fractions having different denominators require rst nding a common denominator or least common denominator (LCD) before you can either add or subtract them 1 2 Example: __ + __ 5 3 The LCM of 5 and 3 is 15; therefore the LCD is 15 1 3 3 __ __ = ___ 5 3 15 Multiply the numerator and denominator of the rst fraction by the number required to change the denominator to 15 in this case, 3 2 5 10 __ __ = ___ 3 5 15 Repeat the process for the second fraction by multiplying the numerator and denominator by 5 (the number required to change the denominator to 15) 3 10 13 ___ + ___ = ___ 15 15 15 Then add the numerators and place the sum over the common denominator
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Note: Multiplying the denominators together to get a common denominator allows you to omit having to nd the LCD, and sometimes will, in fact, give you the least common denominator However, there are two drawbacks to this approach: rst, you may be working with larger numbers since you may not be using the least common denominator; and second, you will have to reduce your answer to the lowest form of the fraction
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Multiplying and Dividing Fractions
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To multiply fractions, multiply their numerators and denominators 4 5 20 Example: __ __ = ___ 9 7 63
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PART III: REVIEW FOR THE WRITTEN EXAMINATION
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To divide fractions, simply invert the second fraction and multiply the numerators and denominators Remember: multiplication and division are inverse operations (as are addition and subtraction) 7 1 4 1 7 Example: __ __ = __ __ = ___ 3 7 3 4 12
MIXED NUMBERS
A mixed number consists of an integer and a fraction Mixed numbers must be converted into fractions prior to performing addition, subtraction, multiplication, and division operations To convert a mixed number to a fraction, multiply the integer of the mixed number by the denominator of the fraction and then add the product to the numerator of the fraction and put that number over the denominator of the original fraction 3 (4 5) + 3 20 +3 23 Example: 4 __ = _________ = _____ = ___ 5 5 5 5
DECIMALS
Numbers that contain a decimal point are called decimals The number to the left of the decimal point is a whole number, and the number to the right of the decimal point is called the tenths digit The tenths digit gives you the number of tenths that are added to the whole number If there are two numbers to the right of the decimal point, then both numbers to the right are the number of hundredths to be added to the whole number Three numbers to the right of the decimal point would indicate that all three numbers to the right are the number of thousandths to be added to the whole number and so forth
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