Wednesday, October 30, 2013
Absolute Value
Absolute value simply means the amount of "jumps" made on a number line. It is a measurement of distance moved from one place on a number line to another. Because it is measuring distance and not direction, absolute value is always positive. The absolute value of a number is noted between two absolute value bars.
If we take the absolute value of |-6|or|6| or and look at it as the distance from zero on the number line, you can see that in either direction you have moved six spaces. You either move or you don't. This is way the value is always positive.
Important to Remember: Absolute value bars are also considered grouping symbols. Like parentheses, whatever operations occur inside the absolute value bars are done first in order of operations.
| |-5| = 5 | |7| = 7 |
If we take the absolute value of |-6|or|6| or and look at it as the distance from zero on the number line, you can see that in either direction you have moved six spaces. You either move or you don't. This is way the value is always positive.
Important to Remember: Absolute value bars are also considered grouping symbols. Like parentheses, whatever operations occur inside the absolute value bars are done first in order of operations.
Integers & Rational Numbers
Welcome to the new unit on Integers and the Coordinate Plane. In class we talked about two categories of numbers. Integers are any positive or negative whole number including zero. Essentially any whole number and its opposite is considered an integers (for example 4 and -4 are opposites). The other category is called rational numbers. Rational numbers are numbers that can be converted into fractions. Decimals that repeat in consistent patterns or that terminate can be converted into fractions. Numbers like pi or phi can not be converted into fractions because the decimal does not terminate and there is no consistent pattern with the digits. These numbers are called irrational.
One clue to remember what a rational number is to look at the word rational itself. RATIOnal. Notice the root of the word is ratio. Remember ratios are the comparison of one quantity to another (numerators as compared to denominators) and are typically written in fraction form.
A set of integers ordered least to greatest may be {-5, -1, 0, 4, 10}
A set of rational numbers ordered least to greatest may be {-3/5, -.25, 1, 1/2, .4444....}
One clue to remember what a rational number is to look at the word rational itself. RATIOnal. Notice the root of the word is ratio. Remember ratios are the comparison of one quantity to another (numerators as compared to denominators) and are typically written in fraction form.
A set of integers ordered least to greatest may be {-5, -1, 0, 4, 10}
A set of rational numbers ordered least to greatest may be {-3/5, -.25, 1, 1/2, .4444....}
Monday, October 14, 2013
Fractions, Decimals, and Percent Conversions
Click on the link to go to the Math is Fun website to review your understanding of fraction, decimal, and percent conversion. There is a great interactive manipulative for you to use. My only issue with this page is when it explains how to convert decimals into percents and back into decimals again, it does not explain why you move the decimal two places.
Remember: converting a decimal to a percent requires you to multiply by 100 (percent means for every hundred). You are moving the decimal to the right because you are multiplying by a number greater than one. You are moving it twice because 100 is equivalent to 10 to the 2nd power which is equivalent to two place values. Moving from a percent to a decimal requires you to divide by 100. It should make sense that you would move the decimal to the left now because you number should get smaller.
Remember: converting a decimal to a percent requires you to multiply by 100 (percent means for every hundred). You are moving the decimal to the right because you are multiplying by a number greater than one. You are moving it twice because 100 is equivalent to 10 to the 2nd power which is equivalent to two place values. Moving from a percent to a decimal requires you to divide by 100. It should make sense that you would move the decimal to the left now because you number should get smaller.
Suggested Strategies for Comparing & Ordering Fractions
The following document was created by Mrs. A. Salinger.
Comparing Fractions
Converting Decimals to Fractions
To convert decimals to fractions first you should remember that all decimal places have a base-ten place value. So, the first place behind the decimal point is the tenths, the second place is the hundredths, the third place is the thousandths, and so on.
If you are given a decimal such as 0.312, simply say the decimal in the proper notation. ("three hundred twelve thousandths"). You should be able to 'hear' the denominator of your fraction. Therefore the fraction form is 312/1000.
BUT WAIT!
You must always reduce your fractions to their simplest form. Since the GCF of 312 and 1000 is 8, take 312/1000 divide your numerator and denominator by 8/8 to get 39/125. This is the fraction form of the decimal 0.312.
If you are given a decimal such as 0.312, simply say the decimal in the proper notation. ("three hundred twelve thousandths"). You should be able to 'hear' the denominator of your fraction. Therefore the fraction form is 312/1000.
BUT WAIT!
You must always reduce your fractions to their simplest form. Since the GCF of 312 and 1000 is 8, take 312/1000 divide your numerator and denominator by 8/8 to get 39/125. This is the fraction form of the decimal 0.312.
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