Transcript PowerPoint Chapter 7

Chapter 7
Review of Mathematical Principles
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Learning Objectives
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Work basic multiplication and division
problems
Interpret Roman numerals correctly
Apply basic rules in calculations using
fractions, decimal fractions, percentages,
ratios, and proportions
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Arabic Numerals
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Number system we are most familiar with
Includes fractions, decimals, and whole
numbers
Examples include numbers 1, 2, 3, etc.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Basic Rules of Roman Numerals
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1. Whenever a Roman numeral is repeated
or a smaller Roman numeral follows a larger
number, the values are added together.
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For example: VIII
(5 + 1 + 1 + 1 = 8)
2. Whenever a smaller Roman numeral
appears before a larger Roman numeral, the
smaller number is subtracted.

For example: IX (1 subtracted from 10 = 9)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Basic Rules of Roman Numerals
(cont.)
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3. The same numeral is never repeated more
than three times in a sequence.
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For example: I, II, III, IV
4. Whenever a smaller Roman numeral
comes between two larger Roman numerals,
subtract the smaller number from the numeral
following it.

For example: XIX = 10 + (10-1) = 19
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions
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One or more equal parts of a unit
Part over whole, separated by a line:
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3 parts of 4 = ¾
3 is the top number, 4 is the bottom number
The “numerator,” or top number, identifies
how many parts of the whole are discussed
The “denominator,” or lower number,
identifies how many equal parts are in the
whole
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Question 1
In the fraction ⅔, the number 3 is the:
1.
2.
3.
4.
Numerator.
Denominator.
Divisor.
Fraction.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions (cont.)
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Fractions may be raised to higher terms by
multiplying the numerator and denominator
by the same number:
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Fractions can be reduced to lowest terms by
dividing the numerator and denominator by
the same number:
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¾ x 3/3 = 9/12
9/12 ÷ 3/3 = 3/4
A fraction is easiest to work with when it has
been reduced to its lowest term.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions (cont.)
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Proper fraction: numerator is smaller than
denominator
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For example: ¾ is a proper fraction, 3 is less than
4
Improper fraction: numerator is larger than
denominator

For example: 8/6 is an improper fraction, 8 is
greater than 6
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Mixed number: whole number is combined
with a proper fraction

For example: 1 ⅔ is a mixed number
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Question 2
The number 9 5/8 is a(n):
1.
2.
3.
4.
Proper fraction.
Improper fraction.
Mixed number.
Complex fraction.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions (cont.)
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To add two fractions or subtract them, the
denominators must be the same number.
If two fractions have the same denominator,
add the numerators and put the sum over the
common denominator:
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2/3 + 5/3 = 7/3
If two fractions have different denominators, a
common denominator must be found. The
common denominator is a number that both
denominators can be divided into evenly.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Question 3
What is 2/6 + 4/9?
1.
2.
3.
4.
15/18
5/6
7/9
9/12
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions (cont.)
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Multiplying fractions; multiply the numerators
together and the denominators together
For example: 2/4 × 3/9 = 2 × 3 (6)/ 4 × 9 (36)
 Tip: it is easier to reduce the fractions to lowest terms
before multiplying.
 Therefore: ½ × 1/3 = 1/6

Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Fractions (cont.)
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To divide two fractions, invert (or turn upside
down) the fraction that is the divisor and then
multiply.
For example: ¾ ÷ ½ =
¾ × 2/1 =
3 × 2 / 4 × 1 or 6/4
*** 6/4 can be reduced to 3/2 or 1 ½.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Decimals
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All fractions can be converted to a decimal
fraction by dividing the numerator into the
denominator.
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To add two decimal fractions, first line up the
decimal points.
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For example: ¾ is 3 ÷ 4 = 0.75
For example: 0.345 + 2.456 = 2.801
To subtract two decimal fractions, first line up
the decimal points.

For example: 1.6 − 0.567 = 1.033
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Decimals (cont.)
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Multiplying decimals
1.467 (3 decimal places)
× 0.234 (3 decimal places)
________
0.343278 (6 decimal places in answer)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Decimals (cont.)
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To divide two decimals, first move the
decimal point in the divisor enough places to
the right to make it a whole number.
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6 ÷ 0.23 (the decimal must be moved two places
to the right to change 0.23 into “23”)
600 ÷ 23 (move the decimal two places to the
right in the dividend) = 26.09 (rounded)
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Learning Objectives

Apply basic rules in calculations using
fractions, decimal fractions, percentages,
ratios, and proportions
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Ratios and Percents
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A ratio is a way of expressing the relationship
of one number to another or expressing a
part of a whole number. The relationship is
reflected by separating the numbers with a
colon (e.g., 2:1).
Percent (%) means parts per hundred; can be
written as fractions or decimals
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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Proportions
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A way of expressing a relationship between two ratios
The two ratios are separated by a double colon (::)
which means “as.”
If three variables are known, the fourth can be
determined.
When solving for “x,” the numerators must be the same
measurement and the denominators the same
measurement.
The numerators and denominators in the proportion
must be written in the same units of measure.
Copyright © 2013, 2010, 2006, 2003, 2000, 1995, 1991 by Mosby, an imprint of Elsevier Inc.
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