Download Writing Fractions to Represent Parts of Figures or Real

Math 64
4.1 "Introduction to Fractions and Mixed Numbers"
Objectives:
*
Write a fraction to represent parts of …gures or real-life data.
*
Graph fractions on a number line.
*
Write mixed numbers as improper fractions.
*
Write improper fractions as mixed numbers or whole numbers.
Writing Fractions to Represent Parts of Figures or Real-Life Data
Whole numbers are used to count whole things or units, such as cars, horses, dollars, and people. To refer to a part of
a whole, fractions can be used. In a fraction, the top number is called the numerator and the bottom number is called the
denominator. The bar between the numbers is called the fraction bar.
One way to become familiar with the concept of fractions is to visualize fractions with shaded …gures. We can then write
a fraction to represent the shaded area of the …gure (or diagram).
Example 1: (Writing fractions)
Write a fraction to represent the shaded part of each …gure.
a)
b)
c)
d)
Example 2: (Drawing fractions)
Draw and shade a part of a …gure to represent the fraction.
2
a)
of a …gure
3
b)
Page: 1
7
of a …gure
11
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
4.1
Example 3: (Writing fractions from real-life data)
There are 31 days in the month of March. What fraction of the month does 11 days represent?
F A proper fraction is a fraction whose numerator is less than its denominator. Proper fractions are less than 1. For
example,
F An improper fraction is a fraction whose numerator is greater than or equal to its denominator. Improper fractions
are greater than or equal to 1. For example,
F A mixed number contains a whole number and a fraction. Mixed numbers are greater than 1. For example,
Example 4: (Writing fractions)
Represent the shaded part of each …gure group as both an improper fraction and a mixed number.
a)
b)
c)
d)
Graphing Fractions on a Number Line
Another way to visualize fractions is to graph them on a number line. To do this, think of 1 unit on the number line as
2
a whole. To graph ; for example, divide the distance from 0 to 1 into 5 equal parts. Then start at 0 and count 2 parts
5
to the right.
Page: 2
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
4.1
Example 5: (Graphing fractions on a number line)
Graph each proper fraction on a number line.
5
2
a)
b)
7
3
c)
4
6
Recall that improper fractions are greater than or equal to 1. This is always true since the numerator of an improper
fraction is greater than or equal to the denominator.
Example 6: (Graphing fractions on a number line)
Graph each improper fraction on a number line.
8
a)
3
c)
7
7
b)
5
4
d)
5
1
Let n be any integer except 0. then
Writing Mixed Numbers as Improper Fractions
Writing a Mixed Number as an Improper Fraction:
To write a mixed number as an improper fraction.
1: Multiply the denominator of the fraction by the whole number.
2: Add the numerator of the fraction to the product from Step 1.
3: Write the sum from Step 2 as the numerator of the improper fraction over the original denominator.
Example 7: (Writing mixed numbers as improper fractions)
Write each mixed number as an improper fraction.
a) 5 27
b) 6 32
Page: 3
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
4.1
d) 4 51
9
c) 10 10
Writing an Improper Fraction as a Mixed Number or Whole Number
Just as there are times when an improper fraction is preferred, sometimes a mixed or a whole number better suits a
situation. To write improper fractions as mixed or a whole number, we use division.
Writing an Improper Fraction as a Mixed Number or a Whole Number:
To write an improper fraction as a mixed number or a whole number:
1: Divide the denominator into the numerator.
2: The whole number part of the mixed number is the quotient.
The fraction part of the mixed number is the remainder over the original denominator.
Example 8: (Writing an Improper Fraction as a Mixed Number or Whole Number)
Write each improper fraction as a mixed number or a whole number.
9
23
a)
b)
5
9
d)
62
13
e)
51
7
Page: 4
c)
48
4
f)
21
20
Notes by Bibiana Lopez