Download Notes #4

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Equivalent Fractions and Decimals 2-6
*
* Write these in the “Vocabulary” section of your binder.
Make sure to add an example!
* Equivalent fractions are different expressions for the same
nonzero number.
* Relatively prime numbers have no common factors other than 1.
* A rational number is a number that can be written as a fraction
with an integer for its numerator and a nonzero integer for its
denominator.
* Terminating decimals are decimals that come to an end.
* Repeating decimals are decimals that repeat a pattern forever.
*
In some recipes the amounts of ingredients
are given as fractions, and sometimes those
fractions do not equal the fractions on a
measuring cup. Knowing how fractions relate
to each other can be very helpful.
Different fractions can name the same number.
3
5
=
6
10
=
15
25
In the diagram 3 = 6 = 15 . These are called
5 10 25
equivalent fractions because they are
different expressions for the same nonzero
number.
To create fractions equivalent to a given
fraction, multiply or divide the numerator and
denominator by the same number.
Check It Out: Example 1
Find two fractions equivalent to
6 .
12
6 · 2 = 12
12 · 2
24
Multiply the numerator and
denominator by 2.
6÷2
3
=
12 ÷ 2
6
Divide the numerator and
denominator by 2.
A fraction is in simplest form when the
numerator and denominator are relatively
prime. Relatively prime numbers have no
common factors other than 1.
Check It Out: Example 2
15
Write the fraction 45 in simplest form.
Find the GCF of 15 and 45.
15 = 3
•
5
45 = 3
•
3
The GCF is 3
•
•
5 = 15.
5
15 = 15 ÷ 15 = 1
45 45 ÷ 15
3
Divide the numerator and
denominator by 15.
8 is an improper
5
fraction. Its
numerator is
greater than its
denominator.
8= 13
5
5
3
1 is a mixed
5
number. It
contains both a
whole number
and a fraction.
Remember!
An improper fraction is a fraction where the
numerator is than or equal to the denominator.
Additional Example 4: Converting Between Improper
Fractions and Mixed Numbers
A. Write 13
5 as a mixed number.
First divide the numerator by the denominator.
13 = 2 3
5
5
Use the quotient and remainder to
write a mixed number.
B. Write 7 2
as an improper fraction.
3
First multiply the denominator and whole number,
and then add the numerator.
+
Use the result to
2 = 3 · 7 + 2 = 23
write the improper
3
3
3

fraction.
A rational number is a number that can
be written as a fraction with an integer for
its numerator and a nonzero integer for its
denominator. To write a rational number as
a decimal, divide the numerator by the
denominator.
Additional Example 1: Writing Fractions as Decimals
Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.
1
A. 4
0.2 5
4 1.00
–8
20
– 20
0
1 = 0.25
4
9
B. 5
1.8
5 9.0
–5
40
– 40
0
9 = 1.8
5
5
C. 3
1 .6 6 6
3 5.000
–3
20
– 18
20
– 18
5
20 3 ≈ 1.67
– 18
2
The decimals 0.75 and 1.2 in Example 1 are
terminating decimals because the decimals
comes to an end. The decimal 0.333…is a
repeating decimal because the decimal
repeats a pattern forever. You can also write a
repeating decimal with a bar over the repeating
part.
0.333… = 0.3
0.8333… = 0.83
0.727272… = 0.72
Additional Example 2A: Write Fractions as
Terminating and Repeating Decimals
Write each fraction as a decimal.
9
A. 25
0.3 6
______
25 ) 9.00
–75
150
–150
0
9
= 0.36
25
The remainder is 0.
This is a terminating decimal.
Additional Example 2B: Write Fractions as
Terminating and Repeating Decimals
Write each fraction as a decimal.
17
B. 18
0.9 4
______
18 )17.00
–162
80
– 72
8
17
= 0.94
18
The pattern repeats.
This is a repeating decimal.
Additional Example 3: Writing Decimals as Fractions
Write each decimal as a fraction in simplest
form.
A. 0.018
18
1,000
18 ÷ 2
=
1,000 ÷ 2
9
=
500
0.018 =
B. 1.55
155
1.55 = 100
= 155 ÷ 5
100 ÷ 5
31 or 1 11
=
20
20
Reading Math
You read the decimal 0.018 as “eighteen thousandths.”