Transcript EXAMPLE 1 Writing a Fraction in Simplest Form History One of the Czech Republic’s royal coronation jewels is the St.

EXAMPLE 1
Writing a Fraction in Simplest Form
History
One of the Czech Republic’s royal coronation jewels is
the St. Wenceslas crown. It was made around 1345 and
is decorated with 44 spinels, 30 emeralds, 22 pearls, 19
sapphires, and 1 ruby. Write the fraction of jewels in
the crown that are emeralds in simplest form.
EXAMPLE 1
Writing a Fraction in Simplest Form
SOLUTION
Write the fraction of jewels in the crown that are
emeralds. Then simplify.
Number of emeralds
Total number of jewels in the crown
=
30
116
EXAMPLE 1
Writing a Fraction in Simplest Form
Write the fraction of jewels in the crown that are
emeralds. Then simplify.
METHOD 1
Find and use the GCF of
30 and 116.
30 = 2 3 5
116 = 22 29
EXAMPLE 1
Writing a Fraction in Simplest Form
The GCF of 30 and 116 is 2.
30
30 2
=
116 116 2
=
15
58
Divide numerator and
denominator by GCF.
Simplify.
EXAMPLE 1
Writing a Fraction in Simplest Form
METHOD 2
Use prime factorization.
30
2 3 5
=
116 2 2 29
Write prime factorizations.
1
=
2 3 5
2 2 29
Divide out common factor.
1
15
58
Simplify.
ANSWER
The fraction of jewels that are emeralds is 15 .
58
GUIDED PRACTICE
for Example 1
Use the information from Example 1. Write the fraction
of jewels in the crown that are the given jewel.
Simplify if possible.
1.
Pearls
GUIDED PRACTICE
for Example 1
ANSWER
The fraction of jewels that are pearl is
11
.
58
GUIDED PRACTICE
for Example 1
Use the information from Example 1. Write the fraction
of jewels in the crown that are the given jewel.
Simplify if possible.
2.
Sapphires
GUIDED PRACTICE
for Example 1
ANSWER
The fraction of jewels that are sapphires is
19
116
GUIDED PRACTICE
for Example 1
Use the information from Example 1. Write the fraction
of jewels in the crown that are the given jewel.
Simplify if possible.
3.
Spinels
GUIDED PRACTICE
for Example 1
ANSWER
11
The fraction of jewels that are spinels is
29