Transcript Interactive Chalkboard - Tuslaw Local School District

Lesson 5-1 Greatest Common Factor
Lesson 5-2 Simplifying Fractions
Lesson 5-3 Mixed Numbers and Improper Fractions
Lesson 5-4 Least Common Multiple
Lesson 5-5 Comparing and Ordering Fractions
Lesson 5-6 Writing Decimals as Fractions
Lesson 5-7 Writing Fractions as Decimals
Example 1 Find the GCF by Listing Factors
Example 2 Find the GCF by Using Prime Factors
Example 3 Use the GCF to Solve a Problem
Example 4 Use the GCF to Solve a Problem
Find the GCF of 36 and 48 by making a list.
Factors of 36
1, 36
2, 18
3, 12
4, 9
6, 6
Factors of 48
1, 48
2, 24
3, 16
4, 12
6, 8
The common factors are 1, 2, 3, 4, 6, and 12. The
greatest common factor, or GCF, of 36 and 48 is 12.
Use a Venn diagram to show the factors. Notice that the
factors 1, 2, 3, 4, 6, and 12 are the common factors of 36
and 48 and the GCF is 12.
Answer: 12
Find the GCF of 45 and 75 by making a list.
Answer: 15
Find the GCF of 52 and 78 by using prime factors.
Method 1 Write the prime factorization.
52
78
Method 2
Divide by prime numbers.
Divide both 52 and
78 by 2. Then divide
the quotients by 13.
Using either method, the common prime factors are
2 and 13.
Answer: So, the GCF of 52 and 78 is
Find the GCF of 64 and 80 by using prime factors.
Answer: 16
SALES Annessa sold bags of cookies at a bake sale.
She sold small, medium, and large bags, with a
different number of cookies in each size bag. By the
end of the sale, she used 18 cookies to fill the small
bags, 27 cookies to fill the medium bags, and 45
cookies to fill the large bags. She sold the same
number of bags for the three sizes. What is the
greatest number of bags that she could have sold?
factors of 18: 1, 2, 3, 6, 9, 18
factors of 27: 1, 3, 9, 27
factors of 45: 1, 3, 5, 9, 15, 45
List all the
factors of each
number. Then
find the greatest
common factor.
The GCF of 18, 27, and 45 is 9.
Answer: So, the greatest number of bags she could have
sold is 9 of each size, or
CANDY Sarah is making bags of candy for a school
fund-raiser. She is making three different sizes of bags.
By the time Sarah had finished making the bags, she
had used 24 lollipops to fill the small bags, 40 lollipops
to fill the medium bags, and 64 lollipops to fill the large
bags. She completed the same number of bags for the
three sizes. What is the greatest number of bags she
could have made?
Answer: 24 bags
SALES Annessa sold bags of cookies at a bake sale.
She sold small, medium, and large bags, with a
different number of cookies in each size bag. By the
end of the sale, she used 18 cookies to fill the small
bags, 27 cookies to fill the medium bags, and 45
cookies to fill the large bags. If Annessa sold
nine bags of each size, how many cookies were in each
size bag?
small bags:
medium bags:
large bags:
Answer: 2 in the small bags, 3 in the medium bags, and
5 in the large bags
CANDY Sarah is making bags of candy for a school
fund-raiser. She is making three different sizes of bags.
By the time Sarah had finished making the bags, she
had used 24 lollipops to fill the small bags, 40 lollipops
to fill the medium bags, and 64 lollipops to fill the large
bags. If Sarah sold eight bags of each size, how
many lollipops were in each size bag?
Answer: 3 in the small bags, 5 in the medium bags,
and 8 in the large bags
Example 1 Write Equivalent Fractions
Example 2 Write Equivalent Fractions
Example 3 Write Fractions in Simplest Form
Example 4 Express Fractions in Simplest Form
Replace the  with a number in
are equivalent.
so the fractions
multiply the numerator and denominator
by 4.
Answer:
Replace the  with a number in
are equivalent.
Answer:
so the fractions
Replace the  with a number in
are equivalent.
so the fractions
divide the numerator and denominator by 8.
Answer:
Replace the  with a number in
are equivalent.
Answer:
so the fractions
Write
in simplest form.
Method 1
Divide by common factors.
2 is a common
factor of 14 and 42.
7 is a common
factor of 7 and 21.
Answer: Since 1 and 3 have no common factor greater
than 1, the fraction
is in simplest form.
Method 2
Divide by the GCF.
factors of 14: 1, 2, 7, 14
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The GCF of 14 and 42 is 14.
Divide the numerator and denominator by
the GCF, 14.
Answer: Since the GCF of 1 and 3 is 1, the fraction
in simplest form.
is
Write
Answer:
in simplest form.
GYMNASTICS Lin practices gymnastics 16 hours each
week. There are 168 hours in a week. Express the
fraction
in simplest form.
Divide the numerator and
denominator by the GCF, 8.
Answer: In simplest form, the fraction
So, Lin practices gymnastics for
is written
of the week.
TRANSPORTATION There are 244 students at
Longfellow Elementary School. Of those students, 168
ride a school bus to get to school. Express the fraction
in simplest form.
Answer:
Example 1 Mixed Numbers as Improper Fractions
Example 2 Mixed Numbers as Improper Fractions
Example 3 Improper Fractions as Mixed Numbers
Draw a model for
fraction.
Then write
as an improper
Since the mixed number
is greater than 3, draw four
models that are divided into
eight equal sections to
show eighths.
Then shade three wholes
and three eighths.
Answer: There are twenty-seven
written as
So,
can be
Draw a model for
fraction.
Answer:
Then write
as an improper
ASTRONOMY If a spaceship lifts off the Moon, it must
travel at a speed of
kilometers per second in order
to escape the pull of the Moon’s gravity. Write this
speed as an improper fraction.
2
Answer: The speed is
kilometers per second.
EXERCISE As part of a regular exercise program, Max
walks
miles each morning. Write this distance as an
improper fraction.
Answer:
Write
as a mixed number.
Divide 23 by 4.
Use the remainder as the
numerator of the fraction.
Answer:
Write
Answer:
as a mixed number.
Example 1 Find the LCM by Making a List
Example 2 Find the LCM by Using Prime Factors
Example 3 Use the LCM to Solve a Problem
Find the LCM of 4 and 9 by making a list.
Step 1 List the nonzero multiples.
multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …
Step 2 Identify the LCM from the common multiples.
Answer: The LCM of 4 and 9 is 36.
Find the LCM of 6 and 14 by making a list.
Answer: 42
Find the LCM of 8 and 18 by using prime factors.
Step 1 Write the prime factorizations of each number.
8
18
Step 2 Identify all common prime factors.
Step 3 Find the product of the prime factors using each
common prime factor once and any remaining
factors.
Answer:
Find the LCM of 9 and 21 by using prime factors.
Answer: 63
MONEY Liam, Eva, and Brady each have the same
amount of money. Liam has only nickels, Eva has only
dimes, and Brady has only quarters. What is the least
amount of money that each of them could have?
Find the LCM of 5, 10, and 25 using prime factors.
5
10
25
Answer: The least amount of money that each of them
could have is
or 50 cents.
CANDY Michael, Logan, and Diego each have bags of
candy that have the same total weight. Michael’s bag
has candy bars that each weigh 4 ounces, Logan’s bag
has candy bars that each weigh 6 ounces, and Diego’s
bag has candy bars that each weigh 9 ounces. What is
the least total weight that each of them could have?
Answer: 36 ounces
Example 1 Compare Fractions
Example 2 Order Fractions
Example 3 Compare and Order Fractions
Replace with < , > or = to make
true.
First, find the LCD; that is, the LCM of the denominators.
The LCM of 21 and 7 is 21. So, the LCD is 21.
Next, rewrite each fraction with a denominator of 21.
Then compare the numerators.
Answer:
Replace with < , > or = to make
Answer:
true.
Order the fractions
and from least
to greatest.
The LCD of the fractions is 15. So, rewrite each fraction
with a denominator of 15.
Answer: The order of the fractions from least to greatest
is
Order the fractions
to greatest.
Answer:
and
from least
MULTIPLE-CHOICE TEST ITEM According to the
table, how is most land in the United States used?
A as arable land
Land Use in the
B as permanent pastures
C as forests and woodland
D B and C are equal
United States
arable
(cropland)
permanent
pastures
forests and
woodlands
other
Source: CIA World Fact Book
Read the Test Item
You need to compare the fractions.
Solve the Test Item
Rewrite the fractions with the LCD, 100.
So,
is the greatest fraction.
Answer: C
MULTIPLE-CHOICE TEST ITEM According to a
survey data, what did most people say should be
done with the length of the school year?
A lengthen the school year
B shorten the school year
C keep the length the same
D cannot tell from the data
Answer: A
How long should the
school year be?
lengthen the
school year
shorten the
school year
keep the length
the same
Example 1 Write Decimals as Fractions
Example 2 Write Decimals as Fractions
Example 3 Write Decimals as Fractions
Example 4 Write Decimals as Mixed Numbers
Write the decimal 0.4 as a fraction in simplest form.
The place-value chart shows that the place value of the last
decimal place is tenths. So, 0.4 means four tenths.
0.4 means four tenths.
2
5
Simplify. Divide the numerator and
denominator by the GCF, 2.
Answer: In simplest form, 0.4 is written as
Write the decimal 0.8 as a fraction in simplest form.
Answer:
Write the decimal 0.38 as a fraction in simplest form.
0.38 means thirty-eight hundredths.
19
Simplify. Divide by the GCF, 2.
50
Answer:
Write the decimal 0.64 as a fraction in simplest form.
Answer:
Write the decimal 0.264 as a fraction in simplest form.
0.264 means two hundred sixty-four
thousandths.
33
Simplify. Divide by the GCF, 8.
125
Answer:
Write the decimal 0.824 as a fraction in simplest form.
Answer:
RAINFALL In 1955, Hurricane Diane moved through
New England and produced one of the region’s
heaviest rainfalls in history. In a 24-hour period, 18.15
inches of rain were recorded in one area. Write this
amount as a mixed number in simplest form.
3
Simplify.
20
Answer:
BICYCLING While training for a bicycle race, Ted rides
an average of 23.56 miles per day. Write this distance
as a mixed number in simplest form.
Answer:
Example 1 Write Fractions as Terminating Decimals
Example 2 Write Fractions as Repeating Decimals
Example 3 Write Fractions as Repeating Decimals
Write
as a decimal.
Method 1 Use paper and pencil.
Divide 3 by 8.
0
Method 2
3
8
Answer:
Use a calculator.
ENTER
0.375
Write
as a decimal.
Answer: 0.625
Write
as a decimal.
Method 1 Use paper and pencil.
Divide 5 by 12.
The pattern
will continue.
Method 2
5
12
Answer:
Use a calculator.
ENTER
0.41666666666…
Write
Answer:
as a decimal.
BEVERAGES At a meeting, people drank 23 cans of
soda. This makes
six-packs. Write this number as
a decimal.
You can use a calculator to write
3
5
6
ENTER
as a decimal.
3.83333333
Answer: At the meeting,
were drunk.
six-packs of soda
PIZZA PARTY At a pizza party, people ate 35 slices of
pizza. This makes
decimal.
Answer: 4.375
pizzas. Write this number as a