Lesson 1T ~ Greatest Common Factor
Name__________________________________________
Period______
Date____________
List the factors of each number. Decide whether the number is prime or composite.
1.
9
2. 5
___× ___ = 9
___× ___ = 5
___× ___ = 9
Is 9 prime or composite? ______________
3. 11
Is 5 prime or composite? ______________
4. 15
Is 11 prime or composite? ______________
Is 15 prime or composite?_______________
5. Follow the steps to find the greatest common factor (GCF) of 4 and 6.
a. List the factors of 4: ____, ____, ____
b. List the factors of 6: ____, ____, ____, ____
c. Circle the common factors of 4 and 6 in parts a and b.
d. The largest factor that was circled is: ____. This is the GCF of 4 and 6.
Find the greatest common factor for each set of numbers.
6. 3, 9
7. 6, 8
8. 8, 12
GCF = ________
GCF = ________
GCF = ________
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
Find the greatest common factor for each set of numbers.
9. 10, 20
10. 12, 18
11. 10, 15
GCF = ________
GCF = ________
GCF = ________
12. Jordan has 20 drama DVDs and 25 action DVDs. He wants to arrange them on shelves so that
the two types of DVDs are separate. He wants as many DVDs on a shelf as possible, but an
equal number of DVDs on each shelf. How many DVDs should he put on each shelf?
a. Factors of 20: ____, ____, ____, ____, ____, ____
b. Factors of 25: ____, ____, ____
c. What is the greatest common factor of the two numbers? ________
d. Use the GCF to write your answer in a complete sentence:
Jordan should put ________ DVDs on each shelf.
13. Matt has 32 photos of the Grand Canyon and 24 photos of Mount Rushmore. He wants to put
them in rows on posters to show his class. He wants the same number of photos in each row. He
does not want to mix the photos of different places. What is the largest number of photos he
should put in each row?
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
Lesson 2T ~ Equivalent Fractions
Name__________________________________________
Period______
Date____________
1. Draw a model of each fraction on the rectangle provided.
1.
2
3
2.
1
2
3.
2
5
3
4
4
8
1
4
Equivalent? Yes / No
Equivalent? Yes / No
Equivalent? Yes / No
Solve each problem.
4. William said that 13 of his gumballs were yellow. Christine said that
yellow. Did they have the same fraction of yellow gumballs?
a. Draw a model of
1
3
on the first rectangle provided.
b. Draw a model of
5
8
on the second rectangle provided.
5
8
of her gumballs were
c. Did they have the same fraction of yellow gumballs? ________
5. Asha painted 52 of her room. Monica painted
fraction of their rooms? ________
©2008 SMC Curriculum
4
10
of her room. Did they each paint the same
Oregon Focus on Fractions and Decimals
6. Follow these steps to find the missing number in:
3
=
4 8
3
4
a. What should you multiply the first denominator by
=
to get the second denominator?
8
×
×
b. Multiply the numerator by the same number as in part a
3
4
=
8
to fill in the missing number:
Find the missing number.
7.
1
3
4
=
8.
9. Follow these steps to find the missing number in:
1
6
=
18
10 1
=
20
a. What should you divide the first numerator by
÷
10
20
=
10
20
=
1
to get the second numerator?
b. Divide the denominator by the same number as in
1
÷
part a to fill in the missing number:
Find the missing number.
10.
9
12
=
©2008 SMC Curriculum
3
11.
16
20
=
5
Oregon Focus on Fractions and Decimals
Lesson 3T ~ Simplifying Fractions
Name__________________________________________
1. Follow these steps to simplify the following fraction:
Period______
Date____________
12
14
a. What is the GCF of 12 and 14? _______
b. Simplify the fraction by dividing the numerator (top) and denominator (bottom) of the
fraction by the GCF.
÷
12
14
÷
2. Follow these steps to simplify the following fraction:
5
8
a. What is the GCF of 5 and 8? _______
b. If the GCF of two numbers is 1, then the fraction is in simplest form. Is
5
8
in simplest
form? _____________
Write each fraction in simplest form. If the fraction is already in simplest form, write simplest
form.
3.
8
10
4.
7
9
5.
10
12
6.
11
15
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
Number of Students
Ms. Jensen's Class' Summer Plans
20
15
15
10
10
5
5
0
Summer Job
Summer Camp
Travel
Students' Sum m er Plans
7. a. How many students said they would work a summer job? _____
b. How many students are in Ms. Jensen’s class? Add the following:
Summer Job:
_____
Summer Camp: _____
Travel:
+_____
TOTAL STUDENTS: _____
c. Write the number from part a over the total students from part b.
# of students who said they would work a summer job
total students
=
d. Simplify the fraction from part c. _____
e. Write the answer from part c in a complete sentence.
of the students from Ms. Jensen’s class said they would work a summer job.
8. What fraction of students from Ms. Jensen’s class said they would go to a summer camp? Write
in simplest form.
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
Lesson 4T ~ Least Common Multiple
Name__________________________________________
Period______
Date____________
List the first five non-zero multiples for each number.
1.
5
5 × 1 = ____
5 × 2 = ____
5 × 3 = ____
5 × 4 = ____
5 × 5 = ____
2. 9
9 × 1 = ____
9 × 2 = ____
9 × 3 = ____
9 × 4 = ____
9 × 5 = ____
3. Find the least common multiple (LCM) for the numbers: 4 and 8
a. List the first five non-zero multiples for the number 4: ____, ____, ____, ____, ____
b. List the first five non-zero multiples for the number 8: ____, ____, ____, ____, ____
c. What are the common multiples in your lists for the numbers 4 and 8? _____ and _____
d. Which of the numbers in part c is the smallest? This is the LCM of 4 and 8. _______
Find the least common multiple for each pair of numbers.
4. 3 and 5
5. 5 and 6
LCM = ____________
LCM = ____________
6. 6 and 12
7. 8 and 10
LCM = ____________
LCM = ____________
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
8. Sarah washes light clothes every 2 days. She washes dark clothes every 4 days. She washed both
light and dark clothes today. How many days until she washes both light and dark clothes again
on the same day?
a. Find the least common multiple of the two numbers in the problem. LCM = _______
b. Answer the question using the LCM:
Sarah will wash both light and dark clothes again on the same day in _____ days.
9. T.J. visits his neighbors every 8 days. He visits his sister every 6 days. He visited his neighbors
and his sister today. How many days until T.J. visits both his neighbors and his sister again on the
same day?
10. Find the least common denominator (LCD) of the fractions:
1 1
,
3 4
a. What are the two denominators? _____ and _____
b. Find the least common multiple of the two numbers in part a. LCM = ______
c. The LCD is the same as the LCM.
LCD = ______
Find the least common denominator (LCD) of each pair of fractions.
11.
1 5
,
2 8
LCD = ____________
12.
3 2
,
5 15
LCD = ____________
13.
5 3
,
6 4
LCD = ____________
14.
2 5
,
9 12
LCD = ____________
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
Lesson 5T ~ Ordering and Comparing Fractions
Name__________________________________________
Period______
Date____________
Write the fraction for each drawing. Circle the largest fraction in each pair.
1.
2.
_______
_______
_______
_______
3. Compare fractions.
a. Find the least common denominator (LCD) for the fractions
1
1
and . LCD = ______
3
2
b. Make new fractions with common denominators (the LCD) by multiplying the numerator and
the denominator by the same number.
×
×
1
3
1
2
×
×
LCD
LCD
c. Use the fractions from part b and <, > or = to make a true sentence.
d. Put the original fractions back in the sentence using the <, > or = from part c.
Compare each pair of fractions. Fill in each
1
2
with <, > or = to make a true sentence.
4.
2
3
1
3
5.
3
8
5
8
6.
2
9
5
9
7.
2
4
1
2
©2008 SMC Curriculum
1
3
Oregon Focus on Fractions and Decimals
Compare each pair of fractions. Fill in each
8.
10.
with <, > or = to make a true sentence.
4
10
2
5
9.
2
3
3
4
11.
3
4
1
4
1
2
1
5
12. Follow the steps to put the following fractions in order from least to greatest.
a. Rewrite the fractions,
3 1 1
, , , using the least common denominator (LCD).
4 2 4
1
=
2
3
=
4
1
=
4
b. Put the new fractions in order from least to greatest.
___ < ___ < ___
c. Put the original fractions back in the sentence using the order from part b.
___ < ___ < ___
13. Put the following fractions in order from least to greatest:
3 1 7
,
,
5 10 10
Solve the problems.
14. Which is more,
2
3
of the cookies or
of the cookies? _______________________
7
14
15. Which is shorter,
©2008 SMC Curriculum
5
11
of a yard or
of a yard? _______________________
12
36
Oregon Focus on Fractions and Decimals
Lesson 6T ~ Mixed Numbers and Improper Fractions
Name__________________________________________
Period______
Date____________
1. Write an improper fraction as a mixed number in simplest form:
13
, divide the numerator (13) by the denominator (6) to get a whole number
6
quotient and the remainder.
a. For the fraction,
Whole number quotient: _______
6 13
Remainder: _______
b. Write the quotient as the whole number. The remainder goes over the original denominator to
make the fraction.
Remainder
6
Quotient
Write each improper fraction as a mixed number in simplest form.
2.
11
6
3.
7
2
4.
17
3
5.
20
9
6. Write the mixed number for seven-fourths.
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals
7. Write a mixed number as an improper fraction in simplest form:
a. For 2 14 , multiply the whole number by the denominator.
2 × 4 = ____
b. Add the numerator to the product from part a.
___ + 1 =___
c. Write the answer from part b above the original denominator.
4
Write each mixed number as an improper fraction.
8. 1 13
9. 2 34
10. 3 12
11. 2 52
12. What is three and one-fourth as an improper fraction?
Solve each problem.
13. A child napped for 1 83 hours. Write this time as an improper fraction.
14. A worm measured
©2008 SMC Curriculum
13
4
inches long. Write this measurement as a mixed number.
Oregon Focus on Fractions and Decimals
Lesson 7T ~ Measuring in Inches
Name__________________________________________
Period______
Date____________
1.
a. On the ruler, draw an arrow pointing at 1 18 in.
b. Is 1 18 inch closer to 1 inch, 1 12 inches or 2 inches? __________
Round each measurement to the nearest half inch.
2. 3 83 inches ≈ __________
15
3. 2 16
inches ≈ __________
4.
a. On the ruler, draw an arrow pointing at 1 165 in.
b. Is 1 165 inch closer to 1 inch, 1 14 inches, 1 12 inches or 2 inches? __________
Round each measurement to the nearest quarter inch.
13
inches ≈__________
5. 2 16
©2008 SMC Curriculum
6. 4 169 inches ≈__________
Oregon Focus on Fractions and Decimals
Measure each line to the nearest sixteenth of an inch.
7.
Answer: __________
8.
Answer: __________
9.
Answer: __________
10. Measure the length of the line to the nearest quarter of an inch.
a. Measure the exact length of the line. __________
b. Round the answer from part a to the nearest quarter inch. __________
Measure the length of each line to the nearest quarter inch.
11.
Answer: __________
12.
Answer: __________
Draw a line that has the given length.
13. 3 12 inches
14. 1 14 inches
©2008 SMC Curriculum
Oregon Focus on Fractions and Decimals