Possible answer: The 4 in 1 __ means the whole is divided into 4 Download

Transcript
Name
1-1
Date
Use the fraction bar below for Exercises 1–4.
1
7
1. Label the first part of this fraction bar with the correct
unit fraction.
2. Circle the first four parts of the bar. What fraction of the whole
does this circled portion represent?
4
__
7
3. Write your fraction from Exercise 2 as a sum of unit fractions.
4 = __
1 + __
1 + __
1 + __
1
__
7
7
7
7
7
4. Represent the whole as the sum of the unit fractions.
1 + __
1 + __
1 + __
1 + __
1 + __
1 + __
1 = __
7 =
__
1
7
7
7
7
7
7
7
7
5. Solve the problem below by circling parts of the fraction bar.
Write the appropriate equation below the bar.
© Houghton Mifflin Harcourt Publishing Company
Brett is building a fence around his yard. He has worked on it
3
2
the first week and __
the
for two weeks so far. He finished __
8
8
second week. What fraction of the entire fence has he built?
5
__
8
Eighths
2
8
+
3
8
=
5
8
6. Nena thinks that because 4 < 6, it must also be true that
1 < __
1
__
. Explain to Nena why this is incorrect.
4
6
1
1
Possible answer: The 4 in __
means the whole is divided into 4 parts. __
is
4
4
1
means the whole is divided into 6 parts.
one of those parts. The 6 in __
6
1
__
is one of those parts. The more parts we divide a whole into the
6
1 < __
1
.
smaller each part will be, so __
4
6
UNIT 1 LESSON 1
Introducing the Math Board
1
1-1
Name
Date
List all the factors of each number.
1. 16 1, 2, 4, 8, 16
2. 29 1, 29
3. 33 1, 3, 11, 33
4. 40 1, 2, 4, 5, 8, 10, 20, 40
List the first four multiples of each number.
5. 6 6, 12, 18, 24
6. 11 11, 22, 33, 44
7. 15 15, 30, 45, 60
8. 1 1, 2, 3, 4
Complete.
2
1 + __
1 = __
9. __
3
3
3
1
6 – ___
5 = ___
11. ___
10 10
10
2
4 – __
2 = __
13. __
9 9
9
5
3 = __
2 + __
10. __
7
7
7
6
4 + __
2 = __
, or 1
12. __
6
6
6
3
1 + ___
1 + ___
1 = ___
14. ___
10
10
10
10
Write an equation. Then solve the problem. Equations may vary.
15. Maggie has a ribbon 27 feet long.
What is the length of the ribbon in
yards?
16. Mañuel has 15 goldfish. This is
6 more than Quinn has. How many
goldfish does Quinn have?
Equation: 27 ÷ 3 = n
Equation: n + 6 = 15
Answer: 9 yards
Answer: 9 goldfish
18. Julie bought 19 beads at the craft
store. Now she has 36 beads. How
many beads did she have before she
went to the craft store?
Equation: 4 • 13 = n
Equation: n + 19 = 36
Answer: 52 students
Answer: 17 beads
19. Stretch Your Thinking Rashid bought some baseball cards.
After giving 7 cards to his friend Grace, he arranged the
remaining cards in 6 rows of 4. How many cards did he buy?
Equation: n - 7 = 6 • 4
Answer: 31 cards
2
UNIT 1 LESSON 1
Introducing the MathBoard
© Houghton Mifflin Harcourt Publishing Company
17. In their yearbook photo, students in
the chorus stood in four rows with
13 students in each row. How many
students are in the photo?
Name
1-2
Date
1. Write a chain of equivalent fractions for the shaded parts.
=
1
__
2
=
=
2
__
4
=
=
3
__
=
4
__
=
6
=
8
8
___
16
Use the number lines to complete Exercises 2–7.
Fourths
0
—
4
1
—
4
2
—
4
3
—
4
4
—
4
0
—
8
2
—
8
4
—
8
6
—
8
8
—
8
0
—
12
3
—
12
6
—
12
9
—
12
12
—
12
Eighths
© Houghton Mifflin Harcourt Publishing Company
Twelfths
3
__
2. What fraction is marked by the star?
3. What fraction is marked by the heart?
8
8
___
12
3
4. If you have __
cup of flour, how many eighths do you have?
4
6
__
8
3
5. If you have ___
of an orange, how many fourths do you have?
12
1
__
4
10
___
3
10
__
___
12
6. Which is greater, or ?
4
12
9
3
__
Possible answers: ___
6
4
12
__
7. Give two equivalent fractions for .
8
UNIT 1 LESSON 2
Explain Equivalent Fractions
3
Name
1-2
Date
Add or subtract.
57,533
1. 4,560 + 52,973 =
3. 4,300,129 + 3,426 =
4,303,555
2. 581,002 + 26,596 =
607,598
4. 398,000 – 213,546 =
184,454
5. Solve the problem below by circling parts of the fraction
bar. Write the appropriate equation below the bar.
2
of the
Molly is driving across the country. She covered ___
10
3
___
on the second day. What
distance on the first day and
10
fraction of the distance did she cover in the first two days?
5
___
10
2
—
10
3
—
10
+
=
5
—
10
Complete.
1 + __
1 + __
1 + __
1 =
6. __
8
8
8
4 – __
1 =
8. __
5
1
__
3
8
2
3
__
5
2 =
+ __
1
3
6
9
12. Stretch Your Thinking Alyssa said that __
and ___
are not
8
12
equivalent because there is no whole number you can
6
9
by to get ___
. Is she correct? Explain.
multiply both parts of __
8
12
She is not correct. Possible explanation: You can
3
6
by 2 to get __
and by 3
multiply both parts of __
4
8
9
6
9
to get ___. Because both __ and ___ are equivalent
12
8
12
3
__
to , they are equivalent to each other.
4
4
UNIT 1 LESSON 2
Explain Equivalent Fractions
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10.
5
8
10
3 = ___
7 + ___
, or 1
7. ___
10
10
10
2
___
8 +
=1
9. ___
10
10
1
__
3 =
11. 1 – __
4
4
4
1
__
, or __
Name
1-3
Date
1. Write a chain of equivalent fractions for the shaded parts.
=
2
__
=
3
__
=
4
6
=
1
__
=
=
8
___
=
2
16
=
4
__
8
Write the multiplier or divisor for each pair of equivalent fractions.
6
2 = ___
3. __
4 = __
1
2. ___
12
3
5. Divisor =
9
4
56
5
5. Divisor =
9
4
© Houghton Mifflin Harcourt Publishing Company
56
6
6
10 = __
1
10. ___
45
60
5
6
7. Divisor =
10
5 = ___
35
13. __
7
6. Divisor =
42
7. Multiplier =
3
24 = __
12. ___
42
5. Multiplier =
7
6. Multiplier =
3 = ___
18
11. __
7
7
5 = ___
25
9. __
4
6
5 = ___
30
7. __
8
6. Divisor =
4 = __
1
8. ___
10
7. Divisor =
3
21 = __
6. ___
50
5. Multiplier =
16
60
3
6. Multiplier =
3 = ___
15
5. ___
10
6 = ___
1
4. ___
27
6
8
42
7
7. Multiplier =
Complete each exercise about the pairs of fraction bars.
2 ___
__
, 4
5 10
14. What equivalent fractions are shown?
2
15. Identify the multiplier.
16. What equivalent fractions are shown?
17. Identify the divisor.
6 __
__
,2
9 3
3
18. Write a chain with at least six equivalent fractions.
9
12
3
6
___
___
__
___
=
=
=
15
20
5
10
=
15
___
25
=
18
___
30
Answers will vary. This is one possible answer.
UNIT 1 LESSON 3
Equivalent Fractions and Multipliers
5
1-3
Name
Date
In Exercises 1–3, use this fraction bar.
1. Shade two of the equal parts. What fraction does
the shaded portion model?
2
__
3
2. Split each equal part (each unit fraction) into two equal
parts. What fraction does the shaded portion model now?
4
_
6
3. Fill in the boxes to show how you unsimplified the original
fraction.
2×
2
4
_
= _
3×
2
6
Show your work.
Solve.
4. A restaurant has 60 plates. One night, 9 groups of 6 people
ate dinner at the restaurant at the same time. How many
plates were not used by these diners?
6 plates
2 plants
6. Stretch Your Thinking Carol’s bookshelf has 4 shelves with
6 books on each. Her brother Robert has 3 shelves with
7 books on each. They want to combine their books. If
they put 9 books on a shelf, how many shelves will they need?
5 shelves
6
UNIT 1 LESSON 3
Equivalent Fractions and Multipliers
© Houghton Mifflin Harcourt Publishing Company
5. Clara has a garden that is 7 feet wide and 4 feet long.
She has 30 tomato plants to put in the garden. Each
plant needs 1 square foot of space. How many leftover
plants will Clara have?
Name
1-4
Date
Compare.
5 > __
5
1. __
1 < __
1
2. __
2
< __3
3. __
6
> __2
4. __
10 < ___
11
5. ___
3 < ___
5
6. __
5
< __4
7. ___
1 < __
4
8. __
1 > __
2
9. __
1
1
10. ___
> ___
7 < ___
11
11. ___
8
8
12
12
5
9
11
3
7
15
3
10
4
5
12
8
4
9
15
5
12
9
51
12 < ____
12. ___
25
100
Show your work.
Solve.
13. During his first season on the school football team, Wade
made 5 of the 9 field goals he tried. During his second
season, he made 11 of the 15 field goals he tried. In which
season did he make the greater fraction of the field goals
he tried?
during the second season
11
7
14. Mañuela bought ___
yard of polka dot fabric and __
yard
12
9
of flowered fabric. Which fabric did she buy more of?
© Houghton Mifflin Harcourt Publishing Company
the polka dot fabric
15. Of the 7 pens in Ms. Young’s desk, 3 are blue. Of the 9 pens
in Mr. Fox’s desk, 5 are blue. Which teacher has a greater
fraction of pens that are blue?
Mr. Fox
16. Mr. Sommers spent 10 minutes of his 50-minute math
period reviewing homework. Mr. Young spent 12 minutes
of his 60-minute math period reviewing homework.
Which teacher spent a greater fraction of his math period
reviewing homework?
1
of the period
Neither; both teachers spent __
5
reviewing homework.
UNIT 1 LESSON 4
Strategies for Comparing Fractions
7
Name
1-4
Date
Complete.
3
__
1 + __
1 + __
1 =
1. __
4
4
4 + __
1 =
3. __
5
4
4
5
4
__
8 – __
4 =
2. __
9
5
__
, or 1
3 + __
3 =
4. __
5
9
9
8
8
6
3
__
, or __
4
8
Write the multiplier or divisor for each pair of
equivalent fractions.
5 = ___
10
5. __
6
15
2
Multiplier =
5
4
5
Divisor =
4
___
5 =
12. __
10
___
9
10
22
18
7
Multiplier =
=
6
___
=
15
___
15
27
=
8
___
=
20
___
20
36
=
10
___
=
25
___
25
45
6
11 = __
1
10. ___
28
Complete the chain of equivalent fractions.
5
24
Multiplier =
1 = ___
7
9. __
10
2 =
11. __
4
3
Divisor =
25 = ___
5
8. ___
50
3 = ___
18
7. __
12 = __
4
6. ___
12
=
2
Divisor =
11
Answers may vary. Possible answers
are given.
12
14
___
___
=
=
30
30
___
54
35
=
35
___
63
Solve.
He is not correct. The size of the whole was
different for the two pizzas. Half of a large
pizza is more than half of a small pizza
because it is half of a larger amount.
8
UNIT 1 LESSON 4
Strategies for Comparing Fractions
© Houghton Mifflin Harcourt Publishing Company
4
of a large pizza. Aidan
13. Stretch Your Thinking Harry ate __
8
1
4
__
is equivalent
ate of a small pizza. Harry said that since __
2
8
1
__
to , he and Aidan ate the same amount of pizza. Is he
2
correct? Explain.
Name
1-5
Date
Name the mixed number shown by the shaded parts.
1
3__
1.
2.
2
2
2__
3
1__
3.
3
7
Write the mixed number as a fraction.
7
__
1 =
4. 2__
2 =
5. 4__
3
3
5
22
___
5
3 =
6. 3__
15
___
9 =
10. __
1
4__
5 =
7. 1__
4
4
8
13
___
8
Write the fraction as a mixed number.
1
1__
7 =
8. __
8 =
9. __
6
6
3
2
2__
3
10 =
11. ___
2
2
7
3
1__
7
Complete. Give the answer as a mixed number.
3 + __
4 =
12. __
5
5
8 =
2 + __
14. __
9
9
2
1__
5
6 + __
3 =
13. __
1
2__
2 =
15. 7 + __
2
7__
4
1
1__
9
4
3
4
Show your work.
Solve.
© Houghton Mifflin Harcourt Publishing Company
3
6
7
16. Alicia walked __
mile on Saturday and __
mile on Sunday.
8
8
How far did she walk over the weekend? Give the
answer as a mixed number.
5
1__
miles
8
5
17. The dark chain is ___
yard long. The light one is
12
9
___
yard long. How long will they be if they are
12
joined? Give the answer as a mixed number.
2
yards
1___
12
5 yd
—
12
UNIT 1 LESSON 5
9 yd
—
12
Fractions Greater Than One
9
Name
1-5
Date
Solve.
5
of the way across the yard. How much
1. The dog has gone __
8
farther does it have to go to reach the gate?
3
__
of the way
8
7
2. The cat has gone ___
of the way across the yard. How much
16
farther does it have to go to reach the gate?
9
___
of the way
16
6
2
3. I cleaned __
of my room, and my friend cleaned __
of my
9
9
room. How much of my room do we still have to
clean?
1
__
9
8
4. Mrs. Spencer’s class is signing up to play sports. ___
of the
26
12
students want to play soccer and ___ want to play basketball.
26
The rest of the students want to play baseball. What fraction
of the students wants to play baseball?
6
___
26
13
7 > ___
7. ___
2 > __
1
5. __
4 > ___
4
6. __
3 > __
1
8. __
6
4 = __
9. __
9
5
4 < __
10. __
3 > __
4
12. __
7 < __
7
13. __
6
5
6
3
3
7 < __
11. ___
12
4
9
6
5
10
9
12
5
9
24
6
8
14. Stretch Your Thinking Find two fractions that are
3
4
and __
.
between __
5
5
7 ___
Possible answers: ___
, 11
10 15
10
UNIT 1 LESSON 5
Fractions Greater Than One
© Houghton Mifflin Harcourt Publishing Company
Compare.
Name
1-6
Date
Add or subtract.
3 + __
4
1. __
6 + __
3
2. __
2
1__
1
2__
5
5
4
5
2 + __
3. 4__
27
4
9
7
4
7 + __
4. 1__
33
8
9
2
1
or 5__
5__
4
8
4 - __
7. 6__
32
5
6 - __
6. 4__
25
7 - __
4
5. 1__
8
5
2
3__
7
9
3
1
1__
or 1__
9
7
3
5 1
8. 25__
10__
8
1 + __
9. 4__
51
8
8
1 + __
10. 3__
21
7
7
2
2
5__
1 +
1
12. 50__
50__
7
3
1
3__
7
3
2
1__
3
3
3 - __
14. 5__
27
8
1 - __
15. 2__
15
8
6
6
2
1
__
or __
4
1
2__
or 2__
8
2
6
3
Show your work.
Solve.
© Houghton Mifflin Harcourt Publishing Company
3
2
100__
7
1
13. 2 - __
2
10
2
5 + __
11. 1__
13
7
7
1
2__
4
1
15__
or 15__
5
9
5
7
inches long, but a section 1__
inches
16. I made a clay snake 9__
8
8
long broke off. How long is the snake now?
6
3
7__
in. or 7__
in.
4
8
3
17. A group of campers hiked for 5__
hours today and
4
yesterday. How many hours did they hike in all?
2
1
hours or 12__
hours
12__
4
2
3
6__
hours
4
1
2
18. Deacon had 12__
ounces of juice, but he drank 3__
ounces.
3
3
How much juice is left?
2
8__
oz
3
UNIT 1 LESSON 6
Add and Subtract Mixed Numbers
11
Name
1-6
Date
Complete to form equivalent fractions.
1 = _____
4
1. __
2
24
6 = _____
3. __
12 = __
4
2. _____
5
15
8
7
28
Answers to Exercises 4–6 will vary. Possible answers are given.
6
4 = _____
4. _____
9
6
1
2
3
6. _____ = _____
25 = _____
5. ____
100
8
4
12
Compare.
3 < __
3
7. ___
10
8
5 > ___
19
10. __
6
24
5
4 < __
8. __
5 > __
2
9. __
3
4 < ___
11. ___
1 > ___
1
12. ___
5
15
7
6
10
Solve.
49
3
50
Show your work.
13. Rosa got 5 out of 7 answers correct on her science quiz.
Her older sister Ana got 4 answers out of 6 correct on her
science quiz. Which sister answered a greater fraction of
the questions correctly?
Rosa
© Houghton Mifflin Harcourt Publishing Company
85
14. The number 85% is equivalent to the fraction ____
. Pablo
100
spelled 21 out of 25 words correctly on his spelling test.
Is this more or less than 85% of the words?
less
3
15. Stretch Your Thinking Marla ate __
of a small pepperoni
8
3
2
__
of a
pizza and of a small cheese pizza. Damien ate ___
8
12
5
___
of a small mushroom pizza.
small veggie pizza and
12
Who ate a greater fraction of a whole pizza?
Damien
12
UNIT 1 LESSON 6
Add and Subtract Mixed Numbers
Name
1-7
Date
Add.
1 + __
1
1. __
3
2
7 + __
1
2. ___
5
__
9
4
18
1 + __
2
5. __
6
3
13
___
5 + __
1
6. ___
11
22
6
3 + __
3
7. ___
4
15
___
16
3 + __
1
8. __
7
2
21
___
5
__
32
6
7
___
10
5 + __
1
4. ___
16
2 + __
1
3. __
9
___
6
32
5
10
3
5 + __
3
9. ___
16
___
21
Solve.
12
8
19
___
24
Show your work.
5
were
10. Of the people who attended the school play, ___
12
1
__
students and were teachers. What fraction of the
8
total audience were students or teachers?
13
___
24
© Houghton Mifflin Harcourt Publishing Company
2
1
11. Mara bought __
yard of yellow ribbon and __
yard of blue
4
3
ribbon. How many yards of ribbon did she buy altogether?
11
___
yard
12
5
12. For breakfast, Oliver drank ___
of a pitcher of juice.
16
3
__
His brother Joey drank of the pitcher of juice.
8
What fraction of a pitcher did they drink together?
11
___
16
3
1
13. A recipe calls for __
cup of brown sugar and __
cup of
4
3
white sugar. How much sugar is this altogether?
1
cups
1___
12
UNIT 1 LESSON 7
Add Unlike Fractions
13
Name
1-7
Date
Solve for n or d.
1 = ___
n
1. __
4
3 = ___
15
2. __
20
9 = __
1
3. ___
6
10 = __
n
4. ___
5
3 = ___
18
5. __
42
3 = ___
n
6. __
24
27 = __
n
7. ___
3
14 = __
2
8. ___
7
5 = ___
n
9. __
40
20
1 = ___
10. __
60
3
21 = __
11. ___
8
n
20 = __
12. ___
5
25
4
6
24
7
4
5
d
6
48
3
d
40
54
36
56
d
18
d
4
49
d
9
d
Add or subtract.
2
3__
1 + __
21
13. 1__
3
3
3
6
3
or 2__
2__
3 – __
5 8
__
4
16. 6
3
8
8
3 – __
14. 3__
11
5
5
2
2__
5
3 + __
15. 6__
35
8
8
4
2
or 4__
4__
5 + __
5 6
__
3
17. 1
2
1
18. 7 – 5__
7 > __
2
20. ___
3
1 < ___
21. __
19 < ___
20
23. ___
4 > __
7
24. __
6
6
10
4
3
1__
4
Compare.
3 < __
6
19. __
4
7
15
6 > ____
6
22. ____
100
101
20
5
21
8
Solve.
5
20
9
Show your work.
© Houghton Mifflin Harcourt Publishing Company
25. In a hockey game, Seth took 12 shots and scored 3 times.
Zak took 10 shots and scored twice. Who scored on a
greater fraction of his shots?
Seth
7
26. Jia rode her bike 7__
miles in the morning and another
8
5
__
6 miles in the afternoon. How many miles did she
8
ride altogether?
4
1
miles or 14__
miles
14__
8
2
27. Stretch Your Thinking Last season, Jenny made 3 out of
every 4 free throws she took. If she took 48 free throws,
how many did she make?
36 free throws
14
UNIT 1 LESSON 7
Add Unlike Fractions
Name
1-8
Date
Subtract.
8
4 - ___
2. __
1 - __
1
1. __
7
3
5
15
4
___
4
___
21
15
61 - ___
7
4. ____
100
7
6
9
11
___
18
4 - __
1
5. __
25
5 - __
2
3. __
6
6 - __
1
6. ___
11
2
33
___
17
___
1
___
100
42
22
Circle the greater fraction. Then write and solve a subtraction
problem to find the difference of the fractions. Common denominators in
9 = ___
55 - ___
54 = ___
subtraction problems may vary.
11 - ___
1
9
11 ___
___
7. ___
10
60
60
60
10 12 12
5
8. ___
18
1
__
3
5 = ___
6 - ___
5 = ___
1 – ___
1
__
3
18
18
18
18
Show your work.
© Houghton Mifflin Harcourt Publishing Company
Solve.
9. Marly passes the library on her way to school. The
3
mile.
distance from Marly’s house to the library is __
8
4
mile.
The distance from Marly’s house to the school is __
5
How far is it from the library to Marly’s school?
17
___
mile
40
1
7
10. Tim spends about __
of each weekday sleeping and about ___
3
24
of each weekday in school.
a. What fraction of a weekday does Tim spend either sleeping
or in school?
15
5
___
day or __
day
24
8
more
1
b. Is this more or less than __
a day?
2
3
1
___
day or __
day
8
c. How much more or less? 24
UNIT 1 LESSON 8
Subtract Unlike Fractions
15
Name
1-8
Date
Write each fraction as a mixed number.
1
2__
11 =
1. ___
3
1
57 = 9__
or 9__
3. ___
6
2
6
5
2__
21 =
2. ___
5
5
8
8
Write each mixed number as a fraction.
11
___
5 =
4. 1__
6
35
___
2 =
5. 11__
6
3
55
___
1 =
6. 6__
3
9
9
Add or subtract.
3 + __
2
7. __
7
3
7 – ___
8. ___
7
10
5
__
12
1 – __
12. 5__
12
12
12
3 + __
13. 4__
43
3
2
3
3 + __
1
15. ___
11
8
2
1
or 9__
9__
2
3
2
3__
5
14. 4 – 3__
4
4
10
6
1
or 4__
4___
6
4
7
___
5
10
11 – ___
11. 6___
25
6
5
10
4
2
___
or __
7
1 + __
10. 2__
35
6
3 + __
2
9. ___
10
3
3
__
20
___
8
33
Show your work.
Solve.
© Houghton Mifflin Harcourt Publishing Company
16. Ayala and Sam were partners on a science project. Ayala
3
hours working on the project. Sam spent
spent 2__
4
3
__
1 hours working on the project. How long did they
4
work altogether?
2
1
4__
hours or 4__
hours
4
2
17. Stretch Your Thinking Marti grouped all her CDs into
2
of my CDs are rock
separate categories. She said, “__
5
1
1
1
are country music.”
music, __ are jazz, __ are hip hop, and __
4
6
3
Explain why Marti’s statement cannot be correct.
Possible answer: The sum should be 1 to represent
2 + __
1
the whole collection, but it is greater than 1: __
5
6
10
20
15
9
3
1
1
24
__
__
___
___
___
___
___
___
+ + =
+
+
+
= 1 or 1 .
3
16
4
UNIT 1 LESSON 8
60
60
60
60
60
20
Subtract Unlike Fractions
Name
1-9
Date
Add or subtract.
1.
1
7__
2
5
+ 6__
8
_
2.
15
1
- 1__
5
_
5.
1
2___
7.
1
8__
6
7
- 2___
12
__
7
5___
12
5
9__
6.
6
1
- 4__
_8
9
5
+ 3__
_8
72
7
6__
9.
9
2
- 4__
_3
9
3___
14
2
- 1__
7
__
5
2___
1
2__
14
9
Show your work.
Solve.
© Houghton Mifflin Harcourt Publishing Company
1
1__
53
4___
24
8.
8
3
+ 2__
_4
8
17
5___
15
3
5__
1
8__
20
8
4
3___
3.
5
1
+ 5__
_4
17
7___
1
14__
4.
3
2__
5
1
feet tall. This year it is 10___
10. Last year my elm tree was 8__
6
12
feet tall. How much did it grow in one year?
1
1__
feet
4
3
1
11. Luis rode his bicycle 2___
miles before lunch. He rode 1__
4
10
miles after lunch. How far did Luis ride altogether?
11
3___
miles
20
1
1
12. Carrie spent 2__
hours trimming bushes and 1__
hours
4
2
weeding the garden. She is supposed to work in the yard
for 5 hours. How much longer does she need to work?
1
1__
hours
4
UNIT 1 LESSON 9
Solve with Unlike Mixed Numbers
17
Name
1-9
Date
Add or subtract. Try to do these in your head.
2
1
3 - __
1 = 2__
or 2__
2. 2__
4
4
4
2
1 + __
23 =
1. 3__
6
6 - __
4. 6__
52 =
4
1__
2 + __
5. 8__
12 =
3 + __
7. 3__
33 =
1
7__
4
1
7 - __
8. 7__
3 3 = 4__ or 4__
8
8
8
2
4
7
5
4
7
5
7
5
3
3
2 + __
3. 3__
44 =
1
8__
6 - __
6. 5__
12 =
4
4__
3 + __
9. 5__
35 =
9
5
1
10__
3
5
5
7
7
7
8
8
Write the fractions in order from least to greatest.
1 __
1 __
, 1 , __
,1
10. __
1 __
1 __
__
, 1 , __
,1
8 __
4 __
11. __
, 2 , __
,1
2 __
1 __
12. __
, 3 , __
,3
1 __
2 __
__
, 3 , __
,3
11 __
2 ___
13. ___
, 3 , __
, 19
9 3 6 2
3 5 2 4
9 6 3 2
1 __
4 __
__
, 2 , __
,8
9 9 9 9
9 9 9 9
2 5 3 4
3 ___
2 ___
__
, 19 , __
, 11
5 30 3 15
15 5 3 30
List three fractions equivalent to the given fraction. Answers will vary.
1
14. __
15
15. ___
4
16. __
9
17. ___
5
18
7
12
Show your work.
Solve.
1
cups of flour and
18. Ted is making a bread recipe that uses 3__
4
3
a muffin recipe that uses 2__ cups of flour.
4
b. How much flour does Ted need for both recipes?
6 cups
19. Stretch Your Thinking Find the values
of x and y in the drawing at the right.
7
4__
8
inches
x=
5
__
8 _1_ in.
14
8
8
inches
y=
6 _4_ in.
8
x
8 _1_ in.
8
3_2_ in.
8
y
18
UNIT 1 LESSON 9
Solve with Unlike Mixed Numbers
© Houghton Mifflin Harcourt Publishing Company
a. How much more flour is in the bread than in the muffins?
2
1
__
cup or __
cup
4
2
Name
1-10
Date
Add or subtract.
1.
3
2.
2
- 1__
_5
5.
29
5___
13
___
16
2
+ __
3
_
23
1___
48
5
7__
9
2
- 3___
15
__
19
4___
45
1
5__
8
1
- 4__
_5
6.
79
4____
100
9
+ 5___
10
__
37
___
42
7.
3.
2
5
6
6
+ __
_7
10
4
+ 2__
5
__
1
5__
3
1__
5
4. 4__
7
2___
69
10___
40
8.
1
8__
4
9
- 3___
20
__
100
9.
8
7__
9
7
+ 9__
_8
55
17___
4_4_
72
5
© Houghton Mifflin Harcourt Publishing Company
Solve.
1
cups of food each
10. The Taylors have four dogs. Molly eats 4__
2
3
3
2
__
__
cup.
day, Roscoe eats 3 cups, Milo eats 1 cups, and Fifi eats __
4
4
3
How much do the Taylors’ dogs eat each day altogether?
2
10__
cups
3
11. Refer to Problem 10. How much more food does Molly eat
each day than Roscoe?
_5_ cup
6
12. The vet told the Taylors (from Problem 10) to decrease the
3
cup. After Molly’s food is adjusted,
amount Molly eats by __
4
will she eat more or less than Roscoe each day? How much
more or less?
1
more; ___
cup
12
UNIT 1 LESSON 10
Practice with Unlike Mixed Numbers
19
Name
1-10
Date
What mixed number is shown by each shaded part?
2.
1.
3
2__
3.
1
1__
4
1
3__
2
3
Answer the questions about the bar graph. Give your answers
as simple fractions.
Cookies for the Bake Sale
4. How many cookies are there altogether?
45
15
10
8. Melanie baked 25 cookies. Did she bake more or
less than half of the cookies? more
Pe
Bu an
tt ut
er
l
ea
m
at
O
oc
Ch ola
ip te
7. What fraction of the cookies are peanut butter?
2
__
9
5
Ch
5. What fraction of the cookies are chocolate chip?
4
__
9
_1_
3
6. What fraction of the cookies are oatmeal?
Number
20
Flavor
How do you know?
© Houghton Mifflin Harcourt Publishing Company
1
Answers will vary. Half of 45 is 22__
;
2
1
25 is greater than 22__
2
9. Stretch Your Thinking Colby nailed together four wood
1
boards as shown at the right. All four boards are 5__
2
inches wide.
a. Find the perimeter of the outside rectangle.
88 inches
b. Find the perimeter of the inside rectangle.
44 inches
20
UNIT 1 LESSON 10
Practice with Unlike Mixed Numbers
Name
1-11
Date
1
Use benchmarks of 0, __
, and 1 to estimate the sum or difference.
2
Then find the actual sum or difference.
1
13 + __
3. ___
2
18
Estimate:
13 - ___
3
2. ___
2 + __
4
1. __
5
7
20
1
Estimate:
34
___
Sum: 35
10
0
Estimate:
7
___
20
Difference:
1
2
1__
9
Sum:
Estimate the sum or difference by rounding each mixed number to
the nearest whole number. Then find the actual sum or difference.
5 - __
4. 3 __
11
8
4 + ___
5. 6__
57
2
9
2
Estimate:
8
Sum:
15
18
12
Estimate:
1
2__
Difference:
11 - ___
6. 7___
41
12
Estimate:
1
12___
36
Difference:
4
49
3___
90
Tell whether the answer is reasonable or unreasonable. Explanations will vary.
Explain how you decided. Possible explanations are given.
8
1 + __
7. 2__
5 1 = 7___
5
9
7 - ___
2 = ___
8. __
15
3
19
Reasonable; Using
Unreasonable; Using
rounding gives the
benchmarks gives the
estimate 2 + 5 = 7.
estimate 1 - 0 = 1.
3 + __
4 = ___
7
9. __
8
© Houghton Mifflin Harcourt Publishing Company
11
8
5
1 - __
1
10. 4 __
1 5 = 2__
40
Unreasonable; Using
benchmarks gives the
1 + = __
estimate __
1 11.
2
2
3
6
2
Reasonable; Using
rounding gives the
estimate 4 - 2 = 2.
Solve.
7 - __
4
4 7 - ___
.
11. Estimate the difference 8 ___
12
8
10
Explain how you found the answer.
1
7
Sample answer: Use the 0, __
, 1 benchmarks. 8 ___
is
2
12
1 __
4
1
closer to 8 __
, 4 7 is closer to 5, and ___
is closer to __
;
2
8
10
2
1 - - __
8 __
5 1=3
2
2
UNIT 1 LESSON 11
Reasonable Answers
21
Name
1-11
Date
Add or subtract. Give your answer in simplest form.
1.
4
2.
7
- 3__
_8
3.
2
3
+ 6__
_4
1
12__
1
__
6
__
7
3
+ __
_5
6.
8
7
- 1__
_8
1
8__
16
1___
10
5
- 1__
6
__
15
13
2___
25
99
+ 3____
100
__
51
6___
2
35
1
3___
4
1___
4
3
5. 10__
8
4.
1
5__
100
Compare.
5 > __
5
7. __
7
9
6 > __
4
10. ___
11
9
99 < ____
100
8. ____
100
101
1 > ___
1
11. ___
21
22
9
7 > ___
9. ___
15
20
5 > __
1
12. ___
Solve.
16
4
Show your work.
13. On the first math test, Octavia answered 24 out of
30 questions correctly. On the second math test,
she answered 19 out of 25 questions correctly.
On which test did she answer the greater fraction
of the questions correctly?
© Houghton Mifflin Harcourt Publishing Company
the first test
14. Stretch Your Thinking Isidro is riding his bike 22 miles
1
miles and then took a
to the art museum. He rode 7__
2
7
mile. How
break. Since his break, he has ridden 5___
10
much farther does he have to ride to get to the museum?
4
8__
miles
5
22
UNIT 1 LESSON 11
Reasonable Answers
Name
1-12
Date
Solve. Explain why your answer is reasonable.
Explanations may vary.
Show your work.
1
feet long. She cut off a piece. Now the
1. Zoe had a board 5__
4
5
__
board is 3 feet long. How long was the piece she cut off?
6
5
1___
feet
12
Answer:
Why is the answer reasonable?
5
1
5__
rounds to 5. 3__
rounds to 4. The answer should
4
6
be about 5 - 4, or 1.
3
2. A rectangle has a length of 10___
inches and a width of
16
7
6__ inches. What is the perimeter of the rectangle?
8
1
34__
inches
8
Answer:
Why is the answer reasonable?
3
7
10___
rounds to 10. 6__
rounds to 7. The answer
16
8
should be about 10 + 10 + 7 + 7 = 34.
2
3. Max is making trail mix. He combines __
pound of dried fruit
5
1
and __ pound of mixed nuts. He adds sunflower seeds to make
3
a total of 1 pound. What is the weight of the seeds?
4
___
pounds
15
Answer:
© Houghton Mifflin Harcourt Publishing Company
Why is the answer reasonable?
2
1
1
__
and __
are each a little less than __
, so their sum is
5
3
2
a little less than 1. It would take a small fraction,
close to 0, to make a total of 1.
4. At the start of party, a bowl contains 16 pints of punch.
1
1
pints. Then the host adds another 7__
pints
Guests drink 10__
4
2
to the bowl. How much punch is in the bowl now?
1
pints
13__
4
Answer:
Why is the answer reasonable?
1
10__
rounds to 10, so about 6 pints are left and then
4
1
1
7__
are added, so the answer should be about 13__
.
2
2
UNIT 1 LESSON 12
Real World Problems
23
Name
1-12
Date
Tell whether the answer is reasonable or unreasonable. Explain
how you decided. Explanations may vary.
8 + ___
39
1 = ___
1. __
9
10
37
1 - __
2. 5__
4 2 = 2___
90
6
8
Unreasonable; __
is very close to
9
39
1
1, but ___
isn’t even __
.
90
8
42
the estimate 5 - 4 = 1.
2
5 + __
1
4. 5__
1 3 = 5___
11 - __
7 = ___
1
3. ___
12
7
Unreasonable; Rounding gives
24
6
4
12
Reasonable; Using benchmarks
Unreasonable; Using rounding
gives the estimate 1 - 1 = 0.
gives the estimate 6 + 2 = 8.
Add or subtract.
5 =
7 + __
5. __
8
8
3 =
7 - ___
7. ___
15
10
4 - __
9. 5__
21 =
5
3
4
1
1__
or 1__
8
2
21
7
3
3 - ___
5 =
8. __
4
12
5 + ___
10. 7__
2 11 =
6
12
5
1
___
or __
30
7
3___
15
5
1___
4 + __
2=
6. __
6
4
1
___
or __
12
3
9
3
or 10__
10___
4
12
Compare.
5
5 > __
11. __
9
8
7
12. 1___
< 1__2
3
5 > __
13. __
7
9
1
1 > ___
14. ___
90
89
2
5 > __
15. ___
9
18
55
65 > ___
16. ___
56
66
12
3
© Houghton Mifflin Harcourt Publishing Company
Solve.
17. Stretch Your Thinking Find two mixed numbers such that
when you estimate their sum by rounding to the nearest
whole number you get a different estimate than when you
round to the nearest half. Demonstrate that your numbers
satisfy this condition.
5
5
Possible answer: 2__
and 3__
. When you round to
8
8
the nearest whole number, the estimated sum is
3 + 4 = 7. When you round to the nearest half,
1 + __
the sum is 2__
3 1 = 6.
2
24
UNIT 1 LESSON 12
2
Real World Problems
1-13
Name
Date
In the space below, design and sketch a bird hotel.
Assume your design will be made from wood,
and includes these characteristics.
1
-inch
‣ Walls not exposed to weathering are __
4
thick.
1
-inch thick.
‣ Walls exposed to weathering are __
2
‣ The rooms are identical.
© Houghton Mifflin Harcourt Publishing Company
State the number of birds your design will
accommodate, and the dimensions of one room.
Then use the dimensions to compute the overall
length, width, and height of your hotel.
UNIT 1 LESSON 13
Focus on Mathematical Practices
25
Name
1-13
Date
Add or subtract. Give your answer in simplest form.
1.
1
7__
2.
4
5
- 4__
6
_
9
1___
5
2___
12
4.
3.
10
9
+ 1___
10
__
6
- 1__
_7
1
2__
7
4
3__
5
7
___
5.
10
11
+ 1___
12
__
37
2___
4
4__
6.
5
7
- 1__
_8
37
2___
60
4
5
3___
12
2
+ 1__
3
__
1
5___
40
12
Compare.
1 < ___
1
7. ___
57
47
5 > __
2
10. __
6
3
5 < __
4
8. __
7
15
14 < ___
9. ___
5
15
3 <
7
11. 15__
15___
8
10
16
9
1 >
12. 14___
13___
10
10
Show your work.
Solve.
3
1
of a movie on Friday, __
of the movie
13. Blake watched __
5
6
on Saturday, and the rest on Sunday. What fraction of
the movie did he watch on Sunday?
7
___
30
a. What is the sum of the three fractions?
3
1__
7
b. Why does it make sense for the sum to be greater than
1 whole?
Some students have a sister and a brother. Because the
three parts overlap, the total is more than 1 whole.
26
UNIT 1 LESSON 13
Focus on Mathematical Practices
© Houghton Mifflin Harcourt Publishing Company
14. Stretch Your Thinking Marshall surveyed his classmates
5
3
1
have a sister, __
have a brother, and ___
and found that __
7
14
2
don’t have any siblings.