1. No category

NAME ________________________________________ DATE ______________ PERIOD _____
Rounding Fractions and Mixed
Numbers (pages 219–222)
The following guidelines can help you round fractions and mixed numbers
to the nearest unit.
• If the numerator is almost as large as the denominator, round the
number up to the next whole number.
• If the numerator is about half of the denominator, round the fraction
1
Rounding Fractions
and Mixed Numbers
to .
2
• If the numerator is much smaller than the denominator, round the
number down to the next whole number.
• When measuring actual quantities, you may have to round up or
down, despite what the rule says, to get useful numbers.
7
3
A Round 8 to the nearest half.
B Round 3 5 to the nearest half.
7
–
8
0
1
–
2
3
3 –5
1
The numerator is almost as large as the
7
denominator, so round up. Since is
8
closer to 1 than
1
,
2
1
3
4
3 –2
The numerator is about half of the
denominator. Round the fraction to
3
3
5
round up to 1.
rounds to
1
.
2
So,
1
3
.
2
Try These Together
Round each number to the nearest half.
2
1. 5
HINT: The numerator is about half of
the denominator.
1
HINT: The numerator is much smaller
than the denominator.
2. 5 8
Round each number to the nearest half.
5
7
4. 12
5. 2 8
9
4
7. 6
8. 1 9
3. 1 8
6. 8 10
B
C
C
B
C
9. Standardized Test Practice A hot air balloon can carry 400 pounds of
cargo and people. There are four men who want to ride in the balloon.
The average weight of the men is 180 pounds. Estimate how many men
can ride in the balloon.
A 4
B 2
C 3
D 1
6. 9 7. 2
1
8. 1 9. B
40
1
© Glencoe/McGraw-Hill
5. 2 2
B
A
1
8.
4. 2
A
7.
1
B
6.
2. 5 3. 1 2
A
5.
1
4.
2
Answers: 1. 2
3.
3
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Estimating Sums and Differences
(pages 223–225)
When you add or subtract fractions or mixed numbers, round to estimate
the sum or difference.
Estimate the Sum or
Difference of Fractions
• Round each fraction to the nearest half, and then add
or subtract.
Estimate the Sum or
Difference of Mixed Numbers
• Round each mixed number to the nearest whole
number, and then add or subtract.
13
7
9
A Estimate .
15
16
13
15
rounds to 1 and
1
2
Add 1 13
15
9
16
9
16
rounds to
1
.
2
7
2
5
rounds to 6 and 2 rounds to 2.
8
5
Subtract 6 2 4.
1
1
.
2
is about
2
B Estimate 5 8 2 5 .
7
2
5
2
is about 4.
8
5
1
1
.
2
Try These Together
Estimate.
7
1
1. 12
7
1
3
2. 5 8 9 5
HINT: Round to the nearest half.
HINT: Round to the nearest whole number.
Estimate.
2
4
3. 3 5
4. 3 4 2 8
1
5
5
5. 8 6
1
4
7. 10
9
2
3
8. 5 8
9. 1 7 10
1
5
1
1
3
3
3
6. 8 4 1 16
9
3
1
10. 1 5 5
1
11. Estimate the sum 2 3 6 3 4 6 .
9
1
2
12. Estimate the difference between 4 5 and 3 .
3
B
C
C
B
C
13. Standardized Test Practice Estimate the following total.
43 2 81 1 51 1 53 1
B 2
A 0
8. 1 9. 0 10. 2 11. 13
12. 0 13. A
B
A
1
D 1
2
C 1
1
6. 8 7. 2
8.
1
4. 1 5. 1 2
A
7.
© Glencoe/McGraw-Hill
41
1
B
6.
3. 1 2
A
5.
2. 15
4.
1
Answers: Sample answers are given. 1. 2
3.
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Adding and Subtracting Fractions
with Like Denominators (pages 228–231)
Fractions with the same denominator are like fractions. You add and
subtract the numerators of like fractions the same way you add and subtract
whole numbers.
Adding Like
Fractions
• To add fractions with like denominators, add the numerators. Use the
same denominator in the sum.
Subtracting
Like Fractions
• To subtract fractions with like denominators, subtract the numerators.
Use the same denominator in the difference.
1
3
3
Estimate. 0 1
7
3
7
1
2
13
7
4
7
1
B Find the difference 4 .
4
A Find the sum of and 7 .
7
1
2
Estimate. 1 3
4
1
4
1
2
31
4
Compared to the estimate,
the answer is reasonable.
1
2
2
4
or
1
2
Compared to the estimate,
the answer is reasonable.
Try These Together
Add or subtract. Write in simplest form.
2
2
1. 3 3
5
3
2. 8 8
HINT: Add the numerators. Write the sum as
a mixed number.
HINT: Subtract the numerators. Write the
answer in simplest form.
Add or subtract. Write in simplest form.
1
2
3. 3 3
4
2
4. 5 5
7
3
5. 16
16
9
3
6. 10
10
2
3
7. 7 7
6
9
8. 15
15
7
3
9. How much larger is than 8 ?
8
1 3
5
10. Find the sum of , , and 8 .
8 8
11. Standardized Test Practice Find the following total. 16
16 16
16 11
5
5
C 16
8. 5
1
9. 2
1
42
5
10. 1 8
1
11. C
© Glencoe/McGraw-Hill
7. 7
1
B 2
3
8
3
D 1
16
3
7
A 16
6. 5
C
B
A
1
8.
5. 4
A
7.
1
3. 1 4. 1 5
C
B
B
6.
1
C
A
5.
2. 4
4.
1
Answers: 1. 1 3
B
3.
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Adding and Subtracting Fractions
with Unlike Denominators (pages 235–238)
When you add or subtract fractions, the fractions must have the same
denominators. To add or subtract fractions with unlike denominators,
rename the fractions using the least common denominator (LCD). Then
add or subtract and simplify.
1
2
3
The LCD of
3
1
2
3
6
3
3
,
6
4
6
1
2
and
7
,
6
and
2
3
or
2
2
1
1
6
1
B Find 5 4 .
A Add 2 and 3 .
2
3
4
6
is 6.
The LCD of
4
Rename the fractions.
3
5
Add, then simplify.
12
20
4
12
,
20
5
20
3
5
and
and
1
4
is 20.
5
1
4
5
5
20
Rename the fractions.
7
20
Subtract.
Try These Together
Add or subtract. Write in simplest form.
3
1
3
5
1. 4 6
2. 8 12
HINT: Find the LCD, then rename the fractions.
HINT: Find the LCD, then rename the fractions.
Add or subtract. Write in simplest form.
3
1
3. 8 4
2
1
4. 3 6
1
7
5. 8 2
2
1
6. 5 3
11
5
7. 6
12
3
1
8. 6 4
3
1
9. 7 2
8
2
10. 3
11
4
1
11. 9 6
5
9
12. What is the sum of and ?
8
16
11
9
2
13. How much is 5 ?
10
1
14. How much more is than 4 ?
16
15. Carpentry You are building a bookcase. The board that makes up the
7
1
-inch screws to attach
side of the bookcase is inch
thick.
If
you
use
2
8
the shelves of the bookcase, how far into the shelves do the screws extend?
B
4.
C
B
C
B
6.
A
7.
8.
1 3
C
A
5.
B
A
9
16. Standardized Test Practice What is the sum of 6 , , and ?
4
12
7
A 12
11
B 12
5
C 1
12
2
D 1 3
7
19
5
5
3
11
3
11
13
2
5
3
1
7
3
Answers: 1. 2. 3. 4. 5. 1 6. 7. 1 8. 9. 10. 11. 12. 1 13. 14. 15. inch 16. D
12
24
8
6
8
15
4
12
14
33
18
16
2
16
8
3.
© Glencoe/McGraw-Hill
43
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Adding and Subtracting Mixed
Numbers (pages 240–243)
Use the following rules to add and subtract mixed numbers.
Adding and
Subtracting
Mixed Numbers
5
• Add or subtract the fractions.
• Then add or subtract the whole numbers.
• Rename and simplify if necessary.
1
5
A Find 5 8 1 .
8
Add the fractions. Add the whole numbers.
5
5
8
→
1
1 8
1
B Find 3 6 2 2 .
Subtract the fractions. Subtract the whole numbers.
5
8
5
3
6
5
1
2 2
→
1
1 8
6
8
5
6
5
3
6
3
6
→
3
2 6
3
3
2 6
2
6
6
or 6 Simplify.
8
4
2
1
1
or 1 Simplify.
6
3
Try These Together
Add or subtract. Write in simplest form.
1
1
11
1. 7 4 10 2
3
2. 9 4 8
12
HINT: Rename the fractions. Add the
fractions. Then add the whole numbers.
HINT: Rename the fractions. Subtract the
fractions. Then subtract the whole numbers.
Add or subtract. Write in simplest form.
1
3
4. 9 5 2 15
3
1
1
7. 15 8 12 4
3. 2 3 5 8
7
6. 8 3 6 4
7
1
B
3
12. Standardized Test Practice A bag of potatoes weighs 5 4 pounds. At the
1
1
first meal, 1 3 pounds of potatoes are eaten. At a later meal, 2 4 pounds
of potatoes are eaten. How many pounds of potatoes remain in the bag?
1
5
2
C 1 6
4. 7 5
2
5. 9 6
1
6. 2 12
1
7. 3 8
1
44
17
8. 6 24
7
9. 6 30
1
10. 15 6
1
11. 2 12
1
12. A
© Glencoe/McGraw-Hill
D 2 3
3. 7 24
B 2 3
13
1
A 2 6
2. 5 24
B
A
3
C
B
8.
2
3
11. 4 4 2 3
C
B
A
7.
5
10. 9 3 5 6
C
A
5.
6.
1
5
8. 8 2 8
12
Answer: 1. 17 4
4.
1
2
5. 5 3 3 2
3
1
9. 1 4 3
10
3.
3
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Subtracting Mixed Numbers with
Renaming (pages 244–247)
When you subtract mixed numbers, sometimes the fraction in the number
you are subtracting is greater than the fraction in the number you are
subtracting from. When this happens, you must rename the first fraction as
an improper fraction in order to subtract.
1
3
Find 12 8
.
3
5
The LCM of 3 and 5 is 15.
12 3
1
→
12 15
3
→
8 15
8 5
9
15
Since
5
11 15
9
8 15
is greater than
20
5
,
15
5
20
20
11 15
→
9
20
rename 12 as 11 , and then subtract.
15
15
9
8 15
11 15
→
9
8 15
11
15
11
3
15
Try These Together
Subtract. Write in simplest form.
3
7
3
1. 4 1
10
10
5
2. 8 5 7
14
HINT: Rename the fraction in the first
mixed number.
HINT: First find the LCD. Then rename using
the LCD. Then, rename the first fraction as an
improper fraction.
Subtract. Write in simplest form.
5
11
4. 4 2 10
10
3
7
7. 5 8 1 8
3. 9 4
12
12
3
6. 18 7 8
4
3
1
9. 4 4 3 8
9
3
5
1
5
2
3
5. 7 5 6 10
1
2
8. 9 6 7 5
5
10. 3 2 1 8
11. 18 6
5
4
12. Algebra Solve the equation m 9 8 6 5 . Write the solution in
simplest form.
B
C
1
13. Standardized Test Practice Sam swam 2 8 hours on Saturday and 3 3
hours on Sunday. How many more hours did he swim on Sunday than
on Saturday?
3
C 1 8
6. 10 8
7
7. 3 4
3
8. 1 30
45
1
23
9. 1 8
5
10. 1 8
7
11. 17 6
1
12. 2 40
33
13. B
© Glencoe/McGraw-Hill
1
D 1 4
5. 1 10
23
B 24
2
1
A 1
24
4. 1 5
C
B
A
1
8.
3. 4 2
A
7.
1
B
B
6.
3
C
A
5.
2. 2 2
4.
3
Answers: 1. 2 5
3.
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 6 Review
Pie-Eating Contest
You’ve just entered a pie-eating contest, but this contest is a little different
from most. You must eat the correct amount of pie in each round of the
contest to win. The instructions for each round tell you how much pie to
eat. Shade the blank pies below to show how much pie you would eat in
each round.
2
1
Round 1: Eat 5 + 5 of the pie.
2
1
Round 2: Eat 3 – 4 of the pie.
1
3
1
7
Round 3: Eat 1 + 1 8 of the pies.
2
Round 4: Eat 2 – 1 8 of the pies.
4
Answers are located on p. 106.
© Glencoe/McGraw-Hill
46
Parent and Student Study Guide
Mathematics: Applications and Concepts, Course 1