Download 7-1 7-2 Worksheet KEY

Name
Reteaching
Adding and Subtracting:
Like Denominators
7-1
6
2
Find __
⫹ __
.
14
14
The fractions have like denominators,
so you can just add the numerators.
6
8
2
__
⫹ __
⫽ __
Write the sum over the common
denominator.
14
14
14
8
__
⫽ __4
Simplify if possible.
7
14
Find __57 ⫺ __27.
The denominators are the same, so
you can subtract the numerators.
5
__
⫺ __2 ⫽ __3
3
__
cannot be simplified, so
7
7
7
7
5
__
⫺ __2 ⫽ __3
7
7
7
Find each sum or difference. Simplify your answer.
1. _16 ⫹ _36 ⫽
3. _67 ⫺ _27 ⫽
5. _89 ⫺ _59 ⫽
11 ⫽
4 ⫹ __
7. __
15
15
_
2
3
_
4
7
_
1
3
__
15
15
9 ⫺ __
4 ⫽
2. __
11
11
3 ⫹ __
8
4. __
12
12
8
1 ⫹ __
6. __
10
10
or 1
16 ⫺ __
9
8. __
20
20
__
5
11
__
11
⫽ 12
__
9
⫽ 10
__
7
⫽ 20
9. Number Sense Give an example of two fractions whose sum
can be simplified to _12 .
Anything that can be reduced to _12 , for
example, _18 ⴙ _38
15 in. A dime has a diameter of
10. A quarter has a diameter of __
16
13 in. If you put each coin side
11 in., and a nickel has a diameter of __
__
16
16
by side, what is the combined width of the three coins?
__
39 in., or 2__
7 in.
16
16
© Pearson Education, Inc. 6
Reteaching 7-1
How to find sums or differences of fractions with like denominators:
28
Topic 7
Name
Practice
7-1
Adding and Subtracting:
Like Denominators
Find each sum or difference. Use a number line. Simplify your answers.
1. _78 2 _38
1
8
2. _35 1 _45
2
2
8
3
8
4
8
5
8
6
8
7
8
1
0
1
5
1_25
2
5
3
5
4
5
1
2
3
4
1 15 15 15 15
Find each sum or difference. Simplify your answers.
3. _67 1 _17
3 1 __
1 1 __
4
6. __
11
11
11
1
9 2 __
4
4. __
10
10
11
7. _16 1 _26 1 _56
__
8
Evaluate 9 through 11 for x 5 _29.
9. _89 1 x
1_19
10. _59 2 x
12. Use30422_T09-9-1PR-1
the table to answer the questions.
_
1
8 2 __
5
5. __
15
15
2
1_13
5 1 __
2 1 __
7
8. __
20
20
20
_
1
11. (_79 2 x) 1 _19
3
Practice 7-1
0
_
1
2
_
1
5
__
7
10
_
2
3
30422_T09-9-1PR-2
a. What is the total amount of seafood in the soup?
1_34 lb
b. How much more shrimp than cod is in the soup?
_
1 lb
4
Seafood for Soup
Cod
5
_
lb
8
Scallops
2 lb
_
8
Shrimp
7 lb
_
8
13. Critical Thinking Max has 12 pairs of socks. Of them,
6 pairs are blue, 3 pairs are brown, and 2 pairs are white. Max
wants to know what fraction of the socks are blue or brown.
How can he find the numerator?
A Add 6 1 3 1 2.
B Add 6 1 3.
C Subtract 11 from 12.
© Pearson Education, Inc. 6
D Subtract 9 from 12.
14. Writing to Explain Explain how you can add two fractions with
denominators of 10 and end up with a sum whose denominator is 5.
Sample answer: By simplifying a sum, such as
__
__
__
_
5
6
3
1
10 1 10 5 10 , which simplifies to 5 .
Topic 7
29
Name
Reteaching
7-2
Least Common Multiple
There are different ways to find the least common multiple (LCM) of two
numbers. Here are two ways of finding the LCM of 4 and 5:
List Multiples
Use Prime Factors
Step 1: List multiples of each number.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…
Step 3: Determine which of the common multiples is the
least.
20 and 40 are both common multiples, but 20 is
the least.
The LCM of 4 and 5 is 20.
4: 2 2
5: 5
Step 2: Circle the greatest number
of times each different
factor appears.
4: 2 2
5: 5
Step 3: Find the product of the
factors you circled.
2 2 5 20
The LCM of 4 and 5 is 20.
Find the LCM of each set of numbers.
42
2, 5, 10 10
12, 20 60
20
6, 21
42
5, 10, 25 50
1. 6, 7
2. 4, 5
3. 10, 15
4.
5.
6. 8, 10
7.
8.
9. 7, 8
30
40
56
10. Number Sense If you know the LCM of 4 and 5, how could you
find the LCM of 40 and 50?
Multiply the LCM of 4 and 5 by 10.
11. Writing to Explain Peter says the least common multiple of 4, 6, and 12 is 24.
Do you agree or disagree? Explain.
Disagree. 24 is a common multiple of 4, 6,
and 12, but it is not the least common multiple.
The number 12 is.
34
Topic 7
© Pearson Education, Inc. 6
Reteaching 7-2
Step 2: Check the multiples the numbers have in common.
Step 1: List the prime factors of
each number.
Name
Practice
7-2
Least Common Multiple
Find the LCM of each set of numbers.
60
14, 42 42
6, 7, 8 168
100
21, 30 210
16, 20 80
24
3, 7, 10 210
12, 16 48
1. 15, 20
2. 4, 50
3. 8, 12
4.
5.
6.
7.
8.
10:00 a.m., 12:00 p.m.,
2:00 p.m., 4:00 p.m.
Science Museum
— Show Schedule —
Chemistry — Every 30 minutes
Electricity — Every 20 minutes
Recycling — Every 40 minutes
Fossils
— Every 45 minutes
The first showing for all shows
11. The museum does shows in schools every Monday
is at 10:00 A.M.
and shows in public libraries every fifth day (on both
weekdays and weekends). If the museum did both a
school show and a library show on Monday, how many
days will it be until it does both shows on the same day again?
35 days
12. Which of the following pairs of numbers is correctly listed with its
LCM?
A 5, 15; LCM: 30
B 20, 30; LCM: 60
C 24, 36; LCM: 12
D 7, 9; LCM: 21
© Pearson Education, Inc. 6
13. Writing to Explain What method would you use to find the LCM
of a group of four numbers? Explain and give an example.
Sample answer: prime factorization;
To find the LCM of 3, 6, 8, and 10,
multiply the greatest number of
times each factor appears in each
prime factorization: 23 3 3 3 5 5 120.
Topic 7
35
Practice 7-2
10. At what times of the day between 10:00 a.m.
and 5:00 p.m. do the chemistry presentation and the
recycling presentation start at the same time?
9.