Name
7.4
?
Simplify Numerical Expressions
Essential Question
In what order must operations be simplified to find
the solution to a problem?
Connect Remember that a numerical expression is a
mathematical phrase that uses only numbers
and operation symbols.
(5 − 2) × 7
Algebraic
Reasoning—5.4.F
MATHEMATICAL PROCESSES
5.1.B, 5.1.F, 5.1.G
72 ÷ 9 + 16
Order of Operations
1. Perform operations in parentheses.
2. Multiply and divide from left to right.
(24 − 15) + 32
3. Add and subtract from left to right.
To simplify, or find the value of, a numerical expression
with more than one operation, you must follow rules called
the order of operations. The order of operations tells
you in what order you should simplify an expression.
Unlock
Unlock the
the Problem
Problem
A cake recipe calls for 4 cups of flour and 2 cups of sugar. To triple
the recipe, how many cups of flour and sugar are needed in all?
Simplify 3 × 4 + 3 × 2 to find the total number of cups.
A Heather did not follow the order of
operations correctly.
B Follow the order of operations
by multiplying first and then adding.
Name______
Heather
3 x 4 + 3 x 2 First, I added.
3x7x2
3x4+3x2
Then, I multiplied.
© Houghton Mifflin Harcourt Publishing Company
42
Explain why Heather’s answer is not correct.
So, _ cups of flour and sugar
are needed.
Module 7
309
Simplify Expressions with Parentheses To simplify an expression
with parentheses, follow the order of operations. Perform the operations
in parentheses first. Multiply from left to right. Then add and subtract
from left to right.
Example
Each batch of cupcakes Lena makes uses 3 cups of flour, 1 cup of milk, and 2 cups
of sugar. Lena wants to make 5 batches of cupcakes. How many cups of flour, milk,
and sugar will she need in all?
Write the expression.
5 × (3 + 1 + 2)
First, perform the operations in parentheses.
5 × (_)
Then multiply.
_
So, Lena will use _ cups of flour, milk, and sugar in all.
Share
Share and
and Show
Show
Simplify the numerical expression.
1. 10 + 36 ÷ 9
2. 10 + (25 − 10) ÷ 5
3. 9 − (3 × 2) + 8
Think: I need to divide first.
_
_
_
Math Talk
Mathematical Processes
4.
5.
Use Symbols Write 12 + 17 – 3 × 2 with parentheses
so it has a value of 23.
Multi-Step The value of 100 – 30 ÷ 5 with parentheses
can have a value of 14 or 94. Explain.
310
Raina simplified the expression
5 × 2 + 2 by adding first and
then multiplying. Will her answer
be correct? Explain.
© Houghton Mifflin Harcourt Publishing Company
Problem
Problem Solving
Solving
Name
Unlock
Unlock the
the Problem
Problem
6. Multi-Step A movie theater has 4 groups of seats. The largest group
middle
side
a. What do you need to know?
back
side
of seats, in the middle, has 20 rows, with 20 seats in each row. There
are 2 smaller groups of seats on the sides, each with 20 rows and
6 seats in each row. A group of seats in the back has 5 rows, with
30 seats in each row. How many seats are in the movie theater?
b. What operation can you use to find the number of seats in the back
group of seats? Write the expression.
c. What operation can you use to find the number of seats in both
groups of side seats? Write the expression.
d. What operation can you use to find the number of seats in the
middle group? Write the expression.
e. Write an expression to represent the total
number of seats in the theater.
7.
f. How many seats are in the theater? Show the
steps you use to solve the problem.
Multi-Step In the wild, an adult giant panda eats about 30 pounds of
© Houghton Mifflin Harcourt Publishing Company
food each day. Write and simplify a numerical expression that shows
how many pounds of food 6 pandas eat in 3 days.
8.
Connect Write and simplify two equivalent numerical
expressions that show the Distributive Property of Multiplication.
Module 7 • Lesson 4 311
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
9. The books in an unusual library are labeled with numerical expressions.
Katrina needs to find the book with a numerical expression that has a
value of 12. Which one should she choose?
A
(6 + 26) – (4 × 5)
B
2 × (15 – 7)
C
10 + 8 – 36 ÷ 9
D
(25 – 4) ÷ 7
10. Franco needs to simplify 3 × (8 – 4) + 7. What should be his first step?
11.
A
Add 7 to 4.
B
Subtract 4 from 8.
C
Multiply 3 by 7.
D
Add 3 to 7.
Multi-Step Sarah simplified each of the expressions shown. What is
the difference between the values of the two expressions?
3 × 12 – 9 + 10
3 × (12 – 9) + 10
A
9
C
12
B
18
D
22
TEXAS Test Prep
312
A
(6 ÷ 3) × 4 + 8
B
27 − 9 ÷ 3 × (4 + 1)
C
(18 + 12) × 6 − 4
D
71 − 5 × (9 + 4)
© Houghton Mifflin Harcourt Publishing Company
12. Which expression has a value of 6?
H o mewo rk
and Practice
7.4
Algebraic Reasoning—5.4.F
MATHEMATICAL PROCESSES 5.1.B,
5.1.F, 5.1.G
Name
Simplify Numerical Expressions
Simplify the numerical expression.
1. 10 − (2 × 4) + 12
2. 14 + 35 ÷ 7
3. 11 + (31 − 4) ÷ 9
4. 25 − 4 × 5
5. 3 × (6 + 3) − 15
6. 30 − 14 ÷ 2
Rewrite the expression with parentheses to equal the given value.
7. 12 + 6 ÷ 2 + 4; value: 13
8. 42 − 24 ÷ 6; value: 3
10. 60 − 3 + 2 × 5; value: 35
11. 18 + 9 ÷ 3; value: 21
9. 9 + 16 − 2 × 4; value: 17
12. 5 × 2 + 4 + 3; value: 45
Problem Solving
Problem
Problem Solving
Solving
13. Julian paid his library fines. He paid $2 each for
© Houghton Mifflin Harcourt Publishing Company
4 overdue books and $16 for a lost book. Write
and simplify a numerical expression that shows
how much Julian paid in library fines.
14. For 5 days in a row last week, Addison read
9 pages of a poetry book and 16 pages of her
favorite novel. Write and simplify a numerical
expression that shows how many pages Addison
read last week.
Module 7 • Lesson 4 313
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
on the board that has a value of 16. Which
expression does Mrs. Harrison write?
A
(15 + 3) − 14 ÷ 2
B
20 − 4 ÷ 2
C
3 × (5 + 1)
D
18 + 13 − (5 × 3)
17. Which is the value of the numerical
expression below?
30 ÷ (3 + 2) × 8
A
96
B
48
C
26
D
40
19. Multi-Step Kalani and Porter each simplified
one of the expressions below. If they add their
results together, what will be their sum?
16. Omar wants to simplify the expression below.
What should be his first step?
6 × (3 + 9) − 5
A
Multiply 6 by 3.
B
Subtract 5 from 9.
C
Add 9 to 3.
D
Subtract 5 from 6.
18. Becka says that when she simplifies the
expression below, the value is 6 less than her
age. What is Becka’s age?
(7 + 11) − 8 ÷ 2
A
20
B
14
C
26
D
11
20. Multi-Step Nicole simplified the expression
below. Then she multiplied the value of the
expression by 5. What is Nicole’s product?
Kalani: 4 × 11 − 5 + 12
314
36 + 6 ÷ 3 + 2
Porter: 4 × 11 − (5 + 12)
A
16
A
78
B
80
B
44
C
40
C
102
D
200
D
54
© Houghton Mifflin Harcourt Publishing Company
15. Mrs. Harrison writes a numerical expression