1-10A Solve Real-World Problems with
Operations and Properties
Name
Objective
To use operations, properties, and Order of Operations to solve real-world problems
Anna and Ben are deep-sea divers. Ben dived 12 feet per minute for 3 minutes
and stopped. He did this 4 times. Anna made one dive that was 12 feet deeper
than the total depth of Ben’s dives. How deep did Anna dive?
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
! To find how deep Anna dived, use two steps. First, write and simplify
a numerical expression to find the total depth of Ben’s dives. Then
write and simplify another numerical expression to find the depth of
Anna’s dive. To simplify both expressions, use the Properties of
Integers and the Order of Operations.
Write a numerical expression to find the total depth of Ben’s dives.
Remember
4(!12 " 3)
Use negative integers to write
distances below sea level.
4(!36)
Ben’s dives: !12 ft per minute for 3 minutes, 4 times
Simplify. Use Order of Operations.
The total depth of Ben’s dives.
!144
Write a numerical expression for the depth of Anna’s dive.
!144 # (!12)
Anna’s dive is 12 feet deeper than Ben’s total.
Simplify. Use Properties of Integers.
!156
So, Anna dived to a depth of !156 feet.
Example
Team A’s scores were !2, #6, and #2. Team B’s scores were !6, !5, and !1.
Which team had the lower average score?
To find an average score, divide the total of the scores by the number of scores.
Team A
Team B
!2 # 6 # 2
6
Write an expression to show Team
A’s scores.
Simplify.
6
3 $2
!12
Divide to find the team’s average score.
2 % !4
!6 # (!5) # (!1)
Write an expression to
show Team B’s scores.
Simplify.
!12
3 $ !4
Divide to find the team’s average score.
Compare the average scores.
So, Team B had the lower average score.
Write numerical expressions and use the Properties of Operations to solve.
1. Kate made 3 identical withdrawals from her
2. Bo’s teacher gives extra points for creativity
savings account. Each time, she asked for three
and takes away points for errors. On 4 tests, Bo
$20 bills. What single withdrawal would be the
gained 2 points each. He lost 5 points total for
same amount of money?
errors. Did he gain or lose points? How many?
3. Discuss and Write How do properties help you write different
expressions to represent the same situation?
Use after SourceBook Lesson 1-10.
Chapter 1, Lesson 10A
1
1-10A Solve Real-World Problems with
Operations and Properties
Name
Write a numerical expression. Use properties and Order of Operations.
4. Use 4 twos, parentheses, and 3 operations to get 5. Use 5 fives, parentheses, and 4 operations to
an answer of 0.
make 0.
Solve.
8. Carl made 4 identical dives. In each, he
descended 4 yards a minute for 3 minutes.
How many yards deep would he have to go
to reach the same depth in just one dive?
9. One day, the temperature dropped 2ºC an hour
for 3 hours. Then, the temperature rose 1ºC
an hour for 2 hours. What was the change in
temperature during the 5 hours?
10. Laura has $20. Dan has $24 less than 4 times
the amount Laura has. How much money
does Dan have?
11. George said that the additive inverse of the
result of 4 times the sum of 4 and negative 8
is 8. Explain why this is not correct.
12. Bicycles rent for $15, plus $2 an hour. Jen and
her brother each rented a bicycle for 4 hours.
What was their total cost?
13. Will spent $70 on a canoe rental. If the rental
cost is $25, plus $7.50 for each half-hour, for how
long did Will rent the canoe?
14. Greta climbed stairs in a tall building for
30 minutes at a rate of 40 stairs a minute.
During the climb, she drank 1 pint of water
every 10 minutes. How much more than
1000 stairs did she climb? How many pints
of water did she drink?
15. In football, a touchdown is 6 points, an extra
point is 1 point, a field goal is 3 points, and a
safety is 2 points. The Moles scored 36 points.
The Melons scored 3 touchdowns, each with
an extra point, 2 field goals, and a safety. Which
team won the game? By how many points?
WHAT'S THE ERROR?
16. Jake is going skiing with his parents. They told him that he has to
pay for his equipment and lift tickets. He plans to rent skis and
boots for the 3-day vacation at Big Mountain. The skis cost $15 a
day and the boots cost $12 a day. The 3-day lift ticket costs $100.
Jake has saved $180 so far, and thinks he needs to save another
$201. His mother told him to do the math again. Find and correct
Jake’s error.
2
Chapter 1, Lesson 10A
Use after SourceBook Lesson 1-10.
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
6. Use 4 fours, parentheses, and 3 operations to get 7. Use 5 threes, parentheses, a negative sign, and
an answer of 8.
powers to make 0.