All the solutions provided in **McGraw Hill My Math Grade 5 Answer Key PDF Chapter 7 Lesson 1 Hands On: Numerical Expressions** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 7 Lesson 1 Numerical Expressions

**Essential Question**

How are pattern used to solve problems?

Answer:

Patterns follow a predictable rule and that rule allows us to predict what will come next or to evaluate a problem.

Explanation:

A problem-solution pattern divides information into two main sections,

one that describes a problem and one that describes a solution.

A numerical expression, such as 8 + 7, is a combination of numbers and at least one operation. You can find the value, or evaluate, the numerical expression by completing each operation.

**Draw It**

Gregory and his family went hiking over the weekend. On Saturday, they hiked 5 miles and on Sunday, they hiked 5 miles. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of miles hiked.

Question 1.

Use the bar diagram to write an addition expression.

5 + ___________

Evaluate the expression.

5 + ___________ = ___________

Answer:

5 + 5 = 10

Explanation:

On Saturday, they hiked 5 miles.

On Sunday, they hiked 5 miles.

5 + 5 = 10 miles.

Question 2.

Use the bar diagram to write a multiplication expression.

____________ × 5

Evaluate the expression.

____________ × 5 = ____________

So, they hiked a total of ____________ miles.

Answer:

5 x 5 = 25

Explanation:

**Try It**

Mrs. Yearling has two groups of 5 students and two groups of 4 students. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of students.

Question 1.

Use the bar diagram to write an expression using only addition.

5 + ____________ + 4 + ___________

Evaluate the expression.

5 + ___________ + 4 + ____________ = ___________

Answer:

5 + 5 + 4 + 4 = 18

Explanation:

Mrs. Yearling has two groups of 5 students and two groups of 4 students.

5 + 5 + 4 + 4 = 18

Question 2.

Use the bar diagram to write an expression using multiplication and addition.

(___________ × 5) + (___________ × 4)

Evaluate the expression.

(___________ × 5) + (___________ × 4) = ___________

So, there are _____________ students that are divided into groups.

Answer:

(5 x 5) + (4 x 4) = 41

Explanation:

(5 × 5) + (4 × 4) = 25 + 16 = 41

So, there are 41 students that are divided into groups.

**Helpful Hint**

Parentheses tell you which numbers to group together. Perform operations inside parentheses first.

**Talk About It**

Question 1.

Evaluate the addition expressions to find the sum. Does the order in which the expression is written change the sum? Explain.

Answer:

No, the change in order does not change the sum.

Explanation:

7 + 7 + 5 + 5 = 24

7 + 5 + 7 + 5 = 24

Addition is a process of combining two or more numbers.

Addends are the numbers added, and the result we get after the process is called the sum.

When we change the order of the addends there is no change in the sum.

Question 2.

**Mathematical PRACTICE** Model Math Suppose Mrs. Yearling also had another group of 4 students. Write two new numerical expressions to represent the total number of students.

Expression 1

5 + ___________ + 4 + 4 + ___________

Expression 2

(2 × ___________) + (___________ × 4)

Answer:

5 + 5 + 4 + 4 = 18

(2 x 5) + (2 x 4) = 18

Explanation:

**Practice It**

Question 3.

Caleb’s music class is divided into 5 groups of 4 students for a project. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of students in his music class.

Write and evaluate an expression using only addition.

___________________

Write and evaluate an expression using multiplication.

___________________

So, there are ____________ students in his music class.

Answer:

4 + 4 + 4 + 4 + 4 = 20

5 x 4 = 20 students.

Explanation:

Caleb’s music class is divided into 5 groups of 4 students for a project.

multiplication is the repeated addition of a number.

So, there are 20 students in his music class.

Question 4.

**Mathematical PRACTICE** Identify Structure Bailey’s soccer team had snacks after the game that included 12 granola bars, 12 mini muffins, and 14 bananas. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of snacks after the soccer game.

Write and evaluate an expression using only addition.

___________________

Write and evaluate an expression using multiplication and addition.

___________________

So, there are ____________ total snacks after the game.

Answer:

12 + 12 + 14 = 38

(2 x 12) + 14 = 38

So, there are 38 total snacks after the game.

Explanation:

**Apply It**

Question 5.

Wasah went bird watching and spotted 6 robins, 5 sparrows, 6 cardinals, and 6 doves. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of birds Wasah spotted.

Write and evaluate an expression using only addition.

___________________

Write and evaluate an expression using multiplication and addition.

___________________

So, Wasah spotted a total of ___________ birds.

Answer:

23 birds.

Explanation:

Wasah went bird watching and spotted 6 robins, 5 sparrows, 6 cardinals, and 6 doves.

6 + 5 + 6 + 6 = 23

(3 x 6) + 5 = 18 + 5 = 23

So, Wasah spotted a total of 23 birds.

Question 6.

**Mathematical PRACTICE** Which One Doesn’t Belong? The bar diagram below can be represented by three of the four expressions underneath it. Find the value of each expression and circle the one that does not represent the bar diagram.

Answer:

Explanation:

5 + 4 + 5 + 4 + 5 + 4 = 27

(3 x 5) + (3 x 4) = 15 + 12 = 27

3 + 5 + 3 + 4 = 15

3 x (5 + 4) = 3 x 9 = 27

So, 3 + 5 + 3 + 4 = 15 does not belong to bar diagram.

**Write About It**

Question 7.

How can bar diagrams be used to model numerical expressions?

Answer:

The bar diagram can be used as a visual clue to determine the reasonableness of the solution.

Explanation:

Bar diagrams are the pictorial representation of data in the form of rectangular bars.

These diagrams help us to understand and represent the relationship between quantities to solve problems.

### McGraw Hill My Math Grade 5 Chapter 7 Lesson 1 My Homework Answer Key

Question 1.

Refer to the Homework Helper. Suppose Paul went to the store and bought 4 peaches to add to the basket. Write two new numerical expressions to represent the total number of fruit in the basket.

Expression 1

3 + __________ + 3 + 2 + ___________

Expression 2

(2 × __________) + (_________ × 4) + 2

Answer:

16 fruits.

Explanation:

Expression 1

3 + 4 + 3 + 2 + 4 = 16

Expression 2

(2 × 3) + (2 × 4) + 2

6 + 8 + 2 = 16

**Problem Solving**

Question 2.

Deborah’s playlist on her MP3 player had a variety of songs on it. She had 21 country songs, 18 alternative songs, 16 pop songs, and 18 rock songs. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of songs on Deborah’s MP3 player.

Write and evaluate an expression using only addition.

____________________

Write and evaluate an expression using multiplication and addition.

____________________

So, there are ___________ total songs on Deborah’s MP3 player.

Answer:

73 songs on Deborah’s MP3 players.

Explanation:

Deborah’s had 21 country songs,

18 alternative songs,

16 pop songs,

18 rock songs.

Total songs on Deborah’s MP3 player,

21 + 18 + 16 + 18 = 73

21 + (2 x 18) + 16 = 21 + 36 + 16 = 73

Question 3.

**Mathematical PRACTICE** Identify Structure Mrs. Conrad’s art class was painting murals. She had 4 bottles of red paint, 5 bottles of green paint, 4 bottles of yellow paint, 6 bottles of blue paint, and 5 bottles of orange paint. Use the bar diagram to write and evaluate two numerical expressions to represent the total number of bottles of paint.

Write and evaluate an expression using only addition.

____________________

Write and evaluate an expression using multiplication and addition.

____________________

So, Mrs. Conrad has a total of ___________ bottles of paint.

Answer:

22

Explanation:

Mrs. Conrad’s had 4 bottles of red paint,

5 bottles of green paint,

4 bottles of yellow paint,

6 bottles of blue paint,

5 bottles of orange paint.

4 + 5 + 4 +6 + 3 = 22

(2 x 4) + 5 + 6 + 3

8 + 5 + 6+ 3 = 22