# Eureka Math Grade 6 Module 4 Lesson 9 Answer Key

## Engage NY Eureka Math 6th Grade Module 4 Lesson 9 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 9 Example Answer Key

Example 1.
Create a bar diagram to show 3 plus 5.
Answer: How would this look it you were asked to show 5 plus 3?
Answer:
There would be 5 tiles and then 3 tiles. Are these two expressions equivalent?
Answer:
Yes. Both 3 + 5 and 5 + 3 have a sum of 8.

Example 2.

How can we show a number increased by 2?
Answer:
a + 2 or 2 + a Can you prove this using a model? If so, draw the model.
Answer:
Yes. I can use a bar diagram.

Example 3.
Write an expression to show the sum of m and k.
Answer:
m + k or k + m

Which property can be used in Examples 1 – 3 to show that both expressions given are equivalent?
Answer:
The commutative property of addition

Example 4
How can we show 10 minus 6?
Draw a bar diagram to model this expression.
Answer: What expression would represent this model?
Answer:
10 – 6

Could we also use 6 – 10?
Answer:
No. If we started with 6 and tried to take 10 away the models would not match.

Example 5
How can we write an expression to show 3 less than a number?
Start by drawing a diagram to model the subtraction. Are we taking away from the 3 or the unknown number?
Answer:
We are taking 3 away from the unknown number. What expression would represent this model?
Answer:
The expression is n – 3

Example 6
How would we write an expression to show the number c being subtracted from the sum of a and b?

Start by writing an expression for “the sum of a and b.”
Answer:
a + b or b + a

Now, show c being subtracted from the sum.
Answer:
a + b – c or b + a – c

Example 7
Write an expression to show c minus the sum of a and b.
Answer:
c – (a + b)

Why are parentheses necessary in this example and not the others?
Answer:
Without the parentheses, only a is being taken away from c, where the expression says that a + b should be taken away from c.

Replace the variables with numbers to see if c – (a + b) is the same as c – a + b.

### Eureka Math Grade 6 Module 4 Lesson 9 Exercise Answer Key

Exercise 1.
Write an expression to show the sum of 7 and 1. 5.
Answer:
7 + 1.5 or 1.5 + 7

Exercise 2.
Write two expressions to show w increased by 4. Then, draw models to prove that both expressions represent the same thing.
Answer:
w + 4 and 4 + w Exercise 3.
Write an expression to show the sum of a, b, and c.
Answer:
Answers will vary. Below are possible answers.
a + b + c               b + c + a           c + b + a
a + c + b               b + a + c           c + a + b

Exercise 4.
Write an expression and a model showing 3 less than p.
Answer:
p – 3 Exercise 5.
Write an expression to show the difference of 3 and p.
Answer:
3 – p

Exercise 6.
Write an expression to show 4 less than the sum of g and 5.
Answer:
g + 5 – 4 or 5 + g – 4

Exercise 7.
Write an expression to show 4 decreased by the sum of g and 5.
Answer:
4 – (g + 5) or 4 – (5 + g)

Exercise 8.
Should Exercises 6 and 7 have different expressions? Why or why not?
Answer:
The expressions are different because one includes the word “decreased by”and the other has the words ‘less than.” The words “less than” give the amount that was taken away first, whereas the word “decreased by” gives us a starting amount and then the amount that was taken away.

### Eureka Math Grade 6 Module 4 Lesson 9 Problem Set Answer Key

Question 1.
Write two expressions to show a number increased by 11. Then, draw models to prove that both expressions represent the same thing.
Answer:
a + 11 and 11 + a Question 2.
Write an expression to show the sum of x and y.
Answer:
x + y or y + x

Question 3.
Write an expression to show h decreased by 13.
Answer:
h – 13

Question 4.
Write an expression to show k less than 3. 5.
Answer:
3.5 – k

Question 5.
Write an expression to show the sum of g and h reduced by 11.
Answer:
g + h – 11

Question 6.
Write an expression to show 5 less than y, plus g.
Answer:
y – 5 + g

Question 7.
Write an expression to show 5 less than the sum of y and g.
Answer:
y + g – 5

### Eureka Math Grade 6 Module 4 Lesson 9 Exit Ticket Answer Key

Question 1.
Write an expression showing the sum of 8 and a number f.
Answer:
8 + f or f + 8

Question 2.
Write an expression showing 5 less than the number k.
Answer:
k – 5

Question 3.
Write an expression showing the sum of a number h and a number w minus 11.
Answer:
h + w – 11

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