McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations

All the solutions provided in McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Properties and Equations will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Properties and Equations

Essential Question

How are properties and equations used to group numbers?
Answer: The associative property gets its name from the word “Associate” and it refers to the grouping of numbers. This property states that when three or more numbers are added (or multiplied), the sum(or product) is the same regardless of the grouping of the addends (or multiplicands).

The most commonly used grouping symbols are parentheses. Operations inside parentheses can be done before any other operations in order to simplify the problem. for example 4(3 + 5).

Explanation:
The example for Associative property
The property which states that the grouping of the addends does not change the sum is called Associative property.
19 + (61 + 15) = 95
Associative property is used.

Hence, properties and equations used to group numbers

Am I Ready

Algebra Find each unknown.

Question 1.
8 + McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1 = 11
The unknown is _____________.
Answer: The unknown is 3

Explanation:
Given, 8 + McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1 = 11
Let the unknown be y
8 + y = 11
y = 11 – 8
y = 3 ,
To check, replace y value in the given equation, then we get
8 + 3 = 11
11 = 11
So, The Unknown is 3.

Question 2.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1 × 5 = 20
The unknown is _____________.
Answer:  The Unknown is 4.

Explanation:
Given, McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1 × 5 = 20
Let the unknown be y
5y = 20
y = \(\frac{20}{5}\)
y = 4 ,
To check, replace y value in the given equation, then we get
4 × 5 = 20
20 = 20
So, The Unknown is 4.

Question 3.
36 ÷ 6 = McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1
The unknown is _____________.
Answer: The unknown is 6

Explanation:
Given, 36 ÷ 6 = McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1
Let the unknown be y
36 ÷ 6 = y
y = \(\frac{36}{6}\)
y = 6 ,
So, The Unknown is 6.

Question 4.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 2
The unknown is _____________.
Answer: The unknown is 9

Explanation:
Let the unknown be y
15 – y = 6
y = 15 – 6
y = 9.
So, The unknown is 9

Question 5.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 3
The unknown is _____________.
Answer:  The unknown is 3

Explanation:
Let the unknown be y
9y = 27
y = \(\frac{27}{9}\)
y = 3.
So, The unknown is 3.

Question 6.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 4
The unknown is _____________.
Answer:  The unknown is 6.

Explanation:
Let the unknown be y
42 ÷ 7 = y
y = \(\frac{42}{7}\)
y = 6.
So, The unknown is 6.

Question 7.
Use the number sentence 12 + 15 + McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1 = 36 to find how many books Tony read in August.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 5
The unknown is ______________ books.
Answer: The unknown is 9 books

Explanation:
Given, 12 + 15 + y = 36
let the unknown be y
27 + y = 36
y = 36 – 27
y = 9
So, The unknown is 9 books.

Question 8.
Circle the property which is represented by 6 + 5 = 5 + 6.
Associative Property of Addition
Commutative Property of Addition
Identity Property of Addition
Answer: Commutative Property of Addition

Explanation:
Given, 6 + 5 = 5 + 6.
The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
So, 6 + 5 = 5 + 6 represents Commutative Property of Addition

Question 9.
Abia sold 1 more candle than Mel. Together, they sold 15 candles. Draw a picture that shows how many candles they each sold.
Answer: Mel sold 7 candles and Abia sold 8 candles ,Together, they sold 15 candles.

Explanation:
Given, Abia sold 1 more candle than Mel. Together, they sold 15 candles.
It  will be, Mel sold 7 candles and Abia sold 8 candles , 7 + 8 = 15
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.1
So, Together, they sold 15 candles.

Question 10.
Daniela spent $20 at the grocery store and $15 at the gas station. How much did she spend in all? Write a number sentence with a symbol for the unknown. Solve.
Answer: She spent $35 in all.

Explanation:
Given, Daniela spent $20 at the grocery store and $15 at the gas station.
Let the unknown be y
$20 + $15 = y
y = $35
so, She spent $35 in all.

My Math Words

Review Vocabulary

array
decompose
equals sign (=)
known fact
unknown

Making Connections
Label each section of the flow chart with the correct review vocabulary word.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 6
Answer: McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.2

My Vocabulary Cards

McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 7

Ideas for Use

  • During this school year, create a separate stack of cards for key math verbs, such as evaluate. These verbs will help you in your problem solving.
  • Use the blank card to write examples that will help you with concepts like writing and evaluating expressions.

This property allows you to decompose one factor into addends that are easier to multiply.
How can you use this method to find 7 × 2?
Answer: Distributive property allows you to decompose one factor into addends that are easier to multiply.

Explanation:
Given, 7 × 2 = 14
By using Distributive property, we get
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.3
7 × 2 = 10 + 4
14 = 14.
So, Distributive property allows you to decompose one factor into addends that are easier to multiply.

To find the value of an expression.
How do parentheses help you evaluate the problem on the front of the card?
Answer: By solving inside the parentheses first, in order to find the value of an expression.

Explanation:
For example,
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.4
So, Always solve inside the parentheses first.

A mathematical process, which includes addition, subtraction, multiplication, and division.
Explain in your own words what it means to multiply.
Answer: multiply means the repeated addition of groups of equal sizes. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division.

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.5

The property that states that the grouping of factors does not change the product. It can make multiplying 3 numbers easier.
Write a number sentence that is an example of the Associative Property of Multiplication.
Answer:  The associative property gets its name from the word “Associate” and it refers to the grouping of numbers. This property states that when three or more numbers are added (or multiplied), the sum(or product) is the same regardless of the grouping of the addends (or multiplicands).

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.6
For example,
7 ×(2 × 3) = (7 × 2) × 3 = 42.

A sentence that contains an equals sign (=), showing that two expressions are equal.
How does knowing the meaning of equal help you remember the definition of equation?
Answer:  the equal sign in mathematics describes equality between the values, equations, or expressions written on both sides.

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.7

A combination of numbers and operations that represent a quantity.
How can the meaning of the word “express” help you remember what an expression is?
Answer: An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.8

A letter or symbol, such as McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 1, ?, or m used to represent an unknown quantity.
Variable is a multiple-meaning word. Use a dictionary to write the meaning of variable used in this sentence. The weather during spring can be variable.
Answer:  The sentence meaning of ” The weather during spring can be variable”. is the weather is able to change in the spring.

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.9

My Foldable

Follow the steps on the back to make your Foldable.
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 8

McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 9
Explain
The property which states the ____________ in which two numbers are multiplied does not change the _____________.
Example
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 10
Answer: The property which states the order in which two numbers are multiplied does not change the product is commutative property

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.3
Given , 5 × 3  = 3 × 5
15 = 15.
So, The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

Explain
The property which allows me to _____________ factors into addends that are easier to work with.
Example
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 11
Answer: The property which allows me to decompose factors into addends that are easier to work with is Distributive property

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.4
Given, 2 × 4 = ( 2 × 3 ) + ( 2 × 1)
8 = 6 + 2
8 = 8
So, Distributive property allows you to decompose one factor into addends that are easier to multiply.

Explain
The property which states that the grouping of _____________ does not change the ______________.
Example
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations 12
Answer: The property which states that the grouping of numbers does not change the product is Associative property.

Explanation:
McGraw Hill My Math Grade 3 Chapter 9 Answer Key Properties and Equations.5
Given, (1 × 2) × 3 = 1 × ( 2 × 3 )
6 = 6
So, The associative property gets its name from the word “Associate” and it refers to the grouping of numbers.

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