How to Use Properties of Numbers to Write Equivalent Expressions?

A step-by-step guide to using properties to write equivalent expressions

To write equivalent expressions, you can use properties of operations. There are some common properties:

• Associative property of addition: \(\color{blue}{(a+b)+c=a+(b+c)}\)
• Associative property of multiplication: \(\color{blue}{(a×b)c=a(b×c)}\)
• Commutative property of addition:\(\color{blue}{a+b=b+a}\)
• Commutative property of multiplication: \(\color{blue}{a×b=b×a}\)
• Distributive property: \(\color{blue}{a(b+c)=a×b+a×c}\)

Here’s a step-by-step guide to using properties to write equivalent expressions:

1. Identify the expression you want to simplify.
2. Choose the property that you will use to simplify the expression.
3. Apply the chosen property to the expression to simplify it.
4. Repeat steps 2 and 3 until the expression is in its simplest form.
5. Check your answer to make sure that it is equivalent to the original expression by using the properties in reverse.

Using Properties to Write Equivalent Expressions – Example 1

Complete and solve the expressions.
\(7r+5+6r=7r+… +5=\)?
Solution:
This expression is a commutative property of addition. So, if the order of addends changes, the sum does not change.
The missing number is \(6r\).
Now combine like terms: \(7r+6r=13r\)
\(13r+5\)

Using Properties to Write Equivalent Expressions – Example 2

Complete and solve the expressions.
\((9t+8)×3= ×3+8×3=\)?
Solution:
This expression is a commutative property of multiplication. So, if the order of factors changes, the product does not change.
The missing factor is \(9t\).
Now multiply: \(9t×3+8×3=27t+24\)

Exercises for Using Properties to Write Equivalent Expressions

Write the equivalent of each expression.

1. \(\color{blue}{8y+4y}\)
2. \(\color{blue}{7+n}\)
3. \(\color{blue}{x+5}\)

1. \(\color{blue}{y\:(8+4)}\)
2. \(\color{blue}{n+7}\)
3. \(\color{blue}{5+x}\)