# Evaluate Numerical Expressions with ( ), { } and [ ] – Write Numerical Expressions

## Overview

**Write Numerical Expressions**

We can use what we’ve learned about the order of operations to write our own

numerical expressions. Let’s look at an example.

Write an expression for the sum of **28** and **7**, divided by **5**

__What we know:__

Sum is an addition word

Divided by signals division.

Listing what we know helps us determine which numbers and operations should be included in the expression. We can see that the expression will include both addition and division.

Next, we need to determine the order of operations.

The problem states that the sum of **28** and **7** is divided by **5**. So, we need to add

**28** and **7** before dividing by **5**. We can use parentheses in our expression to ensure

addition is calculated first.

The answer is

Let’s look at another example.

Lara’s garden has two times as many cucumbers as Sarah’s garden. Sarah’s garden has 6 rows of 3 cucumbers. Write an expression to determine how many cucumbers Lara has in her garden. Do not evaluate the expression.

__What we know:__

Lara has two times as many cucumbers as Sarah ✓

Sarah has **6** rows of **3** cucumbers ✓

The phrase two times as many signals that this is a comparison problem, which means our expression will include multiplication. The word of also signals multiplication.

Next, we need to determine the order of operations.

The problem states that Lara’s garden has twice as many cucumbers as Sarah’s garden. So, we need to calculate the number of cucumbers in Sarah’s garden first.

Then, we can double it to find the number of cucumbers in Lara’s garden.

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The picture below represents **5 + 9**.

Draw a picture that represents

Answers may vary, but should represent 4 times the original equation. For example:

Write an expression that represents the product of **3** times **5** more than **3 **

It’s a comparison problem. The addition needs to be calculated first.

Find an expression that represents **4** times as large as the expression

Use braces to ensure the original expression is calculated before multiplying by 4.

Find an expression that represents the sum of **12** and **4**, divided in half.

To express the sum of 12 and 4, we use addition. To represent half, we divide by 2.

Which phrase could represent the expression

- Twice as many as the difference between 9 and 3
- The product of 9 and 3, times 2
- The quotient of 9 and 3, doubled
- 9 minus the product of 3 and 2

Twice as many as the difference between 9 and 3

The difference between 9 and 3 represents (9 – 3). Twice as many represents the multiplication.

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