*Contributor: Ashley Nail. Lesson ID: 13885*

Did you know 6 x (5 + 3) is the same as "the sum of 5 and 3 multiplied by 6"? It's like two different languages! Learn how to translate between written and mathematical expressions!

categories

subject

Math

learning style

Auditory, Visual

personality style

Lion, Otter, Beaver, Golden Retriever

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Sierra is helping her dad plan the grocery list for the week.

She packs lunches for her brothers five times a week. Every day, Max takes four oranges, Jason takes three oranges, and Liam takes one orange.

- How many oranges does Sierra need to put on the grocery list?

- Can you help Sierra solve this problem by writing and translating expressions?

- What does it mean to translate expressions?

Think of translating between two languages. The Spanish expression *Tengo un perro* translates to the English expression *I have a dog*.

We can translate expressions in math also!

For example, look at this expression written in words:

*82 minus the sum of 13 and 24*

We can translate this statement into a mathematical expression.

We know which symbol to use for minus, and we also know sum means we will be adding:

*82 - 13 + 24*

- Is this expression translated correctly?

No! According to this incorrect translation, you would follow the order of operations and first calculate 82-13, then add 24.

This is not what the written expression is asking you to do. You are supposed to take 82 - (*the sum*).

The correct translated expression is:

*82 - (13 + 24)*

Now, according to the order of operations, you would first add inside the parentheses and then subtract that amount from 82.

Parentheses are very important when translating mathematical expressions!

Let’s translate another expression!

Look at the written expression:

*5 times as large as the difference of 64 and 11*

Now, let’s translate the expression into a mathematical expression.

- What is the first thing this expression will want us to calculate?
- The
*difference*or the*times*?

The difference will be evaluated first, so it will be in parentheses. We also know that difference means the answer to a subtraction problem:

*(64 - 11)*

That’s one part of the expression translated!

The last part is *5 times as large as the difference*. Well, we know the difference now, we just need to show what 5 times that difference will look like:

*5 x (64 - 11) *

- Is translating expressions starting to make sense to you?

If you need to review the order of operations or definitions of mathematical words, check out the **Additional Resource** found in the right-hand sidebar.

Let’s look at even more examples of translating expressions!

Click on each to see its translation:

Answer the following out loud:

- What does
*half*mean?

- What is a
*quotient*?

- What is a
*product*?

- How can
*and*help you translate expressions?

- What would happen if you forgot parentheses or put them in the wrong place?

If you need more help understanding how to translate mathematical expressions, check out *Writing Expressions (5.OA.2) | 5th Grade Math (Part 2)* from Math with Mr. J:

When you are ready, click next to visit the* Got It?* section to practice translating expressions on your own!

After practicing, you will be able to help Sierra finish her grocery list!

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