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12.1: Addition and Subtraction Phrases as Expressions

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Have you ever gone on a field trip?

Mrs. Hawk's sixth grade class wants to go on a field trip. They are trying to decide between the zoo and the amusement park. If they go to the zoo, then the seventh grade will join them on the trip.

Mrs. Hawk tells the class that if the seventh grade joins them that they will bring 23 students and so 59 students will go on the trip.

Based on these numbers, how many students are in the sixth grade?

Can you write an expression to demonstrate this situation?

This Concept is about writing addition and subtraction expressions. Pay attention and you will know just how to handle these questions at the end of it.

Guidance

In earlier Concepts, you learned about numerical and algebraic expressions. A variable expression is a type of expression. First, let’s review what we mean by the word “ expression ”.

What is an expression?

An expression is a combination of variables, numbers and operations without an equals sign. An expression can have changeable parts to it. The variables in an expression can have different values. Therefore, we evaluate an expression, we don’t solve it. That is the reason why there isn’t an equal sign with an expression.

What is a variable?

A variable is a letter used to represent an unknown quantity.

Notice that variables are a part of an expression. You have already learned how to evaluate expressions when you have been given a value for the variable.

Evaluate 3x+1 when x=4

To figure this out, we substitute the four in for x and then evaluate the expression.

&3(4) + 1\\&12 + 1\\&13

The answer to this problem is 13.

Here, the expression was given to you. Someone else wrote the expression. Now it is time for you to learn how to write an expression from a phrase.

How can we write an expression from a phrase?

We can write expressions to represent different situations. To write an expression, you will need to pay attention to key words which identify different operations, unknown variables and numbers. When you have identified these things, you will be able to write variable expressions from phrases.

Today, we are going to start by writing expressions involving addition and subtraction.

Five more than an unknown number

First, we break down this phrase. Identify the numbers involved. The only number involved here is the number five.

5

Next, we look for an operation, “More than” is a key word that means "add", so our operation is addition.

+

Finally there are the words “an unknown number”. An unknown number is represented by a variable. In this expression, we can use the letter x .

Now we can put it all together.

5 + x

To write expressions from phrases, you will need to work like a detective. You have to decipher the meaning of the words in the phrase and then put the pieces of the puzzle together by writing the expression.

Key words help you in identifying which operation is involved in the expression. Let’s look at some key words that mean addition and subtraction.

Addition

Sum, plus, altogether, and

Subtraction

Difference, less than, subtract, take away

Nine less than an unknown quantity

First, let’s look for the numbers in this phrase. The only number here is the number nine.

9

"Less than" means subtraction.

Finally, we have the words “unknown quantity” and so we use a variable. Let’s use the variable y .

Now we can write the expression. Notice that we have 9 less than an unknown quantity so we write the variable first, then the subtraction symbol and finally the number 9.

The answer is x-9 .

Practice writing expressions from the following phrases.

Example A

An unknown number and four

Solution: x + 4

Example B

The difference between ten and an unknown number

Solution: 10 - x or x - 10

Example C

Seven less than a number

Solution: x - 7

Now back to Mrs. Hawk's sixth grade class. Here is the original problem once again.

Mrs. Hawk's sixth grade class wants to go on a field trip. They are trying to decide between the zoo and the amusement park. If they go to the zoo, then the seventh grade will join them on the trip.

Mrs. Hawk tells the class that if the seventh grade joins them that they will bring 23 students and so 59 students will go on the trip.

Based on these numbers, how many students are in the sixth grade?

Can you write an expression to demonstrate this situation?

First, let's write an expression to describe the situation.

23 students are in the seventh grade

59 will be the total number of students.

The unknown is the number of students in the sixth grade. We can use x to represent this unknown quantity.

Here is our expression.

23 + x + 59

Based on this expression, we can use mental math to figure out that there are 29 students in the sixth grade.

This is our answer.

Vocabulary

Here are the vocabulary words in this Concept.

Variable Expression
a variable expression has variables or unknown quantities, numbers and operations without an equal sign.

Guided Practice

Here is one for you to try on your own.

Seven less than the quantity of six and an unknown number.

Answer

This one is tricky because it has both addition and subtraction in it. The key here is the word "quantity". This lets you know that there is going to be a set of parentheses in your problem.

"Seven less than" tells you that seven is being taken away from this quantity.

Here is the expression:

(6 + x) - 7

This is our answer.

Video Review

Here are videos for review.

James Sousa, Introduction to Variables and Variable Expressions

James Sousa, Example of Writing Variable Expressions

Practice

Directions: Write addition and subtraction phrases as single-variable expressions.

1. The sum of six and an unknown number

2. A number and seven

3. Four less than a number

4. The sum of a number and fourteen

5. The difference between twenty and an unknown number

6. Twenty-five take away a number

7. Ten less than a number

8. Thirty-seven plus an unknown quantity

9. The sum of nine and an unknown number

10. An unknown number and eight

11. An unknown number plus the quantity six plus seven.

12. The sum of fifteen and an unknown number

13. Thirty less than the quantity of twenty - five and an unknown number.

14. Twelve less than an unknown number

15. Sixteen and seven plus an unknown number

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Date Created:

Oct 29, 2012

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Aug 18, 2014
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