# Keywords for Addition and Subtraction

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Susan S.

## Basics on the topicKeywords for Addition and Subtraction

In order to translate word problems into mathematical expressions, it is helpful to know certain keywords to look for which indicate which mathematical operations to use. Specifically, words like sum, total, increase, add, plus are commonly used for addition, as well as words like altogether, combine, more than, all, both, and so on. The same goes for subtraction: decrease, minus, fewer, take away, difference, left, less than, subtract, remain, and so on. Learn how to recognize keywords for addition and subtraction by helping Caulleen solve a mystery at her school, the Academy of Magic. Common Core Reference: CCSS.MATH.CONTENT.6.EE.A.2

### TranscriptKeywords for Addition and Subtraction

At the Academy of Magic, Caulleen is hot on the trail of a breaking story for her school paper. According to rumors, the school's Switch Quitch Team has been experiencing an odd phenomenon: Brooms from the equipment room are going missing, only to mysteriously return a few hours later, as if nothing had happened! In order to crack this case, we will need to identify keywords for using addition and subtraction.

### How you turn keywords into mathematical expressions

Caulleen plans to start her investiagation by interviewing the Switch Quitch coach. She needs to start with the basics: who had access to the equipment room? The coach tells her that one of the new boys on the team is in charge of equipment. But he can't remember his name. But he knows the number of boys and girls on the team altogether is equal to 20. He knows this because the total sum of players on the team was 16 last year, but increased by 4 this year. How can we turn this information into mathematical equations so we can be sure of how many players are on the team?

### Keywords which are indicating Addition

When information about math operations is presented in a word problem format, look for keywords that indicate the correct operation to use. Let's start with the first fact the coach told us. The total number of boys and girls on the team is 20, altogether. The keywords 'total' and 'altogether' tell us that this is an addition problem. We don't know exactly how many boys and girls there were, but we can use the variables 'b' and 'g' to represent them. Finally, we know that the total number is 20, so that goes to the right of the equal sign. Let's move on to the second thing we learned. She told us that last year, the total sum of players on the team was 16 but increased by 4 this year. The words "total sum" and "increase" tell us that this is also an addition problem. We can use the variable 'p' to represent the players on the team. The number 16 tells us the number of players last year and 4 is the number we are increasing by.

### Keywords which are indicating subtraction

Hm...very interesting, but we're going to need some more clues to solve this mystery. Caulleen decides to talk to the Switch Quitch team captain to see what she knows about the missing brooms. The captain tells Caulleen there should be 20 brooms in the supply room, but today, that amount decreased by 3. Let's convert this to an algebraic expression. By focusing on the keyword decreased, we know to use subtraction. Now we can insert the number of brooms there should be and take away the number that are missing. That's another helpful clue, but still we aren't any closer to solving the mystery. But suddenly the team captain remembers that, actually, today there wasn't just brooms missing. There was one ball fewer than there normally in the equipment closet. Even though we don't know how many balls there normally are in the equipment closet, we can write this as an algebraic expressions. The keywords "fewer than" indicate that we should be using subtraction in our expression. We can use the variable 'n' to represent the number of balls that there usually are. Since there was one fewer than the number of balls there usually are, we can write this as the expression n - 1. Two more pieces have been added to the puzzle. But what does it all mean?

### Keywords overview - Addition and subtraction

Before we get back to Caulleen, remember that there are a lot of keywords that can be used to indicate addition and subtraction. For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference. Can you think of any others?

Back to the missing brooms. As she's going over her notes, Caulleen starts to hear a strange rustling sound coming from outside. Is someone playing Switch Quitch? It looks like those missing brooms are having fun without the students of the Academy of Magic. But actually, you know what? These guys are pretty good!

## Keywords for Addition and Subtraction exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Keywords for Addition and Subtraction.
• ### Identify the keywords that indicate subtraction.

Hints

The expression describing the information above is given by $20-3$.

$1$ ball fewer means $-1$.

Further keywords which indicate subtraction are

• take away
• less than
• difference
• minus
• subtract
Perhaps you can replace one of the words above by one of these keywords; try it.

Solution

Keep the keywords for subtraction pictured beside in mind in this exercise.

Using those keywords you can solve word problems:

• "There should be $20$ brooms in the supply room, but today there are $3$ less brooms in the supply room." ... this sentence translates to $20-3$ brooms in the supply room.

• "There was $1$ ball fewer than there normally are in the equipment closet."... this sentence translates to means $n-1$, where $n$ stants for the normal number of balls in the equipment closet.
So the words less and fewer in these sentences indicate subtraction.

• ### Decide if the keywords indicate addition or subtraction.

Hints

Let's have a look at an example: Paul has $20$ dollars more than Anne. Let $p$ be the amount Paul has, and let $a$ be the amount of money Anne has. We can then see that $p=a+20$.

Let's look at another example: Frank ate two pieces of cake less than Mary. Mary ate $3$ pieces of cake. We then know that Frank ate $3-2=1$ pieces of cake.

$+$ is the plus sign, while $-$ is the minus sign.

Solution

$+$ is the plus sign. So the following phrases indicate plus:

• total sum
• altogether or one can also say in total
• and or plus are rather clear
• combine
• increase
• more than
$-$ is the minus sign. So the following phrases indicate minus:

• fewer than
• decrease
• less than
• take away is another expression for subtract
• Subtraction means
• minus
• ### Explain how to transfer the word problem to an equation.

Hints

Check the word problems above for the keyword of addition or subtraction.

• $+$ is the sign for addition
• $-$ is the sign for subtraction

Let's have a look at another example:

The total sum of all spell books and wands is $35$.

• Total sum indicates addition.
• You have to assign variables to the unknown values; let's let $s$ stand for the number of spell books and $w$ for the number of wands.
• The sum of all spell books and wands can be written as $s+w$.
• The fact that this sum is equal to $35$ leads to the equation, $s+w=35$.
Solution

If you have to transform a word problem in a mathematical expression, you first have to decide which kind of operator you have to use.

Here we have to distinguish between addition and subtraction. The corresponding keywords are pictured beside.

So, let's have a look at the given examples for word problems. The keywords are written in bold:

• Last night the total of spell books in the classroom was $24$, but there were $5$ less in the classroom this morning.
This keyword indicates subtraction. We have to subtract $5$ from $24$. This leads to the expression, $24-5$.

• The difference between the students’ wands last night and this morning is $13$.
The result of a subtraction is the difference. Because neither the number of students' wands last night nor this morning are known, we assign variables to those unknown values: $l$ for last night and $m$ for morning. The difference of those values is $l-m$. Pay attention to the order of subtraction, as it matters here.

The value of the difference, $13$, is known. So we get the equation, $l-m=13$.

• Last but not least, the number of potion ingredients combined with the number of black cats increased by $3$.
Here we have two keywords for addition. Again we assign variables to the unknown values: $p$ for the number of potions and $b$ for the number of black cats. Combining those values can then be written down as $p+b$. The combination of those values is increased by $3$. So we have to add $3$ to get the corresponding expression, $p+b+3$.

• ### Decide how to express the word problems in the form of equations.

Hints

First think about which operation you need to use: addition or subtraction?

You don't have to solve the corresponding equations.

Solution

If you have to transform any word problem into a mathematical expression, you first have to decide which operations you need to use.

To help you decide which operations are needed, you can highlight the corresponding keywords:

• The difference between the number of boys ($x$) and girls ($y$) is $5$.
Here we have to subtract: $x-y=5$. Take care of the order because $x-y\neq y-x$ in general.

• The total sum of boys ($x$) and girls ($y$) is $45$.
This indicates addition. So we get $x+y=45$.

• The number of wands $x$ is $5$ more than $45$.
Once again we have an addition exercise: $x=45+5$.

• If you take away $5$ from the number of brooms $x$ you get $5$.
This keyword indicates subtraction, $x-5=5$.

• ### Find all keywords that indicate addition.

Hints

Try to examine the corresponding expression. How can you recognize if you have to add or to subtract?

The expression for the information above, with $b$ representing the number of boys and $g$ representing the number of girls is $b+g=20$.

Keep these keywords pictured in mind.

Solution

It's better to keep the keywords for addition, pictured beside, in mind, as well as those for subtraction, so we can solve word problems.

Let's have a look at the examples above:

• Combining the number of boys and girls on the team gives $20$ members of the team altogether.
• The total sum of players on the team was $16$, but increased by $4$.
So the words combining, altogether, total sum, and increased indicate addition in these sentences.

• ### Express the word problems as equations.

Hints

When constructing the expressions corresponding to the word problems given, units shouldn't be included.

Keywords like sum, add, combine, and more than indicate addition.

Keywords like minus, difference, fewer, and take away indicate subtraction.

Solution

First let's have a look at the temperature: the average temperature of the last year ($x$) increased by $2^\circ F$ to $92^\circ F$. So we have $x+5=92$.

Next, let the price of the Richard's preferred car be $x$, and let the price of his wife's preferred car be $y$. If Richard combines both prices he gets $23000$ dollars. Thus, we have $x+y=23000$.

Richard would like to buy a new broom: the Super Broom Number $1$ costs $450$ dollars, while Top Broom Highlevel's price is unknown, say $x$. The price $x$ is $5$ dollars fewer than the price of the Super Broom Number $1$. This leads to the equation $450-35=x$.

Last we examine the stock exchange together with Richard: the sum of $x$ and $y$ is given by the expression $x+y$. Next, minus $23$ - this gives us $x+y-23$. The keyword more than indicates that $x+y-23$ is equal to $z+45$, finally giving us the equation $x+y-23=z+45$.