Keywords for Addition and Subtraction

Keywords for Addition and Subtraction exercise

• 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 $n$ stands 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 $x+y-23=z+45$.