Writing and Evaluating Expressions with Addition and Subtraction

Writing and Evaluating Expressions with Addition and Subtraction exercise

• Determine the total number of bags of sour sweets the scarecrow has.

  Hints

  If Peter has $8$ candies and Paul has $2$ candies more candles than Peter, then Paul has $10$ candies.

  More than indicates that the number of bags of sour sweets that the scarecrows has is greater than the number of bags the pumpkin has.

  Imagine this situation as follows: you have $6$ bags of sour sweets and you put $5$ more bags with those $6$ bags.

  Solution

  How many bags of sour sweets does the scarecrow have:

  The scarecrow has $6$ more bags of sour sweets than the pumpkin.

  The keyword more indicates addition.

  So we have to add the number of bags the pumpkin has to $6$.

  We already know the number of pumpkins bags, it's $5$.

  Thus, we have $6+5=11$.

  The scarecrow has eleven bags of sour sweets.

• Establish the corresponding algebraic expression.

  Hints

  More than indicates addition. The pumpkin has more jelly bean packs than the witch.

  Also the word receives is a keyword for addition.

  The pumpkin already has a certain number of jelly bean packs and he gets $7$ more packs.

  If you want to know how many more packs the pumpkin has, then take the difference.

  Pay attention to the order: while you can use the commutative property for addition, $a+b=b+a$, it is the case that $a-b\neq b-a$.

  Solution

  The witch has three packs of jelly beans. So this is the number to put into the first row.

  The pumpkin has $6$ more packs than the witch and receives $7$ packs from the scarecrow; we can proceed as follows:

  1. Add $6$ to $3$. This leads to $6+3=9$.
  2. Next add $7$ to the resulting sum, $9$, to get $9+7=16$.

  To answer the question, "How many more packs the pumpkin has than the witch?", we look at the difference between the number of packs the pumpkin and the witch have. This is $16-3=13$.

  So the pumpkin has $13$ more packs of jelly beans than the witch.

• Find the mistakes in the calculation.

  Hints

  First look at the keywords:

  • More than indicates addition.
  • In total implies addition as well.
  • Take away indicates subtraction.

  Pay attention to the order.

  There is a difference between $4-2=2$ and $2-4=-2$.

  Check the expressions by evaluating them. Next check if the result coincides with the word problem.

  Solution

  To write a word problem as an algebraic expression you have to detect keywords.

  • Tim has eaten $3$ muffins. Gina has eaten $4$ muffins more.

  More than indicates that we have to add $3+4=7$. This is number of muffins eaten by Gina.

  • Tim has eaten $3$ muffins and Gina has eaten $2$ muffins.

  In total indicates addition.

  So, in total they have eaten $3+2=5$ muffins.

  • Tim has eaten $3$ muffins and Gina has eaten $2$ muffins. How many muffins more has Tim eaten than Gina?

  More than would indicate addition. The number of muffins more is unknown, so we assign $m$ to this unknown value. The regarding expression is $3=2+m$. We can determine the difference, and thus the answer to the question:

  $3-2=1$.

  So we can conclude that Tim has eaten $1$ more muffin than Gina.

  • Gina has eaten $4$ muffins. If you take away $2$ muffins you get the number of muffins eaten by Tim.

  Take away indicates subtraction. $4-2=2$.

  Tim has eaten $2$ muffins.

• Decide how many more muffins Ben has eaten than Jerry.

  Hints

  More than indicates addition. The number of Ben's muffins is greater than the number of Jerry's muffins.

  Pay attention to the order:

  While you can use the commutative property, $a+b=b+a$, note that $a-b\neq b-a$.

  Give away indicates subtraction.

  Solution

  Let's start with Jerry's $4$ Muffins. Ben has $2$ muffins more. This gives us $4+2=6$ muffins.

  The $8$ muffins from aunt Mary should be added to the $6$ muffins we already have:

  $6+8=14$.

  Now Ben gives $5$ away to his friend Paul. This reduces the number of muffins to

  $14-5=9$ muffins.

  Last we want to know how many muffins Ben has more than Jerry. For this we have to subtract $4$, the number of Jerry's muffins, from $9$. This results in $9-4=5$.

  So we can conclude that Ben has $5$ Muffins more than Jerry.

• Decide which keyword belongs to which operation.

  Hints

  Create an example for each given keyword.

  For example, Paul has $4$ books and Anne has $3$ books more than Paul.

  So Anna has $7$ books.

  Keep the following in mind:

  • Summand $+$ summand $=$ sum. The corresponding operation is addition.
  • Minuend $-$ subtrahend $=$ difference. The corresponding operation is subtraction.

  • $+$ is the plus-sign for addition.
  • $-$ is the minus-sign for subtraction.

  Solution

  To write and to evaluate algebraic expressions you first have to recognize keywords for the corresponding operation.

  The following are some keywords for addition:

  • add
  • altogether
  • more than
  • both
  • in all
  • in total
  • sum

  The following are some keywords for subtraction:

  • difference
  • fewer than
  • left
  • minus
  • remains
  • subtract

• Identify the unknown quantity in each word problem. Write the corresponding expression down and evaluate it.

  Hints

  First determine the corresponding algebraic expression or equation using keywords.

  Put the value for the variable in the corresponding expression.

  Solve an equation if it's possible.

  Just have a look at the example beside.

  Solution

  Sarah and Erin: Sarah has been swimming for $4$ years more than Erin, $e$. This leads to $4+e$. If we know the number of years Erin swims, namely $5$ years, we can determine the corresponding number of years Sarah has been swimming: $4+5=9$.

  The Braves scored $3$ fewer runs than the reds; this leads to $r-3$. With the known runs of the reds, $7$, we can calculate $7-3=4$, the number of Braves runs.

  Paul counts the number of the visitors of Matteo's taco bar. There are $2$ more males than females. This leads to $f+2$. If the number of female visitors, namely $23$, is known, then this gives us the number $23+2=25$ of male visitors.

  Matteo and Lucy practice $m+l$ word problems together. The total number of tasks is $22$. Thus we get the equation $m+l=22$. Knowing that Matteo does $13$ tasks we can follow $13+l=22$. Subtracting $13$ leads to $l=22-13=9$.