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Mixed Addition and Subtraction Word Problems

Mixed Addition And Subtraction Word Problems


Internal performance of the operation helps improve confidence, but determining which math operation is required to solve a certain problem is a key word problem skill. The exercises in this topic combine addition and subtraction word problems on the same page, requiring students to not only answer the problem but also to figure out exactly how to solve it. Students need to be able to apply what they’ve learned in class to real-world situations. Term problems involving addition and subtraction present pupils with such possibilities. Here, the emphasis is on determining the operation that is necessary. Is it necessary to add? Is subtraction necessary?

While the level of difficulty may vary, solving word problems takes a methodical strategy that includes identifying the problem, acquiring relevant data, formulating the solution, solving, and double-checking the work.

Steps to solved mixed word problems

Determine the issue

First, figure out what scenario that problem wants us to address. This could be expressed as a query or a comment. In either case, the word problem has all of the material we’ll need to solve it. One can determine the unit of measurement for the final answer once you’ve identified the problem. The question in the following example asks students to calculate the total number of socks owned by the two sisters. Pairs of socks are the unit of measurement for this problem. look at the problem, Vanessa’s sock collection comprises of four pairs of red socks and twelve pairs of blue socks. Mark, Vanessa’s brother, owns eight pairs of socks. How many pairs of purple socks do the sisters have left if she owns nine pairs and her smaller sister loses two pairs?

Collect information

Make a table, list, graph, or chart that summarizes the information you already have and leaves holes for what you don’t. Each word problem may require a different structure, but having a visual representation of the data makes it a lot easier to deal with.

Because the question in this case is about how many socks the sisters own jointly, you can ignore the information regarding Mark. It also doesn’t matter what color socks you wear. This removes a lot of the data, leaving you with simply the total number of socks the siblings started with and the number of socks the smaller sister lost.

Construct a formula

Any of math terms can be converted to math symbols. These words and phrases “sum,” “more than,” “increased,” and “in addition to” all mean “to add,” therefore draw the “+” symbol over them. Make an algebraic expression that expresses the problem by using a letter for the unknown parameter.

Add up the total number of pairs of socks Suzy has in the scenario — eight plus six. Take her sister’s total number of pairs, which is nine. Both sisters have a total of 4+ 12 + 9 pairs of socks. Remove the two missing pairs for a final equation of (4 + 12 + 9) – 2 = n, where n is the remaining separation between two of socks for the sisters.

Resolve the Problem

Resolve the issue by entering in the data and solving for the unknown parameter that use the equation. To avoid making any mistakes, double-check your calculations along the way. Using the order of operations, multiply, divide, and subtract in the correct order. The order of operations is exponent and roots first, followed by multiplications, and then addition and subtraction.

By adding and subtracting the numbers in the example, you get an answer of n = 23 pairs of socks.

Check the Answer

Examine your response to see if it makes sense in light of what you already know. Calculate an answer using basic logic and evaluate if it is close to what you expected. Search through the problem to determine where we went wrong if the answer seems ridiculously large or little.

You can tell you have a maximum of 25 socks by adding up all the numbers for the sisters in the example. The final answer must be less than 23, because the smaller sister lost two pairs, according to the problem. Unless we get a greater number, you’ve made a mistake. Apply this approach to every word problem, no matter how difficult it is.

Words that denote the addition of something

Search for keywords that suggest the correct operation used when information about arithmetic operations is provided in a word problem form. Let’s begin with the first fact that the coach shared with us. The team has a total of 20 players, both boys and girls. This is an addition problem, as the phrases ‘total’ and ‘altogether’ indicates. We don’t know how many males and females there were, and we can express them using the values ‘b’ and ‘g.’ lastly, we understand that the total number is 20, thus the equal sign is moved to the right. Let’s get to the second reason we discovered. She told us that team’s overall group of players was 16 last year, but had risen by four this year. This is really an addition issue, as the words “total sum” and “rise” indicate. The variable ‘p’ can be used to represent the team’s players. The figure 16 represents the number of players we had last year, and the number 4 represents the set of participants we will have this year.

Subtraction keywords are those that are used to indicate that something is being taken away.

Subtraction keywords are those that are used to indicate that something is being taken away. Interesting, but we’ll need some additional information to answer this puzzle. Nill chooses to speak with the Switch Quits team leader about the lost wooden sticks to see what she knows. The was Nill that there should be 20 brooms in the stock room, but that number has dropped by three today. Let’s make an algebraic expression out of this. We know to apply subtraction by focusing on the keyword reduced. Now we can put in the number of brooms that should be there and subtract the amount that isn’t. That would be another useful hint, but we’re still no closer to a solution the puzzle. However, the team captain suddenly recalls that it’s not just brooms that were currently missing. In the equipment cupboard, there was one fewer ball than usual. Despite the fact that we have no idea how so many balls are usually in the gear room? We can formulate this as an algebraic equation even though we don’t know how many balls are regularly in the gear room. We should use subtraction in our phrase because the terms “fewer than” suggest that. The parameter ‘n’ can be used to represent the number of balls that are generally present. We can put this as the phrase n – 1 since there was one less than the normal number of balls. The problem has been expanded by two additional parts.

Hence, there are three categories of unknowns in organizational change management: result, change, and start. One distinguishing element of all organizational change management is that, as the name implies, something about the circumstance changes with time. Problems with traditional addition and subtraction arise as a result of unforeseen circumstances. Students must, however, graduate to solving unexpected change and unknown beginning problems. Even though the examples in Table 1 are straightforward, students face progressively complicated transition circumstances as they progress through respective educational endeavors.

Let’s take one problem and try to understand it and then solve


Sana and Elisa decided to run a race at the park. Sara was chosen to keep track of their runs or progress. Elisa outscored Sana by 20 runs. They scored 418 points as a group, but Sara offers them two more points for their development. What was Sana’s total score?

Then, based on condition = x+20, Elisa’s score

‘They scored 418 as a group, according to the statement.

Hence, we can formulate and solve this problem as follows 

Let Sana’s score = x

Then the score of Elisa according to condition = x+20

According to the statement ‘together they scored 418’

So, x+x+20 = 418 

2x= 418-20 

2x= 398

X= 398/2

X= 199

But Ali gave two extra marks for good progress. Hence 199+2 = 201

Hence 201 is correct answer.

Important key words


More than, joined together, total, whole on, summing, increased to, extra, plus all, additional, greater words used for addition.

Fewer, differences, how very much, what more than, how far less than, how about the same as, how less than what, how even less than used for subtraction. 

Children are although sometimes confused by figures that appear large or frightening that they stop up right away. In those circumstances, increase up to the talent in question. For example, instead of getting immediately into subtraction four-digit integers start with smaller numbers. Each subsequent problem may be a bit more difficult, but children will learn that regardless of the numbers, students use same strategy.

Conditions to construct and remove

The structure of numbers and the links between adding and subtracting are demonstrated through lay and turn scenarios. Although they are related to change situations, putting together and dismantling situations are not the same.

a shift in a situation These questions, on the other hand, illustrate scenarios in which some elements are uncertain and students must change their thinking. From of the sum to the operand, this is how they think. The equal sign (=) gets a huge amount of attention in put-together and take-apart scenarios. Rather than only executing an operation, as a marker of equivalence.

There are various sorts of subtraction word problems:

(a) Going to be divided: removing, attempting to remove, 

(b) Reducing: Determine how much has been given away and how much is still available.

(c) Contrast: more than/less than.

(d) Addition in reverse: How much more should be added? Take; how many more; however many less ; how so many left ; greater ; smaller are the essential words to search for in a subtraction problem total.

Errors that occur when turning a world problem to a mathematical expression:-

 Nevertheless, students still find it challenging to solve mathematical word problems. The sources of word problem errors are well-documented.

Lack of capacity to recognize pattern and relationships

The learner transfers a portion of the real circumstance to the situation model, transforms this into the real model, and solves the problem correctly. However, he or she is unable to conceptually structure other required processes and thus abandons the problem.

Improper diagrams

The student attempts to address the problem by creating a diagram, but it is improperly structured. This type of error is caused by a failure to comprehend the actual situation or a failure to execute the about others spite of knowing it.

Significance of the number

The student use forecasting and control tactics in an attempt to solve the challenge. Irrespective of all the implemented in the real scenario, he or she follows the mathematical model. He/she just considers one aspect of the problem when predicting and controlling operations.

Operator with a number

 The learner focuses on the mathematical formula before even comprehending the real situation, that is, without first developing the scenario model and genuine modeling of the issue

Types of problems

There are three types of problems 


Addition issues with a total unknown are common. There are two parts to this puzzle. Frequently, this is not the same thing. It could, for instance, be a combination of red and green apples. Alternatively, cat owners and dogs, so because change is those two sets joining, it’s typically, but not always, a beginning scenario because it’s the same object. 

Subtraction is a part of the concerns and challenges. We know how many objects there are in total, but we don’t know how many are in each set. We reinforce the inverse correlation between addition and subtraction by working with part unknown situations. To connect the two procedures, we can use the equation 5 +? = 8. Working with unknowns in any position is crucial, and part unknown situations are where I want to practice inverse operators and fact groups.

Unexpected difficulties in both parts are less common. There are various answers to these scenarios. Students are given the total number of objects and are asked to suggest a suitable arrangement for how those items should be divided. My preferred technique to present the unknowns to the right of the equal sign 8 =? +? is to use both parts unknown situations. This explains why students shouldn’t solve problems from left side as well as what the equals symbol signifies.


There were some birds in the tree. Three more birds landed on the branch, bringing the total number of birds in the tree to eight. To begin with, how many birds were in the tree?  ?  + 2 Equals 8


There were five birds in the tree. There are now eight birds in the tree after some birds flew onto the limb. What was the total number of birds that had landed on the branch?

8 = 5 +?

There were five birds in the tree. On the branch, three birds flutter. How many birds are now perched on the tree?

What is the sum of 5 and 3?


There were some birds in the tree. Three birds have flown away, leaving the tree with eight birds. To begin with, how many birds were in the tree? ? –  3 =  8 


x = 8 +3 

x = 11

There were 11 birds in the tree. Some of the birds had flown away, leaving the tree with only eight birds. What was the total number of birds that flew away?

8 = 11 –?

There were 11 birds in the tree. Three pigeons took off. How many pigeons are now perched on the tree?  11 – 3  =?

How and what to Learn WORD PROBLEMS WITH Adding and Subtracting:- 

The following are the key elements of teaching addition and subtraction word problems:

Using Numbers to Teach Relationships – As a teacher, be aware of the problem type and assist pupils in determining the problem’s action.

Divide the Numbers — provide just the right numbers for children to read the issue without getting entangled in the computation.

Use Scientific Vocabulary – And make sure you’re using it consistently.

Stop looking for the “solution” – it’s all about the process, not the answer.

Distinguish between Models and Strategies — one is concerned with the numerical relationship, while the other is concerned with how learners “solve” or calculate the issue.

We begin by discussing the problem’s activity. We determine whether its being added to or subtracted from another. As a result, we have our equation. We figure out what we need to solve and fill in the blanks with such a square again for unknown value.

Link/Reference Us


  • "Mixed Addition and Subtraction Word Problems". Helping with Math. Accessed on January 27, 2022. https://helpingwithmath.com/mixed-addition-subtraction-word-problems/.

  • "Mixed Addition and Subtraction Word Problems". Helping with Math, https://helpingwithmath.com/mixed-addition-subtraction-word-problems/. Accessed 27 January, 2022.

  • Mixed Addition and Subtraction Word Problems. Helping with Math. Retrieved from https://helpingwithmath.com/mixed-addition-subtraction-word-problems/.