The Solving Number Word Problems Series

Word Problems are difficult to many. The Solving Number Word Problems Series is the first series of detailed tutorials on how to solve various number problems. Here are the posts.

(1) How to Solve Number Problems Mentally

This introduction discusses various strategies used to solve easy number word problems. Before you solve a problem using paper and pencil, you should try to solve it first mentally.

(2) How to Solve Number Problems Part 1 

This part solves the same numbers in (1) but using algebra. The objective of this part is to introduce how to set up equations based on “word phrases.”

(3) How to Solve Number Problems Part 2

This part introduces more problems that are slightly more complicated than in (2). It also introduces “number problems in disguise.”

(4) How to Solve Number Problems Part 3

This part of the series focus on how to solve consecutive numbers. Problem of consecutive numbers are very common in math tests.

(5) How to Solve Number Problems Part 4

This post discusses more complicated problems and also introduces how to set up solutions to number problems with fractions.

What’s more to come?

Maybe, I’ll have one more post for this series in the future. But for now, I will focus on the next topic which is about age problems.

How to Solve Number Word Problems Part 4

This is the fourth part and the conclusion to the Number Word Problem Series. In the introduction to this series, we have learned How to Solve Number Problems Mentally. In Part 1 and Part 2, we have discussed the basic number word problems, and in Part 3, we have learned how to solve word problems about consecutive numbers.

In this post, we discuss about more complicated problems especially problems that involve fractions. We have already discussed 9 problems in the previous parts of this series, so, we now solve the 10th problem.

Problem 10

There are 5 consecutive numbers. The sum of the second and the fourth number is 82. What is the largest number? » Read more

How to Solve Number Word Problems Part 3

This is the third part of The Number Word Problem Series. In this post, we will be solving number word problems about consecutive numbers.  In number word problem solving, consecutive numbers are numbers that follow each other in order.  Here are the examples of consecutive numbers (integers).

consecutive numbers: 4, 5, 6, 7, 8, …

consecutive odd numbers: -2, 0, 2, 4, …

consecutive odd numbers: 7, 9, 11, 13, 15, …

I am quite sure that you have solved consecutive numbers in your high school mathematics class.

In the previous post, we finished our 6th problem, so, we start with the seventh problem. » Read more

How to Solve Number Word Problems Part 2

This is the second part of the the Solving Number  Word Problems Series. In this part, we will discuss how to solve various number problems.  Note that some of these problems are not really number problems per se, but the strategy in solving them is technically the same. You could say that they are really “number problems in disguise.”

We already had three problems in the first part of this series, so let’s solve the fourth problem.

Problem 4

If 8 is subtracted from three times a number, then the result is 34. What is the number? » Read more

How to Solve Number Word Problems Part 1

In the previous post, we have learned How to Solve Number Problems Mentally. In this post, we are going to solve the same word problems algebraically. The objective of this post is for you to be able to learn how to set up equations based on given problems. Once you know how to set up equations for easy problems, it will be easier for you to do so using harder problems which we will discuss in the latter parts of this series. Note that before solving these problems, it is already assumed that you know how to solve equations.

Problem 1

One number is 3 more than the other. Their sum is 45. What are the numbers?

Scratch Work

The strategy in solving algebraic problems is to take a specific case. For instance, in the problem above, if one number is say, 5, then the larger number is 5 + 3 because it is 3 greater than the first number. Since we do not know the numbers yet, we can represent the smaller number by x and the larger number by x + 3. » Read more

How To Solve Number Word Problems Mentally

Most students in high school would rush and get a pencil or pen and write the equation if they see word problems such as Problem 1. I’m sure many of you will do the same. But you should really stop wasting lead and ink because problems such as this can be solved mentally.

Many are poor in mental math because most of us did not develop the habit of solving the problem mentally first, before getting a pencil and paper. Most of us, and our high school teachers too, are so obsessed and always in a hurry to write “let x = something” when we see word problems. If you want to be a good problem solver, the pencil and paper (and other tools) should be the last resort. Before getting a tool, try solving any problem in your head first.

Before you get excited, take 3-5 minutes to solve Problem 1 in your head and see if you can get the right answer before you continue reading. » Read more

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