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Aug22

## How to Solve Multiplication Word Problems

Are you good at solving word problems? Solving word problems is a very important part of mathematics because with them you understand and practice what you have learned to do (adding, subtracting, multiplying…)

Today we are going to look at multiplication word problems: how we recognize them, what to do to solve them…all of which we will look at in this post.

1. ##### Multiplication word problems: Repetition

This is the first type of multiplication word problem that one learns how to do. For example:

Anna has 5 egg cartons. Each carton has 12 eggs. How many eggs does she have in total?

We find:

• A number of sets: Anna has 5 egg cartons.
• The number of things that there are in each set: Each carton has 12 eggs.
• The question about the total number of things there are: How many eggs does she have in total?

To solve this word problem, we ought to think: if there are 12 eggs in each carton and Anna has 5 cartons, in order to know how many eggs there are in total, we will add 12 + 12 + 12+ 12+ 12, or, what ends up being the same: we will multiply 5 x 12: In total, Anna has 60 eggs.

1. ##### Multiplication word problems: One-step comparisons

In this type of multiplication word problem, one quantity is compared with another quantity that is bigger or smaller:

In order to buy their father’s gift, John has put in $10 and Patricia has put in 3 times as much money as John. How much money has Patricia put in? We find: • A number that expresses one quantity: John has put in$10.
• A number that expresses the comparison between the second quantity and the first: Patricia has put in 3 times as much money as John.
• The question about the second quantity: How much money has Patricia put in?

In order to solve this word problem, we ought to think: if Patricia has put in 3 times as much money as Juan, that she has put in triple the amount of money, we will multiply 10 x 3. Patricia has put in \$30.

1. ##### Multiplication word problems: One-step formulas

In this type of multiplication word problem, formulas will appear to us, for example, a speed formula:

Justin is a bus driver. He told me that if he didn’t make any stops and always maintained the same speed of 80 miles per hour, he would complete his route in exactly 2 hours. How many miles is his route?

We find:

• A speed: If he maintained a speed of 80 miles per hour…
• A time: He would arrive in 2 hours.
• A question about distance: How many milles is his route?

In order to solve this word problem, we ought to think: if he maintains a speed of 80 miles per hour, it will mean that each hour he drives he covers 80 miles. We also know that he drives at this speed for 2 hours. Therefore, in order to know the number of miles he covers in total, we will have to multiply 80 x 2: His route is 160 miles.

1. ##### Multiplication word problems: Combination or Cartesian product

In this type of multiplication word problem, we will find two or more sets of things or people. These sets ought to be combined among themselves, forming all possible pairs:

Today we went to eat at an Italian restaurant which specializes in pasta. It was difficult for me to decide which dish to order since there were 9 types of pasta and 11 types of sauce on the menu and you could combine any pasta with any sauce. How many different pasta and sauce combinations could you choose from?

We find:

• The number of elements that the first set has: 9 types of pasta.
• The number of elements that the second set has: 11 types of sauce.
• The question, which refers to the number of possible combinations between the sets: From how many different pasta and sauce combinations could you choose?

In order to solve the word problem, we ought to think: we could combine each type of pasta with 11 available types of sauce.  Therefore, with just the first type of pasta, we can get 11 different dishes. Combining the second type of pasta with each of the 11 sauces, we could get 11 more dishes. That is, for each of the 9 types of pasta, we will get 11 different sauce combinations. Thus, in order to find out the number of possible dishes, we will multiply 9 x 11You could choose from 99 different pasta dishes.

These are the 4 principal models for multiplication word problems. At Smartick we have a lot of these types of word problems and more. If you want to practice them, register now!

And that is all for today. What did you think of this post? Has it helped you to better understand multiplication word problems? If you like it, share it with your friends so that they can also learn.