# In a mixed number or fraction problem, you have dividing and multiplying. Now if you were given a list of multiplying and dividing mixed number and fraction word problems, how can you tell the difference between multipling and divinding word problems.

It would be easier to answer, if you gave a specific example. You need to look for cue words like those given in capitals below.

How many times does 1/2 GO INTO 7 1/2? This indicates division. Change the expression of the mixed number and solve. 7 1/2 = 15/2

If a person could run 1 1/2 miles in 10 minutes, how far could he run in an hour? (Since an hour = 60 minutes, this is 6 TIMES 10 minutes.)

Although I cannot give you cues that will apply to all problems, I hope that this give you a good idea. Thanks for asking.

## To differentiate between multiplying and dividing word problems involving mixed numbers or fractions, you can look for cue words or phrases that indicate either operation.

For multiplication, you can look for words or phrases such as:

- Times
- Multiplied by
- Product
- Of
- Twice

For example: "If a person could run 1 1/2 miles in 10 minutes, how far could he run in an hour?" In this case, the phrase "in an hour" indicates that you need to multiply the distance (1 1/2 miles) by the number of times the time period fits into an hour (which is 6 times 10 minutes). So, this is a multiplication problem.

For division, you can look for words or phrases such as:

- Divide
- Goes into
- Quotient
- How many times
- Per

For example: "How many times does 1/2 go into 7 1/2?" The phrase "go into" implies dividing 7 1/2 by 1/2 to find out how many times it fits. So, this is a division problem.

It is important to note that not all word problems will have clear cue words, so it is always a good practice to analyze the problem and understand the context to determine the correct operation.

## To differentiate between multiplying and dividing word problems involving mixed numbers or fractions, you can look for cue words. These words give hints about whether you need to perform multiplication or division to solve the problem.

If the word problem includes cue words like "go into," "divide," "split," or "share equally," it is likely a division problem. For example, in the question "How many times does 1/2 go into 7 1/2?", the phrase "go into" indicates division.

To solve a division problem involving mixed numbers, you would convert the mixed number into an improper fraction and then perform the division.

On the other hand, if the word problem includes words like "times," "multiply," "product," or "groups of," it is likely a multiplication problem. For example, in the question "How far could he run in an hour if he can run 1 1/2 miles in 10 minutes?", the phrase "in an hour" suggests multiplication.

To solve a multiplication problem involving mixed numbers, you would generally convert the mixed number into an improper fraction, and then perform the multiplication.

Keep in mind that not all word problems will have explicit cue words, so it's important to carefully read and analyze the problem to determine whether it requires multiplication or division.

I hope this explanation helps you understand how to differentiate between multiplying and dividing word problems involving mixed numbers or fractions!