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Translating Words to Algebraic Expressions

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  • 0:01 Translating Word Problems
  • 0:52 Addition Words
  • 1:51 Subtraction Words
  • 3:13 Multiplication Words
  • 4:05 Division Words
  • 4:34 Equal Words
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

Translating Word Problems

Word problems, math problems written in words instead of math symbols, don't have to be the giant monster that your friends tell you they are. The key to solving them successfully and without losing too much hair is in finding the keywords and then translating them into math symbols. Sometimes, you will have a story behind the words, but you can still look for keywords to help you pinpoint what the problem wants you to do.

In this video lesson, I am going to show you the words you should look for that translate into addition, subtraction, multiplication, division, and equals. Of course, if you read a number, that obviously translates into the mathematical symbol for that number. For example, the word 'three' translates into the number 3. So, now let's see what words translate into what mathematical operations.

Addition Words

For addition, +, we want to look for words that tell us to add or combine things together. Words such as 'increased, combined, total, together, sum, more than, added, etc.' are your keywords. When you see these, highlight them in your problem and write a + symbol next to them to tell you that these words translate into a +.

An example of an addition word problem is this: Bob has fifty dollars to spend on a game, and Sarah has twenty-five dollars to spend. How much do they have to spend in total?

Do you see the keyword that tells us this problem is an addition problem? Yes, you see the word 'total' in the problem. This is when we highlight it and place a + symbol next to it. We haven't written our math problem out yet because we want to capture all our math symbols first and then we will put them in the proper math order so that it matches the meaning of the English words.

Subtraction Words

Next, we have subtraction words. When you see words such as 'decrease, minus, difference, less, less than, fewer, fewer than, etc.,' highlight it and write a minus symbol, -, next to it.

Let's look at an example: What is seven less than twelve?

This particular word problem uses the phrase 'less than.' We go ahead and highlight it and write our minus symbol next to it. Think about the meaning behind the phrase 'less than.' Is this problem asking you to subtract the twelve from the seven or the seven from the twelve? It is telling you to subtract the seven from the twelve, 12 - 7. Remember this point: if you see the phrase 'less than' being used, then when you write the problem in math, your numbers will be switched around.

Here's another subtraction example: What is seven minus three?

In this example, we have the keyword 'minus' which we highlight and write a minus symbol next to. Also in this case, we know that we are going to subtract the three from the seven, 7 - 3. In this case, when we translate this problem into math, the order that the numbers appear in the word problem is also the order that the numbers appear in our math problem.

Multiplication Words

Now, let's talk about multiplication. If you see words such as 'multiplied, of, product, times, increased by a factor, decreased by a factor, etc.,' highlight them and write a multiplication symbol next to them.

See if you can spot the keyword in this example: Maria and Susan are shopping, and they see their favorite shirt on sale for 25% off. They only have $20 to spend. So, they want to figure out if they have enough to pay for the shirt. So, they want to find out the discount that 25% off gives and they ask, 'What is 25% of $20?'

Do you see the keyword? Yes, the keyword is the word 'of' in that last sentence. So, we highlight it and place a multiplication symbol next to it.

Division Words

For division, look for words such as 'per, a, out of, quotient, ratio, percent, and divided by.'

See if you can spot the keyword in this problem: If Sally spent $34.91 on 5 gallons of gas, how much did she spend a gallon?

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