Translating an Equation

# Translating an Equation - Translating an English Phrase...

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Translating an English Phrase Into an Algebraic Expression

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Sometimes, you find yourself having to write out your own algebraic expression based on the wording of a problem. In that situation, you want to 1. read the problem carefully, 2. pick out key words and phrases and determine their equivalent mathematical meaning, 3. replace any unknowns with a variable, and 4. put it all together in an algebraic expression. The following are some key words and phrases and their translations: Addition: sum, plus, add to, more than, increased by, total Subtraction: difference of, minus, subtracted from, less than, decreased by, less Multiplication: product, times, multiply, twice, of Division: quotient, divide, into, ratio Example 1: Write the phrase as an algebraic expression: The sum of -5 and a number. View a video of this example
In this example, we are not evaluating an expression, but we are wanting to rewrite it as an algebraic expression. It looks like the only reference to a mathematical operation is the word sum, so what operation will we have in this expression? If you said addition, you are correct!!! The phrase 'a number' indicates that it is an unknown number - there was no specific value given to it. So we will replace the phrase 'a number' with the variable x . We want to let our variable represent any number that is unknown Putting everything together, we can translate the given English phrase with the following algebraic expression: The sum of -5 and a number *'sum' = + *'a number' = variable x Let’s try another! Example 2: Write the phrase as an algebraic expression: The product of 20 and a number. View a video of this example Again, we are wanting to rewrite this as an algebraic expression, not evaluate it. This time, the phrase that correlates with our operation is 'product' - so what operation will we be doing this time? If you said multiplication , you are right on.

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Again, we have the phrase 'a number', which, again, is going to be replaced with a variable since we do not know what the number is. Let’s see what we get for this answer: The product of 20 and a number *'product' = multiplication *'a number' = variable x Example 3: Write the phrase as an algebraic expression: 7 less than twice a number. View a video of this example First of all, we have the phrase 'less than' which mathematically translates as subtraction. You need to be careful with this phrase. It is very tempting to start off with 7 and put your subtraction sign after the 7. However, think about it, if you want 7 less than something, you are 7 below it. In order to be 7 below something you would have to subtract the 7!!! So you would not have 7 minus but minus 7 as PART of your expression. The other part of the expression involves the phrase 'twice a number'. 'Twice' translates as two
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Translating an Equation - Translating an English Phrase...

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