Once you"ve learned the basic keywords for translating word problems from English right into mathematical expressions and equations, you"ll be gift with miscellaneous English expressions, and also be called to do the translation.

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Don"t see the list of keywords as divine writ, handed under from ~ above high. Instead, use these perform as useful hints. But constantly use her head! If you"re not certain of the suitable translation, use numbers. If you"re not specific of the construction, use it come what you can encounter "in genuine life". Over all, make certain that you understand what you"re doing, and also why. If friend can plainly explain your work to a fellow student, climate you"re fine on your method to mastery.


The keyword "sum" tells me the they"re wanting me to include the two provided quantities. This translates to:

The stimulate of the quantities doesn"t matter here, due to the fact that they"re being added. Yet it"s still a good idea to acquire in the habit of writing things in the stated order, due to the fact that it"ll issue in some contexts. When "y+8" is technically okay, it"s far better to usage the stimulate "8+y", because that"s the order the they supplied in the English.

If you"re mindful now, then you"ll be well-trained by the time you obtain to the test.

translate "4 much less than x" into an algebraic expression.

This is the "less than" construction, which is backwards in the math from the English. They"ve provided me some unknown quantity, x, and also they"re informing me that they want the expression which means the amount that is four units smaller than x. To uncover this quantity, I"ll need to subtract the 4 from the unknown. This converts to:

To it is in clear, "four less than (the unknown)" in English means "(the unknown), much less four" in algebra. If you"re not sure of this, plug number in. If girlfriend get four dollars much less an hour than (an unknown worker), girlfriend wouldn"t subtract the worker"s salary from 4; instead, you"d subtract 4 from that worker"s pay: p–4. Usage this very same order in her algebraic expression.

translate "x multiply by 13" into an algebraic expression.

The keyword below is an extremely obvious; "multiplied by" way that I"ll be multiply (the unknown) by the offered value. The order of the terms right here is (the unknown), followed by the value that is gift multiplied top top (the unknown). However, in algebra, we put the consistent (in this case, the 13) in front of (the unknown). Because order doesn"t issue for multiplication, (x)(13) = (13)(x). For this reason the English expression converts to:

The keyword right here is "quotient", which speak me that among the items is separated by the other. The bespeak of the items is necessary here, due to the fact that order problem in division. Due to the fact that (the unknown) comes first in the English expression, this tells me the it"s on optimal in the fraction. Then this translates to:

The keyword below is "difference", informing me that one of the items is subtracted from the other. Because order matters in subtraction, I"ll should be mindful with the stimulate of the items. Due to the fact that the number comes first in the English expression, it will have to come very first in the math expression. Then this translates to:

English expressions deserve to be more complex than a an easy relation between two items. When confronted with this more-complex expressions, take her time and work carefully. Let the keywords and logic assist you discover the proper corresponding math expressions.

See more: What Is The Difference Between A Formula And An Equation And Formula

translate "the ratio of 9 much more than x to x" into an algebraic expression.

Okay; "the ratio of (this) come (that)" method "(this) divided by (that)", for this reason I know I"ll be finishing up through a division. Yet the items being separated aren"t simple. In particular, the (this) part is "9 more than x", which converts as "x+9" (being "the variable, plus one more nine more"). For this reason this expression will certainly be what goes in the top of the portion which will certainly be my proportion expression. The (that) part is just x, so this variable will certainly be the bottom of my ratio expression. Then this translates to:

analyze "nine less than the full of a number and also two" right into an algebraic expression, and also simplify.

"The total of" suggests that things room being added. The things, in this case, are (a number) and also 2. I"ll should pick a variable because that (a number); I"ll pick:

(By explicitly saying what the change is and also what it stands for, I"ll it is in much much less likely come forget what the means; it likewise puts me in the an excellent habit of naming things clearly, which always makes graders happy, and may obtain me partial credit transaction if my mathematics goes wrong at part point.)

The sum is that (a number) and also the number 2. This sum is created as:

Then I need to translate "nine less than" this sum into math. The "less than" building is backwards in the English native the math. In this case, that method that the "nine much less than", which is first in the English, actually needs to be last in the math. Climate this converts to:

The indict specify the I"m come "simplify" this expression, if possible, and also it is indeed possible. Climate my last answer is:

The size of a football ar is 30 yards much more than that is width. To express the size of the ar in terms of its broad w.

Whatever the width w is, the length is 30 more than this. Remembering that "more than" method "plus the much", I"ll be including 30 to the w.