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

You are watching: 12 less than a number x

Don"t check out the lists of keywords as holy writ, handed under from ~ above high. Instead, usage these list as beneficial hints. But constantly use her head! If you"re not sure of the proper translation, use numbers. If you"re not details of the construction, apply it to what you could encounter "in actual life". Above all, make sure that you recognize what you"re doing, and also why. If you can clearly explain your occupational to a other student, climate you"re well on your method to mastery.


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The keyword "sum" tells me the they"re wanting me to add the two noted quantities. This converts to:


The order of the amounts doesn"t issue here, since they"re gift added. But it"s quiet a an excellent idea to obtain in the habit that writing points in the stated order, since it"ll matter in some contexts. While "y+8" is technically okay, it"s much better to use the stimulate "8+y", because that"s the order that they used in the English.

If you"re careful now, climate you"ll be well-trained by the moment you gain to the test.

analyze "4 much less than x" right into an algebraic expression.

This is the "less than" construction, which is backwards in the mathematics from the English. They"ve given me some unknown quantity, x, and also they"re telling me the they want the expression which stands for the amount that is four units smaller than x. To discover this quantity, I"ll should subtract the 4 from the unknown. This converts to:


To be clear, "four much less than (the unknown)" in English way "(the unknown), less four" in algebra. If you"re not certain of this, plug number in. If friend get four dollars less an hour than (an unknown worker), friend wouldn"t subtract that worker"s pay from 4; instead, you"d subtract 4 from that worker"s pay: p–4. Use this exact same order in your algebraic expression.

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

The keyword here is an extremely obvious; "multiplied by" method that I"ll be multiply (the unknown) by the provided value. The order of the terms below is (the unknown), complied with by the value that is gift multiplied ~ above (the unknown). However, in algebra, we put the continuous (in this case, the 13) in former of (the unknown). Since order doesn"t matter for multiplication, (x)(13) = (13)(x). So the English expression translates to:


The keyword here is "quotient", which tells me that among the item is divided by the other. The bespeak of the items is vital here, due to the fact that order problem in division. Since (the unknown) comes first in the English expression, this tells me the it"s on height in the fraction. Then this equates to:


The keyword right here is "difference", telling me that among the items is subtracted native the other. Since order matters in subtraction, I"ll should be cautious with the bespeak of the items. Due to the fact that the number comes an initial in the English expression, the will must come first in the math expression. Climate this translates to:


English expressions can be more facility than a straightforward relation in between two items. When confronted with this more-complex expressions, take her time and work carefully. Permit the keywords and logic help you discover the proper corresponding math expressions.

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analyze "the proportion of 9 an ext than x come x" right into an algebraic expression.

Okay; "the ratio of (this) to (that)" method "(this) divided by (that)", therefore I understand I"ll be ending up v a division. But the items being split aren"t simple. In particular, the (this) component is "9 an ext than x", which equates as "x+9" (being "the variable, plus an additional nine more"). Therefore this expression will be what walk in the peak of the portion which will certainly be my ratio expression. The (that) part is simply x, so this variable will be the bottom of my proportion expression. Then this equates to:


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

"The complete of" indicates that things are being added. The things, in this case, are (a number) and also 2. I"ll have to pick a variable for (a number); I"ll pick:


(By explicitly saying what the variable is and what the stands for, I"ll be much much less likely to forget what it means; it additionally puts me in the an excellent habit of naming things clearly, which always makes graders happy, and may acquire me partial credit transaction if my mathematics goes not correct at some point.)

The amount is of (a number) and also the number 2. This sum is composed as:


Then I need to translate "nine less than" this sum right into math. The "less than" building is backwards in the English from the math. In this case, that means that the "nine much less than", i m sorry is very first in the English, actually demands to be last in the math. Then this translates to:


The accuse specify the I"m come "simplify" this expression, if possible, and it is undoubtedly possible. Climate my final answer is:


The length of a football ar is 30 yards more than that is width. Express the length of the ar in regards to its width w.

Whatever the broad w is, the size is 30 much more than this. Remembering the "more than" means "plus that much", I"ll be including 30 to the w.