Algebra 1/Unit 2: The Translation of Algebra

Here, we are going to briefly discuss translations of Algebra. What does that mean? Well, we are going to teach you verbal terms for algebraic actions/terms. So, instead of adding a $$+$$ sign, we will say "plus". This is related to what this page will be teaching. Ok? Alright!

Addition
Expressions that could replace the standard $$+$$ symbol would be: more than, sum, total, plus, added to, and increased by. So, when we say 5 more than x, that means: $$x + 5$$. If you don't understand, maybe this story will help you out:
 * Short Dialog
 * "Mom, we have 3 apple pies", Hewqiif states to her mother.
 * Sister goes through bag and finds out we have +6 more apples pies
 * "Oh nevermind mom, we have 6 MORE apple pies" Hewqiif exclaims in glee.

Thus, we can conclude that Hewqiif originally said to her mother that Hewqiif and her family had 3 apple pies. After her sister goes through a bag full of groceries and realizes there are six more apple pies, she then makes the comment: "..we have 6 MORE apple pies". This is the equation that sums up this story algebraically: $$3 + 6$$. The verbal translation of "3 + 6" is 6 more than 3.

So, similarly, when we think of 5 more than x, we should think: x + 5.

A few more examples of verbal expressions representing addition are 6 + z (Total of 6 and z) and x increased by 7 (x + 7).

Subtraction
Key words for subtraction are decreased by, less than, subtracted from, difference between, minus, and fewer than. These words always equal to the action of subtracting, so if you see any of these words, always think about the "–" sign. If, on a quiz or test, or anything really, you are asked to translate "8 decreased by x", you should follow the order the numbers/letters come in. So, the translation of "8 decreased by x" would be "8 - x", since the value of 8 is less now due to another value (in this case, "x"). In this example, x decreases the value of 8. So that is why we have 8, the subtraction sign, and then x. More examples of verbal expressions for subtraction are 5 less than y (refer back to 1), and 2 subtracted from k.

Multiplication
When thinking of words that scream out "multiplication", words like product, multiplied by, per, times, and of should come to mind. So when we say "the product of 4 and u", we should think "4u". Even though quite confusing, but legit, is "of". When we say "6 of r", we are talking about "6r". Division key words are a lot more complicated, so don't be thinking "of" means division. Remember! "Of" matches to multiplication, so "7 of a" and "$$\tfrac{2}{3}$$ of p", would be "7a" and "$$\tfrac{2}{3}$$p".

Division
"Quotient, per, times greater, ratio, divided by (bottom), divided into (the top)" are words associated with the action of dividing/the execution of division. Some examples of verbals expressions of division are n divided by 3 ($$\tfrac{n}{3}$$), c divided into 5 ($$\tfrac{c}{5}$$), and the quotient of z and 4 ($$\tfrac{z}{4}$$). Some more complicated questions could arise into your eyesight, an example being the ratio of w and 6 ($$\tfrac{w}{6}$$; follow the order). A question might arise, being "j is how many times greater than m?". In this question, we are looking how many times j has a greater value than m (or basically, how greater j is from m). To do this, our fraction will be $$\tfrac{j}{m}$$, since we are trying to find how many j's are more than m's.

The division unit of translation of Algebra can really stink, but it's easy once mastered.

Grouping
This should be a short lesson. "Quantity of" and "and" are all related to grouping. A good question that a math teacher really tests a student on (relating to grouping) is "The quantity of l subtracted a is divided by 6". The answer to this would be $$\tfrac{(l - a)}{6}$$. Even though this section of Translating Algebra is probably the short section on the topic of translation, it is the most confusing and trickiest section for Algebra students school-wide. Make sure to understand this section well before preceding to the quiz.