GED Math: Translating English to Math

Trish Wrote:

I am really having a hard time understanding translating word expressions into equations, and wondering if you can help?

Example:
1. the sum of 16 times a number and the number less another number times 3

2. a number less the sum of another number and 13

Workin’ these problems is almost like translating another language. You gotta know exactly what each word translates to a mathematical expression. Here’s a list of how they break down:

+ = “the sum of x and y (you’d put the + where the “and” goes here: x + y)

− = “less” or “minus” (note that if it says something like “a less b” then it’s a − b but if it says “a less than b” it’s b − a)

× = “times” or “the product of a and b” (a times b = a × b)

÷ = “divided by” (a divided by b = a ÷ b)

a,b,c or x,y,z = These are variables, so if it say “a number” that’s one of these variables. You usually wanna start with the first one in a list. Then if it says “another number” you pick the next one. If it said “a third number” you’d pick the last one. I don’t think it’d ever go above three numbers. (a number = a, another number = b, a third number = c)

Where it can get tricky is like when you start gettin’ a bunch of problems all mashed together. So like, take the first one that Trish posted.
“the sum of 16 times a number and the number less another number times 3”

You wanna write this stuff down on paper:

So, I put red parenthesis around the different parts of the problem. Is says the sum of “this” and “this” so you want to make sure to separate the two. Then you can translate things directly:

(16 × a) + (a − b × 3)

Then you can simplify it down:

16a + (a − 3b)

16a + a − 3b

17a − 3b

In this problem, the parenthesis didn’t really do anything. But it’s important to keep things separated in case it does matter. You wanna get into the habit of looking for the way problems are broken apart. Like, if it said “the product of “…” and “…” then the parenthesis would be crucial ’cause you gotta make sure to do any addition inside the parenthesis before you do the multiplication. If you check out the next problem, parenthesis play a bigger part.

So, we got “A number less the sum of another number and 13.” Translating it directly, we get a − b + 13. But since it says “less the SUM” you gotta use the parenthesis to separate the first part, “a number” and the second part, “the sum of another number and 13.” So it gotta look like this:

a − (b + 13)

Now when we simplify it, we distribute the negative:

a − b − 13

As a side note, make sure to read the directions of a problem carefully. If they just want you to write the equation out as a mathematical expression, the answer’d be a − (b + 13). If they want you to simplify, it’d be a − b − 13. If they want you to solve for a number, like a, then the answer would be a = 13 + b. A lot of the time, simply missin’ things like that in the question can make a problem wrong, even though you actually knew what you was doin’.

Good luck, all.