What is twelve more than the difference of six and a number

Answer 1

This is an introductory-level problem which tests your ability to write language as math relationships. It can get tricky because there are so many ways to talk about the relationships between numbers using language, but only a few specific ways to represent the relationships with math.

We have to take each part of the question and understand which parts of a mathematic relationship (an operation like + or -, a power, and sometimes using an =) each bit can be translated into.

"What is twelve more than the difference of six and a number?"

-First, "twelve more than" just means the same thing as +12

-"a number" means there is a number, but we don't know which number. This is exactly what a variable is. We can call it whatever we want; I choose x.

-"the difference of six and a number" just means 6 - x. When we put it all together:

6 - x + 12

So we start with 6 - x (the difference of six and a number), then we add twelve to get twelve more than the difference of six and a number.

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Here are several more examples, each adding a little bit more to the last. The goal is to write the math relationships described by the language in each problem.

(1) Half of a number

A number: x

Half of [something]: [something] ÷ 2

Half of a number: x ÷ 2

(2) Half of a number is nine.

Half of a number: x ÷ 2

[something] is nine: [something] = 9

Half of a number is nine: x ÷ 2 = 9

(3) The difference between half of a number and four is nine.

Half of a number: x ÷ 2

The difference between [something] and four: [something] - 4

[something] is nine: [something] = 9

The difference between half of a number and four is nine: x ÷ 2 - 4 = 9