I was asked by a non-native English speaker how to read math expressions beyond basic arithmetic. So here are some examples:

|a| is read “The absolute value of a”. In Japanese, zettaichi 絶対値（ぜったいち）
x < y is read "x less than y".
x > y is read “x greater than y”.
x(t) is read “x of t”.
x^t is read “x to the power of t” or “x to the t”.
x² is read “x squared”.
x³ is read “x cubed”.
√x is read “the square root of x”.

Popularity: 28%

A lot of activity (as always) is happening in the currency markets and my students sometimes are confused when they hear certain American terms used for money. So here is a quick guide:

penny means 1 cent. It can also be used to emphasize that something was expensive as in “That must have cost you a pretty penny.”
nickel referring to the metal that the coin was stamped in means 5 cents.
dime means 10 cents.
quarter means 25 cents and can be remembered as one fourth (i.e. 1/4) of a US dollar.
buck means 1 US dollar.
grand means 1000 dollars as in “That car cost me 50 grand.” 　－＞　その車は５万ドロ掛かった。

Popularity: 38%

How much days till Christmas? Sounds stange to a native English speaker. But, this could be used by a non-native speaker. Non-native speakers often have difficulty using much and many in sentences. So let’s take a look at trying to explain when to use much and when to use many.

First, the explanation:

• much is used for non-countable items.
• many is used for countable items.

Second, some examples:

1. How much tea should I use to make tea. or
2. How many tea leaves should I use to make tea.

1. How much money do I need to go on vacation?
2. How many dollars should I take on vacation?

1. How many flowers do I need to make an arrangment?
2. How much water do I need to put into the vase?

Oh, by the way, if you use much in the title instead of many, you would say “How much time time until Christmas?”

Popularity: 54%

Non-native speakers generally quickly understand once a day, once per week, once per month, and once per year, but once a quarter or semi-annually can be confusing. So, let’s clearly explain.

1. quarter means one fourth (i.e. 1/4) in terms of a date, this means every 3 months. So when you here the phrase “quarterly report” it refers to the financial report a public company publishes describing their financial condition over the last 3 months. This report is published once a quarter.
2. annually means every year and semi means two parts. So when you here the phrase semi-annually (In Japanese 年に二回), it means twice a year and in fact it means once every 6 months.

You can also use the word quarterly to express once every 3 months (in Japanese ３ヶ月毎). Here are some other phrases and examples:

1. bi means every two so bimonthly (in Japanese 一ヶ月おき) means every two months.
2. biannually (in Japanese 一年おき) means every two years.
3. biweekly (in Japanese 一週おき) means every two weeks.
4. daily (in Japanese 毎日) means every day.

In Japanese 年会費（ねんかいひ nen kai hee） means annual members fee. So if you pay this type of fee every two years, then it is called a biannual members fee.

Popularity: 45%

When I teach non-native English speakers about the Scholastic Aptitude Test (SAT) or the Graduate Management Admissions Test (GMAT) mathematics section, the phrases used to express the mathematical equations are often confusing to them. So here is a brief explanation of the terms along with some examples:

Addition
It is natural to use the word add to describe the addition of two numbers, but other words like include refer to the addition of one number to another number. For example,

Although this month’s sales performance is much lower than expected, if we include first half sales figures to this month’s numbers, the current performance is better than last years.

Subtraction
Although it is common to say something like 10 (ten) minus 1 (one) equals 9 (nine), the word difference is often used to describe the result of subtracting a number from another number. Let’s say you are subtracting the number 5 (five) from 50 (fiftyor in mathematical notation, 50 - 5). To explain this you could say

The difference between 50 (fifty) and 5 (five) is 45 (fourty five).

If you are giving a presentation, and you want to compare this years sales results and last years sales results, you would say “The difference between this years and last years sales result is $5 million dollars.”

Multiplication
Although it is common to say something like 10 (ten) times 9 (nine) equals 90 (ninety), the word product is often used to describe the result of multiplying two or more numbers. Let’s say you are multiplying two or more numbers (e.g. 45, 32 and 20 or in mathematical notation, 45 x 32 x 20). To explain this you could say

The product of 45 (fourty five), 32 (thirty two) and 20 (twenty) is 28800 (two thousand eight hundred).

Division
The word division is usually expressed as the result of seperating something from something else. In business terms, the word divided is used to express such an equation. Let’s say you are dividing the number 50 (fifty) by 5 (five) or in mathematical notation, 50 / 5). To explain this you could say

The result of dividing 50 (fifty) by 5 (five) is 10 (ten).

Popularity: 47%

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