Math Tips

Here are some "how-to's" that will come in handy.

How to Round a Number

To the nearest ten

If the ones digit is 5 or more, round to the next highest ten (68 rounds to 70).
If the ones digit is less than 5, round to the next lowest ten (33 rounds to 30).

To the nearest hundred

If the tens digit is 5 or more, round to the next highest hundred (384 rounds to 400).
If the tens digit is less than 5, round to the next lowest hundred (427 rounds to 400).

To the nearest thousand

If the hundreds digit is 5 or more, round to the next highest thousand (7,602 rounds to 8,000).
If the hundreds digit is less than 5, round to the next lowest thousand (7,268 rounds to 7,000).
How to Find an Average

To find the average of several numbers, add the numbers together and then divide the sum by the number of numbers.

The average of 17, 30, 6, and 7 = 60 ÷ 4 = 15

How to Tell if Two Fractions are Equivalent

Cross multiply the fractions. If both products are the same, the fractions are equivalent.

3 and 9 3 x 24 = 72 3 and 9 are equivalent fractions.
8 24 8 x 9 = 72 8 24

5 and 3 5 x12 = 60 5 and 3 are not equivalent fractions.
8 12 8 x 3 = 24 8 12

How to Find a Percentage

To tell what percentage one number is of a second number, divide the first number by the second. Move the decimal point of the resulting quotient two places to the right.

Example: What percentage is 20 of 300?
20 ÷ 300 = .067 = 6.7%
How to Change a Fraction to a Percentage

Divide the numerator by the denominator. Move the decimal point of the resulting quotient two places to the right.

6 = 6 ÷ 15 = .4 = .40 = 40%
15

How to Change a Decimal to a Percentage

Move the decimal point two places to the right.

0.792 = 79.2%

Refer to these how-to's until you can do them automatically.

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Using Abbreviations To Write Notes Quickly

Using Abbreviations To Write Notes Quickly

Many of the questions you find on class tests will be based upon the information your teachers orally present in class. Therefore, you need to write class notes that completely and accurately include the most important information presented by your teachers. This is hard to do because your teachers can talk faster than you can write.

It would be nice if your teachers talked slower so that you could keep up with what they are saying as you write your notes. This is not realistic though. It is up to you to write more quickly. One way to do this is to write abbreviations for words.

An abbreviation is a shortened form of a word used when writing to represent the complete word. You must be able to recognize the complete word from its abbreviation.

Many words have a commonly used abbreviation. Here are some examples of words that have a common abbreviation:

Word Abbreviation Word Abbreviation
department dept package pkg
introduction intro negative neg
junior jr magazine mag
mathematics math foot ft
weight wt highway hwy

You can form your own abbreviation for just about any word. Here are three ways you can do this.

1. Write just the beginning of a long word. Here are some examples of long words that have been abbreviated by writing just the beginning of the word:

Word Abbreviation Word Abbreviation
different diff feminine fem
incorporated inc population pop
elementary elem ambiguous ambig
molecular molec separate sep
division div hippopotamus hippo

2. Leave out the vowels when writing a word. Here are some examples of words that have been abbreviated by leaving out the vowels when writing the word:
Word Abbreviation Word Abbreviation
century cntry point pnt
mountain mntn school schl
reason rsn clean cln
popular pplr teacher tchr
quality qlty progress prgrss

3. For words that have just one syllable, write just the first and last letter of the word. Here are some examples of words that have been abbreviated by writing just the first and last letter of the word:

Word Abbreviation Word Abbreviation
quart qt land ld
tick tk round rd
girl gl pack pk
night nt field fd
link lk heart ht

Use common abbreviations of words whenever you recognize them. For other words, form abbreviations by using one of the three ways you just learned. Use the way that best fits the word for which you are writing an abbreviation. Do not try to abbreviate every word you write in your notes. Abbreviate those words that are important and for which you can quickly form an abbreviation. REMEMBER: YOU MUST BE ABLE TO RECOGNIZE THE COMPLETE WORD FROM ITS ABBREVIATION. Knowing the context in which you wrote the word will help you recognize the complete word from its abbreviation.

Using abbreviations for words will help you take good notes more quickly. Having good notes will help you do better on tests.

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Writing Techniques

Writing is an important form of communication. Good writers use different writing techniques to fit their purpose for writing. To be a good writer, you must master each of the following writing techniques.

1. Description

Through description, a writer helps the reader use the senses of feeling, seeing, hearing, smelling, and tasting to experience what the writer experiences. Description helps the reader more clearly understand the people, places, and things about which the writer is writing. It is the most common form of writing. You will find descriptive writing in newspapers, magazines, books, and most other forms of written communication.

2. Exposition

Through exposition, a writer informs, explains, and clarifies his/her ideas and thoughts. Exposition goes beyond description to help the reader understand with greater clarity and depth the ideas and thoughts of the writer. Expository writing, like descriptive writing, is commonly found in newspapers, magazines, books, and most other forms of written communication.

3. Narration

Through narration, a writer tells a story. A story has characters, a setting, a time, a problem, attempts at solving the problem, and a solution to the problem. Bedtime stories are examples of short stories while novels are examples of long stories. The scripts written for movies and plays are further examples of narrative writing.

4. Writing Techniques, Pen Persuasion

Through persuasion, a writer tries to change a reader's point of view on a topic, subject, or position. The writer presents facts and opinions to get the reader to understand why something is right, wrong, or in between. Editorials, letters to the editor in newspapers and magazines, and the text for a political speech are examples of persuasive writing.

5. Comparison and Contrast

Through comparison and contrast, a writer points out the similarities and differences about a topic. Comparison is used to show what is alike or in common. Contrast is used to show what is not alike or not in common. Describing living conditions in 1900 and living conditions today would allow for much comparison and contrast.

By using the writing technique that fits your purpose, you will be able to communicate your ideas effectively.

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