Help With Fractions

Things to Remember About Fractions

helpwithfractions — Sat, 02 Aug 2014 16:50:50 +0000

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Make sure you know these fractions fundamentals

While any level of mathematics is relatively easy once you know the rules, there are a few things to remember about fractions that will keep you out of trouble on school assignments.

Take the time to master these simple reminders and you will never have to worry about them again – the best thing about math is that the rules are the rules and they don’t change!

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[expand title=”Uniqueness of the Number 1″ tag=”h4″]

Multiplying any number by 1 does not change the value of the number.

Dividing any number by 1 does not change the value of the number.

Keep in mind…

The number 1 can take on many forms. 3 – 2 = 1 and 20 – 19 = 1 can be used as a substitute for the number 1 because they both have a value of 1. Also… When the numerator of a fraction is equivalent (equal) to the denominator of a fraction, the overall value of the fraction is 1. This only works when you have a legal fraction; that is to say, the denominator does not equal zero. You can substitute any of these fractions for the number 1.

For example…

2/2, 5/5, 31/31, etc., are all the equivalent to the number 1.

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[expand title=”Integers Written as a Fraction” tag=”h4″]

You can express any integer as a fraction by simply dividing by 1, or you can express any integer as a fraction by simply choosing a numerator and denominator so that the overall value is equal to the integer.

Example:

The integer “8” can be expressed as the fraction “8/1” or “16/2” or “32/4” because they all have an overall value equal to “8”.

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[expand title=”Division by Zero” tag=”h4″]

The denominator of a fraction cannot have the value zero. If the denominator of a fraction is zero, this is not a legal fraction because it’s overall value is undefined.

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[expand title=”Zero in the Numerator” tag=”h4″]

The numerator of a fraction can have a value of zero. Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of “zero.”

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[expand title=”One Minus Sign in a Fraction” tag=”h4″]

If there is one minus sign in a simple fraction, the value of the fraction will be negative.

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[expand title=”More Than One Minus Sign” tag=”h4″]

If there is an even number of minus signs in a fraction, the value of the fraction is positive.

If there is an odd number of minus signs in a fraction, the value of the fraction is negative

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[expand title=”Factoring Integers” tag=”h4″]

To factor an integer, simply break the integer down into a group of numbers whose product equals the original number. Don’t forget that the number 1 is the factor of every number (normally the number 1 is omitted). Any factor of a number can be divided evenly into that number.

Example:
The factors of the number 12 are 1, 2, 3, 4, 6, 12
The factors of the number 35 are 1, 5, 7, 35
The factors of the number 53 are 1, 53, because 53 is a Prime Number.

Here is an easy short-cut method for finding the prime factors of a number. Simply divide the number by the lowest possible Prime Number until the final resulting answer is a Prime Number.

Example:

As you can see in the example, the prime factors of 56 are 2 x 2 x 2 x 7

Keep dividing the resulting number by the smallest prime number that will go into the number evenly. Start with “2” if the number is even. Otherwise start with the lowest prime number possible (3, 5, 7, etc.), until you are left with only a Prime Number.

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[expand title=”Reducing Fractions” tag=”h4″]

To reduce a fraction, follow the following three steps:

Factor the numerator.
Factor the denominator.
Cancel-out fraction mixes that have a value of 1.
Re-write your answer as the reduced fraction.

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[expand title=”Equivalent Fractions” tag=”h4″]

Finding an equivalent fraction (also called building fractions) is the reverse of reducing the fraction. Instead of searching for the 1 in a fraction mix so that you can reduce, you insert a 1 and build. The resulting fraction is called an equivalent fraction.

Try to remember this one, because you will use it a lot in other homework assignments.

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[expand title=”Simplifying Improper Fractions” tag=”h4″]

You may remember from other homework assignments that an improper fractions is where the numerator has a greater value than that of the denominator. So each time you do a math operation on fractions and your answer ends up as an improper fraction, you must simplify your answer. Because, the simplified results will be in the form of a mixed number.

So, to convert an improper fraction into a mixed number, just divide the numerator by the denominator. The results will be a whole number part and a fractional part.

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[expand title=”Greatest Common Factor (GCF)” tag=”h4″]

The greatest common factor of two or more whole numbers is the largest whole number that divides evenly into each of the numbers. There are two ways to find the greatest common factor. Remember to follow your homework instructions, if your teacher asks for a particular method.

The first method is to list all of the factors of each number, then list the common factors and choose the largest one.

The second method is to list the prime factors, then multiply the common prime factors…

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[expand title=”Least Common Multiple (LCM)” tag=”h4″]

The least common multiple of two or more non-zero whole numbers is actually the smallest whole number that is divisible by each of the numbers. When doing your homework, keep in mind that there are two widely used methods for finding the least common multiple of a group of numbers.

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[expand title=”Least Common Denominator (LCD)” tag=”h4″]

The least common denominator of a fraction is another way of stating the least common multiple of two or more different denominators. They mean the same. So, if you can find the least common multiple of two or more numbers, you can find the least common denominator.

Once you know the least common multiple, you would simply re-express each fraction by building an equivalent fraction using the newly named denominator.

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[icon name=”process” size=”big”] Homework Helpers

These great tips will really simplify your fractions homework. Click here > [/column] [column width=”1/2″ last=”yes”]

[icon name=”plus” size=”big”] How to Do Fractions

Tutorials on how to add, subtract, multiply and divide fractions! Click here to start with adding > [/column] [column width=”1/2″ first=”yes”]

[icon name=”phone” size=”big”] Fraction Calculator

Learn how to solve fraction problems, then check your work with our online fraction calculator. Click here > [/column] [column width=”1/2″ last=”yes”]

[icon name=”pencil” size=”big”] Fraction Worksheets

Free downloadable worksheets give you tons of practice to learn how to solve fraction problems. Click here > [/column] [line]

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So What is a Fraction Anyway?

helpwithfractions — Tue, 04 Mar 2014 22:59:57 +0000

Before you can make “heads” or “tails” out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.[fusion_builder_container hundred_percent=”yes” overflow=”visible”][fusion_builder_row][fusion_builder_column type=”1_1″ background_position=”left top” background_color=”” border_size=”” border_color=”” border_style=”solid” spacing=”yes” background_image=”” background_repeat=”no-repeat” padding=”” margin_top=”0px” margin_bottom=”0px” class=”” id=”” animation_type=”” animation_speed=”0.3″ animation_direction=”left” hide_on_mobile=”no” center_content=”no” min_height=”none”]

Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b, where “a” and “b” are whole numbers and “b” is not equal to “0”.

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes…

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole – The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole…

As a homework helper, this table shows you how the “same” whole can be divided into a different number of equal parts.

The Division Symbol (“/” or “__”) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6) parts of a whole that is divided into seven (7) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient – The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

For example…

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,…

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here’s a brief explanation of…

A Ratio – A comparison of things as a ratio can be expressed in one of two ways: first, the “old fashioned” method, a:b, pronounced “a is to b“; and second, as found in newer books, a/b. If the ratio of “a to b” is 1 to 4“, or 1/4, then “a” is one-quarter of “b”. Alternately, “b” is four times as great as “a”.

For example:

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or…

7ft/19ft = 7/19
Since we are comparing feet to feet, we don’t need to write the units.

The ratio of its length to its width is…19 to 7[/fusion_builder_column][/fusion_builder_row][/fusion_builder_container]