# How to divide compound fractions

Complex Fractions with Variables

# How to divide compound fractions How to divide fractions: 3 easy steps to solve hard problems

Sep 18,  · How to Divide Mixed Fractions. 1. Multiply the whole number by the denominator of its combined fraction. Do this for both mixed numbers. Set these products aside. They are only part 93%(3). To convert a simple fraction to a compound fraction, the numerator must be larger than the denominator. Separate the whole number first. Example 2: Convert to a compound fraction. Answer. Rewrite as. We have To add or subtract two compound fractions, convert the fractions to simple fractions and follow the steps you use to add or subtract two simple fractions. Example 3: Calculate .

Last Updated: April 8, References. To create this article, 43 people, gractions anonymous, worked to edit and improve it over time. There are 7 references cited in this article, which can be found at divise bottom of the page. This article has been viewedtimes. Learn more Fractions and decimal numbers are simply two different ways of representing numbers that are less than one.

To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the divvide and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. After you divide, you can check your work by multiplying the decimal by the denominator to get the numerator. To learn complund to convert fractions to decimals using power of 10 denominators, keep reading!

Edit this Article. We use cookies to make how to divide compound fractions great. By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article parts. Related Articles. Article Summary. Part 1 of Understand the parts of a fraction and what they represent. The fraction consists frxctions three parts: the numeratorwhich is the top part of the fraction,  X Research source the slash, which goes between the numbers, and factions denominatorwhich is the bottom part.

For example, a pizza might be cut into 8 pieces. The denominator for the pizza would then be "8". If you cut the same pizza into 12 slices, then the denominator would be Either way they how to divide compound fractions the same whole, just cut up differently.

One slice of the whole pizza would be represented by the numerator "1". Four slices would be represented by the numerator "4". Understand what a decimal number represents. Decimals do not use a slash to indicate what divdie of the whole they represent.

Instead, the fractoons point to the left of the numbers signifies that the numbers are below one. With a decimal, the whole is considered to be based on 10, etc, depending on how many spaces to the right of the decimal the number goes. Decimals are also often read in a way that demonstrates their similarity to fractions. For example, 0. The copmound is represented by the numbers placed to the right of the decimal point. Understand how the fractions and decimals are related.

Fractions and decimals are only differing representations of any value that is less than one. The fact that both are fractionss for many of the same things means that you will often need to convert them in order to add, subtract, or compare them. Part 2 of Think of a fraction as a math problem. The easiest way to convert a fraction to a decimal is to read the fraction as if it were a division problem, with the number on the top being divided by the number on the bottom.

Divide the numerator of the fraction by the denominator of the fraction. You can do this math problem in your head, especially if the numerator and denominator are multiples of what is a small harp called other, with a calculator, or with long division. A simple way to do how to apply for jobs in usa from dubai is to simply put the divisor for example, 2 is the divisor in 1 divided by 2 on the bottom and the dividend 1 is the dividend in hos divided by 2 on divie.

Double check your math. Multiply the decimal equivalent you got by the denominator of the fraction you started with. You should come up with the numerator of the fraction you how to clean old pet stains from carpet with.

Part 3 of Try another way of converting a fraction into a decimal. This will help you to understand the relationship between fractions and decimals, as well as improving your other basic math skills. Understand power of 10 denominators. A "power of 10" denominator is bow denominator consisting of any positive number that can be multiplied to make a multiple of The numbers 1, or 1, are powers of 10, but in most practical applications of this method, you will probably only be using numbers such as 10 or Learn to spot the easiest fractions that can be converted.

Any fraction that has 5 as the denominator is an obvious candidate, but fractions sivide have denominators of 25 are just as easily converted. Any number that already has an exponent of 10 as a its denominator will be very easy to convert.

Multiply your fraction by another fraction. This second fraction will have a fravtions that, when both denominators are multiplied together, creates a multiple of The top of this second fraction the numerator will be the same as its denominator. This makes the second fraction equal one. It is a basic rule in fracitons that ddivide anything by one does not change its value. This means that when we multiply ftactions original fraction we had by a fraction that is equal to one we are not changing its value, we are simply changing how we represent that value.

Multiply both numerators together and make the result the numerator of the answer. Then multiply the denominators and make the result the denominator of the answer. You will be left with a new fraction. Convert your "power of 10" fraction into a decimal. Take the numerator of this new fraction and rewrite it with a decimal point at the end. Now look at the denominator and count how many zeros are in the number. Next, move the decimal point on your rewritten numerator to the left the number of spaces that are equal to the number of zeros in the denominator.

The denominator has one zero. So we start by rewriting "2" as "2. That gives us "0. You go quickly learn how to do ro with all sorts of numbers with easy denominators. After a while, this process becomes pretty easy. You just look for a fraction with a power of 10 denominator or one that can be readily made into comound and convert the top number into a decimal. Part 4 of Convert some common fractuons you use regularly into decimals. You can do this by dividing the numerator by the denominator the top number by the bottom numberas was done in the first part of this article.

If you want to convert the fraction really quickly, you can simply use a search engine on the internet to search for the answer. Make divie with the fraction on one side and it's decimal equivalent on the other side. Practicing these will help you memorize these fraction and decimal equivalents.

Recall the decimal equivalents of a fraction from memory. This can be very useful for fractions you use regularly. First, convert the mixed number into an improper fraction. Multiply the whole number by the denominator, then add the result to the numerator to get the new numerator e. Divide the numerator by the denominator to get the decimal. Not Helpful 9 Helpful To convert a fraction into a percent, first convert it into a decimal.

Next, multiply the result by to get a percent. Simply move fractioms decimal point to the right 2 places. For example. Not Helpful 7 Helpful To convert a what to wear with herringbone pants into a decimal, divide the top number by the bottom number.

Add and Subtract Fractions with Variables

Simplifying Complex Fractions When a “normal” fraction contains fractions in either the numerator or denominator or both, then we consider it to be a complex fraction. This type of fraction is also known as a compound fraction. There are two methods used to simplify such kind of fraction. After going over a few examples, you should Simplifying Complex Fractions Read More». How to divide fractions Step 1: Flip the divisor into a reciprocal A reciprocal is what you multiply a number by to get the value of one. If you Step 2: Change the division sign to a multiplication symbol and multiply Dividing and multiplying are opposites of each Step 3: Simplify your answer. This page will show you how to divide two fractions. There are three combinations of this. 1) Dividing two "normal" fractions, 2) Dividing a mixed number by a fraction, and 3) Dividing two mixed numbers. Fill in the boxes for the type of problem you need below, then click "Divide.".

As noted in Section 1. We call a the numerator or dividend and b the denominator or divisor. In Section 1.

We can use this property to help us graph arithmetic fractions on a number line. For example, to graph the fraction , which is equivalent to , we divide a unit on the number line into four equal parts and then mark a point at the third quarter, as shown in Figure 5. In general, we can locate the graph of any fraction by dividing a unit on the number line into a number of equal parts corresponding to the denominator of the fraction, and then counting off the number of parts corresponding to the numerator.

Fractions can involve algebraic expressions. In such cases, since division by 0 is undefined, we must restrict variables so that a divisor is never 0. In our work, we will assume that no denominator is 0 unless otherwise specified. For example,. There are three signs associated with a fraction: the sign of the numerator, the sign of the denominator, and the sign of the fraction itself.

Any two of the three signs of a fraction may be changed without changing the value of the fraction. In this book, the two forms and , which have positive signs on the denominator and on the fraction itself, will be considered standard forms for fractions. Sometimes answers are left in the form instead of the standard form. If the numerator contains more than one term, there are alternative standard forms for a fraction. Example 5 Write in standard form. Solution Since and any of the three forms on the right-hand side of the equals sign may be taken as standard form.

Common Errors When we write a standard form of a fraction such as , we must be careful how we change the signs in the numerator. The use of parentheses helps us avoid errors. Note that in the above example. In algebra, as in arithmetic, to reduce a fraction to lowest terms, we use the following fundamental principle. If both the numerator and the denominator of a given fraction are divided by the same nonzero number, the resulting fraction is equivalent to the given fraction.

When we reduce fractions, it is easiest to first write the numerator and denominator in factored form and then divide each by their common factors.

We have been using the fundamental principle of fractions to reduce fractions. Sometimes, we can reduce fractions by a more direct method.

In cases such as this, where no quotient is indicated above or below the factors "divided out," the quotient 1 is understood. Thus, when we divide powers with the same base, either we can factor each power and divide out common factors or we can use Properties 1 and 2 above. Example 5 Reduce by a. Using the fundamental principle of fractions. Using Properties 1 and 2. Common Errors: Many errors are made in working with fractions.

Careful attention to the following kinds of errors may help you to avoid them. Note that. Thus, while we can divide out common factors, we cannot divide out common terms. As another example, note that. In Section 5. In this section, we will study two alternative methods of rewriting quotients in equivalent forms.

Thus, a fraction whose numerator is a sum or difference of several terms can be expressed as the sum or difference of fractions whose numerators are the terms of the original numerator and whose denominators are the same as the original denominator.

We use the next method when the divisor is a polynomial. In this case, we use a process similar to arithmetic long division, as the following examples illustrate. As always, the division is not valid if the divisor is 0. When using the long division process, it is convenient to write the dividend in descending powers of the variable. Furthermore, it is helpful to insert a term with a zero coefficient for all powers of the variable that are missing between the highest-degree term and the lowest-degree term.

Just as it is often convenient to reduce fractions to lowest terms, it is also often convenient to build fractions to higher terms. In particular, we will have to build fractions when we add fractions with unlike denominators in the following chapter. In algebra, as in arithmetic, we use the fundamental principle in the following form in order to build fractions.

If both the numerator and denominator of a given fraction are multiplied by the same nonzero number, the resulting fraction is equivalent to the given fraction. To change to a fraction with a denominator bc: Divide b, the denominator of the given fraction, into be, the denominator to be obtained, to find the building factor c.

Multiply the numerator and denominator of the given fraction by the building factor c. Solution We can obtain the building factor by mentally dividing 8 by 4 to get 2 and then we multiply the numerator and denominator by 2 to obtain.

First, we obtain the building factor by dividing x 3 y 2 by x 2 y to get. Then, we can multiply the numerator and denominator of the first fraction by this building factor to obtain. If negative signs are attached to any part of the fraction, it is usually convenient to write the fraction in standard form before building it.

Solution First, we write in standard form and then proceed as in Example 2. Now, we multiply the numerator and denominator of by the building factor x - 4 , to obtain. In this section, we will introduce another symbol for a fraction of the form and then we will use this symbol to write certain numbers in simpler form. We will now give meaning to powers in which the exponent is 0 or a negative integer.

Using the property of quotients of powers, we have. Note that for any a not equal to zero, the left-hand member equals 1 and the right-hand member equals a 0. In general, we define:. Example 1 a. Using the two quotient laws for powers, we have.

Thus, for any a not equal to 0, we can view a -3 as equivalent to. In general, we define. Large numbers can be rewritten in a more compact and useful form by using powers with positive exponents. We can also rewrite small numbers by using powers with negative exponents that have been introduced in this section.

First, let us consider some factored forms of 38, in which one of the factors is a power of Although any one of such factored forms may be more useful than the original form of the number, a special name is given to the last form. A number expressed as the product of a number between 1 and 10 including 1 and a power of 10 is said to be in scientific form or scientific notation. To write a number in scientific form: Move the decimal point so that there is one nonzero digit to the left of the decimal point.

Multiply the result by a power of ten with an exponent equal to the number of places the decimal point was moved. The exponent is positive if the decimal point has been moved to the left and it is negative if the decimal point has been moved to the right. If a number is written in scientific form and we want to rewrite it in standard form, we simply reverse the above procedure. The quotient of two algebraic expressions is called a fraction.

We can rewrite a quotient as a product by using the property. A fraction can be changed from one form to another equivalent form by any of the following properties:.

A fraction with a denominator that is a polynomial with two or more terms can be rewritten by using a method of long division. Multiply numerator and denominator of the given fraction by the building factor c. We use scientific notation to rewrite very large and very small numbers.

Solve equations and inequalities Simplify expressions Factor polynomials Graph equations and inequalities Advanced solvers All solvers Tutorials. Partial Fractions. Welcome to Quickmath Solvers! Enter an expression containing the sum or difference of fractions and click the Add fractions button.

Add fractions. Example 1 In Section 1. For example, In general, Example 2 We can use this property to help us graph arithmetic fractions on a number line. Example 3 Fractions can involve algebraic expressions. Fractions that have different signs may have the same value.

For example, Each fraction above names the number 2. Each fraction above names the number The above examples suggest the following rule. For example, In this book, the two forms and , which have positive signs on the denominator and on the fraction itself, will be considered standard forms for fractions. Example 4 Write each fraction in standard form. This fundamental principle is particularly useful in the following form: Example 1 When we reduce fractions, it is easiest to first write the numerator and denominator in factored form and then divide each by their common factors.

Example 3 Reduce Solution First, we factor the numerators and denominators and then divide out common factors. Consider the quotient which, in exponential form, is written as a m-n. Thus, Example 4 If the greater exponent is in the denominator, that is, if n is greater than m, then Thus, when we divide powers with the same base, either we can factor each power and divide out common factors or we can use Properties 1 and 2 above. Solution Common Errors: Many errors are made in working with fractions.

Note that From the fundamental principle of fractions, However, Thus, while we can divide out common factors, we cannot divide out common terms.

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## 1 thoughts on “How to divide compound fractions”

1. Samugul:

By the way, congratulations for this video. Very helpful.