Skip to content Skip to sidebar Skip to footer
Home / what adds to 1 and multiplies to 2

what adds to 1 and multiplies to 2

Post a Comment

ane.ii - Fractions and how to add, decrease, multiply and separate them

Fraction annotation

Fractions (or mutual fractions) are used to describe a part of a whole object. At that place are several notations for fractions:
a is called the numerator and b is chosen the denominator. The notation means that we interruption an object into b equal pieces and we have a of those pieces. The portion or fraction of the object that we take is a/b. For instance if we break a pie into 4 equal pieces and take 1 piece so we accept ane/4 of the pie:


Equivalent fractions

Notice that we get the same corporeality of pie as in the previous instance if we split the pie into 8 equal pieces and go ii of them:
Fractions similar 1/4 and ii/8 that accept the aforementioned value are said to exist equivalent fractions. This instance suggests the following method for testing if two fractions are equivalent.


Two fractions are equivalent if multiplying the numerator and denominator of one fraction by the same whole number yields the other fraction.


For case 4/5 and 24/30 are equivalent considering nosotros tin start with 4/five and multiply the numerator and denominator each by 6 to get 24/30:
Going in the opposite direction (from 24/30 to four/five) suggests the following method for reducing a fraction to everyman terms or to its simplest equivalent fraction:


To reduce a fraction to lowest terms or to its simplest equivalent fraction, factor both the numerator and denominator completely (i.due east. into prime numbers). Then abolish every cistron that occurs in both the numerator and denominator. What remains is the simplest equivalent fraction.

For example, here is how to reduce the fraction 24/42 is its simplest equivalent fraction, namely 4/seven:




Improper fractions, mixed fractions and long partition

A fraction where the numerator is smaller than the denominator is chosen a proper fraction and a fraction where the numerator is bigger than the denominator is called an improper fraction. An example of an improper fraction is vii/4. Using the pie case this ways that you take cleaved many pies each into 4 equal pieces and you have 7 of those pieces:
Improper fractions are sometimes expressed in mixed fraction notation, which is the sum of a whole number and a proper fraction, but with the + sign omitted. For instance 7/4 in mixed fraction notation looks like this:
Mixed fraction notation is not used in this Algebra Help e-book or in the Algebra Coach programme because information technology is besides easy to confuse it with the product of a whole number and a fraction. Instead of writing nosotros volition continue the + sign and write .

Long sectionalization is the method used to catechumen an improper fraction to a mixed fraction. We will illustrate the method on the fraction . Acquit out the following steps:
  • Prepare up the long division format, namely .
  • Since 5 into 9 goes 1 time, write a "1" higher up the 9, write 1 × 5 or "5" beneath the ix, and subtract five from 9 to get a divergence of 4, like this:
  • And then bring downward the two like this:
    Hither is what we take really done: The "1" and "v" are in the tens place and so they actually correspond the numbers 10 and 50 as shown here:
    Therefore we have really shown that .
  • Now echo the entire process with the balance, 42. Since 5 into 42 goes eight times, write an "viii" above the 2, write 8 × 5 or "40" below the 42, and subtract twoscore from 42 to get a remainder of two, like this:
  • This shows that that . Since the remainder, two, is smaller than the divisor, 5, this is our final mixed fraction result.


Some special fractions

In that location are several special fractions that are of import to recognize:

Calculation or subtracting fractions

This picture shows that two/eight of a pie plus three/8 of a pie equals five/8 of a pie:
Fractions that have the same denominator are called similar fractions. If you think about this example, then the following procedure for adding or subtracting like fractions is obvious:

To add two or subtract like fractions (fractions that have a common denominator), simply add or subtract the numerators and put the result over the mutual denominator, like this:

Simply what if the fractions don't have a common denominator? The answer is that they must then exist converted to equivalent fractions that exercise accept a common denominator. The procedure is illustrated in this example:

The steps are:
  1. Find the lowest common multiple of the two denominators 24 and xxx. When applied to fractions this number is called the everyman mutual denominator (LCD). In this case the LCD is 120.
  2. Convert each fraction to an equivalent fraction that has the LCD of 120 as its denominator. To do this in this example multiply the numerator and denominator of the first fraction by 5 and the numerator and denominator of the second fraction by 4 (shown in red).
  3. Add together the numerators and identify over the common denominator.
Sometimes in that location is ane more step. The result should always be expressed every bit the simplest equivalent fraction, like this:

Here are some more examples:




Multiplying fractions


Multiplying fractions produces a new fraction. Multiply the numerators to go the new numerator and multiply denominators to go the new denominator, like this:
Then simplify by reducing the new fraction to lowest terms.

To multiply a fraction by a whole number, but multiply the fraction's numerator by the whole number to get the new numerator, like this:

Then simplify by reducing the new fraction to everyman terms.

Here is an example of why the first process works. Suppose that there is half a pie (the fraction 1/2) as shown on the left. Now suppose that you take 2/3 of that one-half pie. (The word "of" translates into the mathematical performance "multiply".) This means that you cut the half pie into iii equal pieces and have ii of them. The outcome is 2/6 of the pie.


Here is an instance of why the second procedure works. Suppose that you lot ate 1/4 of a pie and that your friend ate 3 times every bit much pie as y'all did. This means that your friend ate 3/4 of the pie.

Here are some more multiplication examples:



Reciprocals and dividing fractions

Reciprocals play an essential role when dividing fractions. Two numbers or fractions are said to be the reciprocals of each other if their product is ane. For case:
iv/v and v/iv are reciprocals because

8 and 1/8 are reciprocals because


Dividing fractions: The procedure is to replace a division by a fraction by the multiplication by the reciprocal of that fraction, similar this:

Find that y'all have the reciprocal of the fraction on the bottom!

Here is why this procedure works:
The primal is that instead of seeing a fraction divided by a fraction, look for a single fraction whose numerator and denominator but happen to exist fractions. In the starting time footstep we multiplied this fraction by a UFOO whose numerator and denominator just happen to be fractions. The UFOO was chosen so the fractions in the denominator would cancel and requite one. After another simplification that left but the final multiplication of fractions.

Instance i: A fraction divided past a fraction:


Example 2: A fraction divided by a number. Detect that nosotros have drawn one divide line longer than the other and then you lot can tell which is the fraction and which is the number. The first step is to convert the whole number 4 into the fraction four/1. Subsequently several steps you go the expression shown in bluish. If you compare this expression to the original one you volition detect a nice shortcut. The number 4 that you are dividing the fraction by simply becomes a new factor in the fraction's denominator.

Case iii: A number divided by a fraction. Check the steps. This one is quite different from the previous example!



If you found this page in a spider web search you won't run into the
Table of Contents in the frame on the left.
Click here to display it.

diazyouspe.blogspot.com

Source: https://mathonweb.com/help_ebook/html/previous_2.htm

Post a Comment for "what adds to 1 and multiplies to 2"