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Fractions Are The Most Helpful Math Concept – OnlineBusinessDegree.org

A fraction represents a portion of something divided into equal parts. Easily converted into decimals and percentages, fractions are a simple way for people to quickly understand the relationship between a part and the whole. Most adults have a working knowledge of fractions and use them to quickly navigate everyday tasks from timekeeping to money management.

Fraction Basics

Fractions’ bad reputation is unfortunate, and likely due to uninspired lessons. Excellent teachers over the years have developed a number of ways to explain how to work with and understand fractions. Many of the best lessons are linked to this guide. In addition, a primer for adding, subtracting, multiplying and dividing fractions is included below.

Besides the arithmetic, it is important to understand some basic fraction concepts in order to make better use of them in everyday life.

Ratios, Decimals and Percentages

Fractions represent ratios, or a proportion of the whole. Thinking of a pizza, when two people share it equally, each gets four pieces – and their proportion is 4/8 of the pie.

Fractions can be transformed easily into decimals. The “ / ” in the middle of the fraction is actually a division symbol like ÷. This means that ¼  is the same as 1 ÷ 4. As an equation:

1/4 = 1 ÷ 4 = .25

Remember that .25 = 25%. Understanding this simple relationship helps at the store, if a $4.00 product is on sale for 25% off, the savvy consumer can quickly take 1/4 of the cost and know that the product is now only $3.00.

Equivalent Fractions

Equivalent fractions can be made, or found, by multiplying the same number to the top and bottom of the fraction. Remember, when you have a fraction with the same number in the top and the bottom, that fraction equals “1” (2/2 = 2 ÷ 2 = 1) and multiplying a number by 1 does not change it.

Cooks often have to work with equivalent fractions, particularly when increasing or decreasing a recipe to suit their number of guests. If this conversion results in an uncommon fraction, such as 12/16 cup of sugar, the savvy cook will convert this to its common equivalent, 3/4 cup, which is easy to measure.

Fraction Primer

Addition

There are three steps to adding fractions.

Step 1: make the denominators the same by finding the least common denominator; this can be found by determining the lowest common factor or the lowest common multiple. For example, if adding 2/8 + 1/2, the lowest common multiple is 8 (2 x 4 = 8). 1/2 is then converted to a fraction with denominator of 8 by multiplying the numerator and denominator by 4, so we get 4/8.

Step 2: Add the numerators. Recall that the denominator will not change, so

2/8 + 4/8 = 6/8.

Step 3: Simplify. Six and eight share the common factor 2. Dividing the top and the bottom by 2 produces:

6 ÷ 2 = 3

8 ÷ 2 = 4

And our simplified fraction is 3/4.

Subtraction

Similar to addition, when subtracting fractions, there are also three steps.

Step 1: Find the least common denominator. For example, if subtracting 3/4 from 14/16. To do this, 3/4 must be converted to a denominator with 16, which is done by multiplying the top and bottom by 4:

3 x 4 = 12 (numerator)

4 x 4 = 16 (denominator)

3/4 = 12/16

Step 2: Subtract only the top numbers and put that number over the denominator:

14-12 = 2

2/16

Step 3: Simplify the fraction by dividing both numerator and denominator by the same number; in this case, their greatest common factor is 2, so the fraction becomes

1/8.

Multiplication

There are three simple steps to multiplying fractions. Our example is 3/5 x 2/3.

Step 1: Multiply the numerators.

3 x 2 = 6

Step 2: Multiply the denominators.

5 x 3 = 15

Putting it together yields 6/15.

Step 3: Simplify the fraction by looking for the greatest common factor, which in this case is 3. Then divide the numerator and denominator by 3.

6 ÷ 3 = 2

15 ÷ 3 = 5

The answer is 2/5.

Division

There are also three simple steps to dividing fractions.

Step 1: Turn the second fraction into its reciprocal. Essentially, the reciprocal fraction is the mirror image of the fraction, which you get by flipping it. For example:

3/4 ÷ 1/2

First, flip 1/2 into its reciprocal, which is 2/1.

Step 2: multiply the first fraction by the reciprocal:

3/4 x 2/1 =

3 x 2 = 6 (numerator)

4 x 1 = 4 (denominator)

This produces 6/4.

Step 3: Simplify the fraction. First, find the greatest common factor, in this case 2, and simplify by that:

6 ÷ 2 = 3

4 ÷ 2 = 2

So the simplified fraction is 3/2. If necessary, you may want to convert this to a mixed number. Recall that 1 in this fraction is represented as 2/2. To convert this, simply subtract 2/2 from 3/2

3/2 – 2/2 = 1/2

Don’t forget that you have already accounted for 1, so the mixed fraction is actually

1½.

Even those with a math phobia see the value in mastering fractions. From cooking to commerce, having a good grasp of the essential concepts makes common tasks easier, and workers more efficient. Use the primer and resources provided here to develop an even better understanding of fractions.

Further Reading

Ask Dr. Math
Fact Monster
Math is Fun

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