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What is fraction ?

A fraction is a quantity that tells how many parts of a whole we have. It consists of numerator and denominator. The above value is called the numerator and the bottom value is called the denominator.you can recognize this value by the slash bar which is in between the numerator and denominator, like \( \frac {3}{5} \).

Types of fraction:

  1. Proper fractionThose fractions in which the numerator is less than the denominator and the fractions that are greater than zero but less than 1 are called proper fractions. Example: \( \frac {1}{4} \).
  2. Top-heavy fractions OR Improper fractions – Those fractions in which the numerator is greater than the denominator are called top-heavy fractions or improper fractions.Improper fraction are always 1 or greater than 1.  e.g.  \( \frac {9}{4} \).
  3. Mixed Fractions: – A combination of proper fraction and a whole number is called Mixed fraction. E.g \( 2 \frac {1}{4} \).

Fraction With Like And Unlike Denominators:

There are two different cases like and unlike denominators.

  1. Solution With Like Denominators: Those fractions that have the same denominators are called like fractions e.g. \(  \frac {1}{4} + \frac {2}{4} = \frac {3}{4} \) Solution with step \(  \frac {1}{4} + \frac {2}{4} = ? \)
  2. The two fractions with like denominators so you can simply add the numerators \( = 1 + \frac {2}{4} = \frac {3}{4} \). This fraction cannot be reduced.

Process Of How to Add Or Subtract the Fraction With Unlike Denominators:

We have the fraction of addition \(  \frac {2}{4} + \frac {3}{6} \) with unlike denominators:

  1. Find Least Common Denominator (LCD) and then write the fractions with common denominator.
  2. The least common fraction of \(  \frac {2}{4} + \frac {3}{6} = 12 \).
  3. Multiply the numerator and denominator of each fraction by the number that makes its denominator equal to the Least Common Denominator (LCD). \(  ( \frac {2}{4} \times \frac {3}{3} ) + ( \frac {3}{6} \times \frac {2}{2} ) = ? \)

Solve the multiplication and the equation become:

\(  \frac {6}{12} + \frac {6}{12} = ? \)

We got fractions with like denominators now simply add the numerator.

\(  \frac {6 + 6}{12} = \frac {12}{12} \)

Since the 12 divided by 12 is equal to 1, \(  \frac {12}{12} = 1 \)

Therefore:

\(  \frac {2}{4} + \frac {3}{6} = 1 \)

You can also use formula fraction for addition to solve this:

Let’s apply fraction formula for Addition:

\(  \frac {a}{b} + \frac {c}{d} = \frac{ad + bc}{bd} \)

\(  \frac {2}{4} + \frac {3}{6} = \frac{(2 \times 6) + (3 \times 4)}{ (4 \times 6) } \)

\(  \frac {12 + 12}{24} \)

\(  \frac {24}{24} = 1 \)

Therefore,

\(  \frac {2}{4} + \frac {3}{6} = 1 \)

Subtraction With Unlike Fractions:

The process of subtracting the fraction is same as addition. The formula of subtracting the fraction is: \(  \frac {a}{b} – \frac {c}{d} = \frac{ad – bc}{bd} \).

\(  \frac {3}{4} – \frac {2}{3} = \frac{(3 \times 3) – (2 \times 4)}{ (4 \times 3) } \)

\(  \frac {9 – 8}{12} = \frac{1}{12} \)

How to Multiply Fractions:

The formula of multiplying the fraction is \(  \frac {a}{b} \times \frac{c}{d} = \frac{ac}{bd} \).

We have the fraction for multiplication: \(  \frac {2}{4} \times \frac{3}{6} \), simply multiply numerator with another numerator and denominator with another denominator like

\(  \frac {2 \times 3}{4 \times 6} \)

\(  \frac {6}{24} \)

Reduce the numerator and denominator by dividing both by greatest common factor:

\(  \frac {6 \div 6}{24 \div 6} = \frac{1}{4} \)

How to Divide Fractions:

The formula of dividing the fraction is: \(  \frac {a}{b} \div \frac {c}{d} =  \frac {ad}{bc} \). Here we have the fraction \(  \frac {4}{8} \div  \frac {6}{2} \)

Dividing fractions is the same as multiplying the fraction just, we take the reciprocal of the second fraction and flip the numerator and denominator and change the sign of division by multiplication.

\( = \frac {4}{8} \times \frac {2}{6} = ? \)

Multiply the numerator and then multiply the denominator to get:

\( = \frac {4 \times 2}{ 8 \times 6 } = \frac{8}{48} \)

This fraction can be reduced by dividing numerator and denominator by GCF. of 8 and 48.

\( \frac {8 \div 8}{ 48 \div 8 } = \frac{1}{6} \)

therefore

\( \frac {4}{8} \div \frac{6}{2} = \frac{1}{6} \)

Apply The Fraction Formula For Division:

\( \frac {4}{8} \div \frac{6}{2} \)

And solve

\( \frac {4 \times 2}{8 \times 6} = \frac{8}{48} \)

Reduce the fraction by dividing the greatest common factor

\( \frac {8 \div 8}{ 48 \div 8 } = \frac{1}{6} \)

Therefore,

\( \frac {4}{8} \div \frac{6}{2} = \frac{1}{6} \)

How to Solve the Mixed Fractions:

Here we have the mixed fractions,

\( = 1 \frac{3}{4} + 2 \frac{3}{8} = 4 \frac{1}{8} \)

Now solve this

\( = 1 \frac{3}{4} + 2 \frac{3}{8} = ? \)

Multiply the denominator with whole number and add the numerator like; \( 4 \times 1 + 3 = 7 \) and \( 8 \times 2 + 3 = 19 \)

(note: denominators will not change in this process)

So we got the fraction: \( \frac{7}{4} + \frac{19}{8} = ? \)

Now apply fraction formula for addition and solve:

\( = \frac{( 7 \times 8 ) + (19 \times 4)}{4 \times 8} \)

\( = \frac{( 56 + 76 )}{32} = \frac{132}{32} \)

Simplify 132/32 and the answer is: \( 4 \frac{1}{8} \)

Importance Of Fractions:

Fractions are very important in our habitual lives. Chemists use fractions to measure the right amount of solution or chemical to use with the other
ingredients to create the required product e.g we take 2/4 cup of water and 1/2 table spoon of sugar to make a sugar solution.

Fractions are not there to give you a headache. Actually, you have already use fractions without even knowing it properly. And without fractions, you wouldn’t be able to tell time or cook with recipes.

Fractions And Shopping:

Imagine you’re shopping with your $100 in pocket money.You really want a few items that u really like while window shopping, but they’re all very expensive. You’re waiting for the items to go on sale, and when they do, you rush down to the store. Instead of being marked with a new price, though, the store has a large sign that reads: All items are currently 75% off. This sounds like great news, but without doing fractions, there is no way to know if you have enough money. Knowing that 75% is ¾ off the cost of each item is the best way to get started. It’s great that fractions can help in your shopping as well.