SIMPLIFICATION

Simplification

Simplification of expressions:

Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex.

The operations required to simplify things are done in a set order called BODMAS.

Where,

B = Bracket

0 = of

D = Division

M = Multiplication

A = Addition

S = Subtraction

• To simplify a fraction, reduce it to its most basic form.
• If a fraction's numerator and denominator only share the number one, it is said to be in its simplest form.
• The process of simplifying difficulties as we work to tackle fractional problems is essential.
• The value of the fraction won't change even after we simplify them.
• This indicates that the true fraction and the simplified fraction are two equivalent fractions.

• simple methods for simplifying fractions.

Simplifying Fractions

How to Simplify Fractions?

Simplify Fractions

• Reducing a fraction to its simplest form is the definition of simplifying a fraction.
• If a fraction's numerator and denominator are coprime or share only the number one as a common factor, it is said to be in its simplest form.

The given fraction is equal to the given fraction in its simplest form. the fraction 34${\displaystyle \frac{3}{4}}$ is in its most basic form since the only element that 3 and 4 have in common is 1.

Let's attempt to gradually simplify the fraction 824${\displaystyle \frac{8}{24}}$.

How to Simplify Fractions Step by Step?

How to Simplify Fractions Stepwise

Following is the process of how to simplify fractions step by step -

Step 1: Write the denominator and numerator's factors in step one.

The ratio between 8 and 24 is 1 through 8 factors: 2; 4; and 8

1, 2, 3, 4, 6, 8, 12, and 24 are the 24 factors.

Step 2: Verify the shared factors between the denominator and the numerator. 1, 2, 4, and 8 are the common factors of the numbers 8 and 24.

Step 3: Subtract the common components from the numerator and denominator until there is only one remaining.

The fraction that is so obtained is in its most basic form. Starting with a division of 2, 824${\displaystyle \frac{8}{24}}$ becomes 82242=412${\displaystyle \frac{{\displaystyle \frac{8}{2}}}{{\displaystyle \frac{24}{2}}}}={\displaystyle \frac{4}{12}}$.

Up until the point where we can no longer divide by 2, we will keep doing so. Thus, 42122=26${\displaystyle \frac{{\displaystyle \frac{4}{2}}}{{\displaystyle \frac{12}{2}}}}={\displaystyle \frac{2}{6}}$, which is equal to 2262=13${\displaystyle \frac{{\displaystyle \frac{2}{2}}}{{\displaystyle \frac{6}{2}}}}={\displaystyle \frac{1}{3}}$.

The fraction 824${\displaystyle \frac{8}{24}}$ is thus represented by its simplest form, 13${\displaystyle \frac{1}{3}}$.

Let's return to the original issue of how to make the fraction 824${\displaystyle \frac{8}{24}}$ simpler. Between 8 and 24, 8 is their largest common factor. The simplest form of the fraction, which is 13${\displaystyle \frac{1}{3}}$, can be obtained by immediately dividing the numerator, 8, by the denominator, 24, and vice versa.

How to Simplify Numbers

How to Simplify Numbers

Following is the way how to simplify numbers-

• Round it Off.

Produce zeros. 200, therefore, becomes 199.

• Round to an Order of Magnitude.

To the nearest "power of 10," round a lot. The result is that 218 becomes 100 and 2,180 becomes 1,000.

• Slide the Decimal Point.

Rounding zeros are compacted by sliding the decimal point.

This makes 200,000,000 into 2 x 108. (exponential notation).

• Replace it with a Number You Can Recall.

Find a nearby number that you can remember rather than rounding.

Thus, 218 can be easily converted to 222, 210, 200, or any number.

Solved Examples

Example 1: Simplify: 660÷22× (2+1)$660÷22\times (2+1)$

Ans: 660÷22× (2+1)$660÷22\times (2+1)$ (Solve parentheses first)

= (660÷22) ×3 (From left to right, division appears first) $=(660÷22)\times 3\text{ (From left to right, division appears first) }$

=30×3=90$=30\times 3=90$

Example 2: Simplify: 37 − 28+(19−7)$28+(19-7)$

Ans: 37− [28+(19−7)]$37-[28+(19-7)]$ First solve =37− [28+12]

$=37-[28+12]$ Next, solve $$

=37−40$=37-40$

=77$=77$

Practice Time

Q1. Simplify the expression: 4+(3×4) ÷2$4+(3\times 4)÷2$

Ans: 10

Q2. Simplify fractions: (i) 124136${\displaystyle \frac{124}{136}}$

(ii) 182192${\displaystyle \frac{182}{192}}$

Ans: (i) 3134${\displaystyle \frac{31}{34}}$

(ii) 9196${\displaystyle \frac{91}{9}}6$

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