Simplification of Decimal

Use the identities to solve the problems based on simplification of decimal. We will make use of these identities in some of the questions related to division of decimals.

Learn the following identities to apply these in simplifying decimal.

(a) (a + b)2 = a2 + b2 + 2ab

(b) (a - b)2 = a2 + b2 - 2ab

(c) a2 - b2 = (a + b) (a - b)

(d) a3 + b3 = (a + b) (a2 - ab + b2)

(e) a3 - b3 = (a - b) (a2 + ab + b2)


Worked-out examples on simplification of decimal:

Let us observe how to simplify decimals using identities with detailed step-by-step explanation.

Simplify the following:

(a) {(0.9 - 0.6)2}/{(0.9)2 - 2(0.9)(0.6) + (0.6)2}

Solution:

Let, a = 0.9 and b = 0.6

So, [(a - b)3]/[a2 - 2(a)(b) + b2]

= (a - b)3/(a - b)2

= (a - b)

Now putting the value of a and b we get,

= 0.9 - 0.6

= 0.3

(b) [(5.8)3 - (2.6)3]/[(5.8)2 + (2.6)2 - 2(5.8) + (2.6)2]

Solution:

Let a = 5.8 and b = 2.6

So, we have

= [a3 - b3]/[a2 - 2ab + b2]

= [(a - b) (a2 + ab + b2)]/[(a - b)2]

= (a2 + ab + b2)/(a - b)

Now putting the value of a and b we get,

= [(5.8)2 + (5.8)(2.6) + (2.6)2]/(5.8 - 2.6)

= 55.48/3.2

= (55.48 × 10)/(3.2 × 10), Multiply both numerator and denominator by 10

= 554.8/32

= 17.3375


(c) [(8.65)2 - (4.35)2]/(8.65 - 4.35)

Solution:

Let a = 8.65 and b = 4.35

So, we have

= [a2 - b2]/(a - b)

= [(a + b)(a-b)]/(a - b)

= a + b

Now putting the value of a and b

= 8.65 + 4.35

= 13

Related Concept

Decimals

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number


7th Grade Math Problems

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