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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