12 divided by 3 4 is a common fraction that can be simplified using basic arithmetic operations. Understanding how to divide fractions is crucial for solving mathematical problems and performing calculations in various fields. In this comprehensive guide, we will explore the concept of 12 divided by 3 4, its simplification, and its applications in different contexts.

To divide fractions, we invert the second fraction (the divisor) and then multiply it with the first fraction (the dividend). Let’s apply this rule to simplify 12 divided by 3 4:

12 / (3/4) = 12 * (4/3) = 48/12

Simplifying further, we divide both the numerator and the denominator by their common factor, 12, to obtain:

48/12 = 4

Therefore, 12 divided by 3 4 equals 4.

Long Division for Fractions

Apart from the invert-and-multiply method, long division can also be used to divide fractions. Long division involves setting up the dividend as the numerator of a fraction and the divisor as the denominator. The following steps illustrate long division for 12 divided by 3 4:

__4
3 | 12
-12
----

Since 12 is not divisible by 3, we multiply 3 by 4 to get 12. The result, 4, is placed above the division symbol as the quotient. We then subtract 12 from 12 to get 0, indicating that the division is complete.

Applications of 12 Divided by 3 4

12 divided by 3 4 has various applications in real-world scenarios, including:

Chemistry

* Calculating the concentration of a solution by dividing the moles of solute by the total volume of the solution.

Physics

* Determining the speed of an object by dividing the distance traveled by the time taken.

Engineering

* Calculating the load-bearing capacity of a structure by dividing the total load by the cross-sectional area of the support.

Finance

* Dividing the total amount of money by the number of people to determine the amount each person receives.

Fraction to Decimal Conversion

To convert 12 divided by 3 4 to a decimal, we can either divide 12 by 3 and then by 4, or we can use long division as demonstrated earlier. Either method yields the decimal equivalent of 3.

Simplified Fraction Representation

12 divided by 3 4 can also be represented as a simplified fraction:

12 / (3/4) = (12 * 4) / 3 = 48 / 3 = 16

Therefore, 12 divided by 3 4 is equivalent to the improper fraction 16.

Percentage Conversion

To convert 12 divided by 3 4 to a percentage, we multiply it by 100:

(12 / (3/4)) * 100 = 4 * 100 = 400%

Therefore, 12 divided by 3 4 is equivalent to 400%.

Reciprocal of 12 Divided by 3 4

The reciprocal of a fraction is found by inverting it. The reciprocal of 12 divided by 3 4 is:

1 / (12 / (3/4)) = (3/4) / 12 = 1/16

Mixed Number Representation

A mixed number is a combination of a whole number and a fraction. 12 divided by 3 4 can be expressed as a mixed number as follows:

12 / (3/4) = 4

Therefore, 12 divided by 3 4 is equivalent to the mixed number 4.

Improper Fraction Representation

An improper fraction has a numerator greater than or equal to its denominator. 12 divided by 3 4 can be represented as an improper fraction:

12 / (3/4) = (12 * 4) / 3 = 48 / 3 = 16

Therefore, 12 divided by 3 4 is equivalent to the improper fraction 16.

Decimal Expansion

The decimal expansion of a fraction is obtained by repeatedly dividing the numerator by the denominator. The decimal expansion of 12 divided by 3 4 is:

12 / (3/4) = 3.9999999… (repeating 9s)

Therefore, 12 divided by 3 4 has a non-terminating, repeating decimal expansion 3.9999999…

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