Question

What value will be assigned to result after the following statement executes? result \(=9 / 12\)

Short answer

Answer: The value assigned to "result" after simplifying the fraction is 3/4.

Step-by-step solution

Perform the division

To find the value that will be assigned to result, we need to simply divide the given numbers: \(result = \frac{9}{12}\)

Simplify the fraction

Now, simplify the faction by finding the greatest common divisor (GCD) of the numerator (9) and the denominator (12). The GCD of 9 and 12 is 3. Divide both the numerator and the denominator by the GCD: \(result = \frac{9 ÷ 3}{12 ÷ 3} = \frac{3}{4}\) So, the value assigned to the result after the given statement executes is: \(result = \frac{3}{4}\)

Key concepts

Fraction Simplification

Understanding fraction simplification is essential in mathematics as it allows one to express fractions in their simplest form. It involves reducing the numerator and denominator to their smallest possible numbers while keeping the value of the fraction unchanged.

To simplify a fraction, one must identify a number by which both the numerator and denominator can be evenly divided. This number is referred to as a common factor. However, for the most simplified form, we must find the greatest common factor (GCF), known as the greatest common divisor (GCD), and divide both parts of the fraction by it.

Looking at our exercise with the fraction \(\frac{9}{12}\), we can see that both 9 and 12 can be divided by 3. When we divide the numerator (9) and denominator (12) by their GCD (3), we get \(\frac{9 \div 3}{12 \div 3} = \frac{3}{4}\), which is the simplified form of the fraction.

Greatest Common Divisor

The Greatest Common Divisor (GCD), also known as the highest common factor (HCF), is the largest number that divides two or more numbers without leaving any remainder. Identifying the GCD is crucial when simplifying fractions, as seen in the previous section, and is also useful in other areas of mathematics such as number theory and algebra.

To find the GCD of two numbers, one can use various methods such as prime factorization, Euclid's algorithm, or simply list out the factors. The GCD is important in programming as well because it allows for more efficient code, especially when dealing with fraction operations and optimization problems.

There are built-in functions in many programming languages designed to compute the GCD. In Python, for example, the math library includes the `gcd` function which can be used to find the greatest common divisor of two numbers, streamlining the process of fraction simplification.

Arithmetic Operations in Python

Python, a versatile programming language, offers various arithmetic operations such as addition, subtraction, multiplication, division, and much more. These operations are fundamental to working with numbers and calculations in Python.

When performing division in Python using the '/' operator, the result is a floating-point number. If an integer result is needed, the '//' (floor division) operator is used instead. Python also supports more complex operations with modules, like the math module, which provides mathematical functions including 'gcd' for greatest common divisor, 'pow' for power calculations, and 'sqrt' for square roots.

For our exercise, we used '/' to divide 9 by 12, which in Python would yield 0.75, a floating-point value. This operation is part of Python's core arithmetic operations and is integral in a myriad of applications spanning from simple calculations to complex algorithms.