Problem 4 Only one of these choices is equ... [FREE SOLUTION] (2024)

Short Answer

common denominator

When adding or subtracting fractions, the first step is to find a common denominator. A common denominator is a shared multiple of the denominators of the fractions you are working with. This allows you to combine the fractions easily.
For example, when adding \(\frac{1}{3}\) and \(\frac{1}{12}\), we need to find a common denominator. The denominators are 3 and 12. The least common multiple (LCM) of 3 and 12 is 12. Therefore, you can rewrite \(\frac{1}{3}\) as \(\frac{4}{12}\).
Switching to a common denominator allows the addition to be straightforward: \(\frac{1}{3} + \frac{1}{12} = \frac{4}{12} + \frac{1}{12} = \frac{5}{12}\).
The same process is used for subtracting fractions. Finding a common denominator streamlines working with fractions.

dividing fractions

Dividing fractions might seem tricky at first, but it becomes simple once you know the steps.
To divide a fraction by another fraction, you multiply the first fraction by the reciprocal of the second fraction.
For example, to divide \(\frac{5}{12}\) by \(\frac{3}{4}\), we multiply \(\frac{5}{12}\) by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).
Therefore, \(\frac{5}{12} \div \frac{3}{4} = \frac{5}{12} \times \frac{4}{3}\).
This reduces the problem to a straightforward multiplication of two fractions, making it much easier to handle.

reciprocal

A reciprocal is what you multiply a number by to get 1. Specifically, the reciprocal of a fraction \(\frac{a}{b}\) is another fraction \(\frac{b}{a}\). This concept is crucial when dividing fractions.
For example, the reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\). When dividing fractions, you take the reciprocal of the divisor (the fraction you are dividing by) and multiply it by the dividend (the fraction you are dividing).
This turns the division problem into a multiplication problem. For example, \(\frac{5}{12} \div \frac{3}{4}\) becomes \(\frac{5}{12} \times \frac{4}{3}\).
Understanding reciprocals makes dividing fractions much simpler.

greatest common divisor

The greatest common divisor (GCD), also known as the greatest common factor, is the largest number that divides two numbers without leaving a remainder.
Knowing how to find the GCD helps in simplifying fractions.
For instance, to simplify \(\frac{20}{36}\), we first find the GCD of 20 and 36, which is 4.
We then divide both the numerator and the denominator by their GCD: \(\frac{20}{36} = \frac{20 \div 4}{36 \div 4} = \frac{5}{9}\).
Using the GCD ensures that the fraction is simplified as much as possible, making the result easy to understand and use.