Problem 146 Divide, and write the answer in ... [FREE SOLUTION] (2024)

Short Answer

fraction division

Dividing fractions might seem tricky at first, but it's actually straightforward once you understand the process.
The key idea is to change the division problem into a multiplication problem. This is done by multiplying by the reciprocal of the second fraction.
Remember, the reciprocal of a fraction is what you get when you swap its numerator (top number) and denominator (bottom number).
For example, when dividing \(-\frac{4}{5} \div \frac{4}{7}\), you will turn \(\frac{4}{7}\) into its reciprocal, \(\frac{7}{4}\), then multiply:
\(-\frac{4}{5} \times \ (\frac{7}{4})\).
Following through with this step will transform your division problem into a more manageable multiplication one.

reciprocal

The reciprocal of a fraction plays a crucial role in fraction division.
To find the reciprocal, simply flip the numerator and denominator.
Let’s say you have a fraction like \(\frac{3}{8}\). Its reciprocal is \(\frac{8}{3}\).
In our example, the second fraction is \(\frac{4}{7}\). Its reciprocal is \(\frac{7}{4}\).
By multiplying with \(\frac{7}{4}\), we change the division into a multiplication problem.
This makes it easier to proceed with solving the fraction operation.

simplifying fractions

Simplifying fractions means reducing them to their simplest form.
This is done by dividing the numerator and denominator by their greatest common divisor (GCD).
In our problem, we initially get \(\frac{-28}{20}\) after multiplication.
Next, identify the GCD of 28 and 20.
Both 28 and 20 can be divided by 4, their GCD.
Dividing both the numerator and denominator by their GCD, we simplify \(\frac{-28 \div 4}{20 \div 4}\), resulting in \(\frac{-7}{5}\).
Always remember, the goal is to make the fraction as simple as possible.

greatest common divisor

The greatest common divisor (GCD) is the largest number that can evenly divide both the numerator and the denominator of a fraction.
When simplifying fractions, identifying the GCD is crucial.
For instance, to simplify \(\frac{-28}{20}\), we determine the GCD of 28 and 20.
Both numbers are divisible by 4.
This makes 4 the GCD.
Therefore, dividing both 28 and 20 by 4, we get a simplified fraction: \(\frac{-7}{5}\).
The GCD helps simplify fractions quickly and accurately, leading to a cleaner, easier-to-understand solution.