91Ó°ÊÓ

The distributive property is a fundamental principle of algebra. It allows us to multiply a single term by each term within a parenthesis.
This property is represented as:
\[ a(b + c) = ab + ac \]
In the provided exercise, we use the distributive property in the term \(-\frac{3}{4}(-8)\). Here's how it works:
• Multiply each part of the parenthesis by \(-\frac{3}{4}\).
• Distribute the \(-\frac{3}{4}\) to \(-8\) to get:
\[ -\frac{3}{4} \times -8 = \frac{3 \times 8}{4} = \frac{24}{4} = 6 \]
Remember, a negative times a negative is a positive, so the result is 6.

Fraction multiplication may seem tricky at first, but it's actually straightforward.
You simply multiply the numerators together and the denominators together. Let's look at the example from the solution:
• We're asked to compute \(12 \cdot \frac{5}{6}\).
• To do this, convert 12 to a fraction, which is \(\frac{12}{1}\).
• Next, multiply the numerators (top numbers): \(12 \times 5 = 60\).
• Then, multiply the denominators (bottom numbers): \(1 \times 6 = 6\).
• The result of the multiplication is \(\frac{60}{6}\).
• Finally, simplify \(\frac{60}{6}\) to 10.
That's all there is to it! Simplification often involves dividing both the numerator and the denominator by their greatest common divisor.

Adding integers is a basic arithmetic skill. Here, it’s essential for combining the simplified terms from the first two steps:
• We have the terms: \(7\), \(6\), and \(10\).
• Firstly, add \(7\) and \(6\) to get \(13\).
• Then, add \(13\) and \(10\) to reach the final result of \(23\).
Remember some simple rules for integer operations:

• Adding two positive numbers gives a positive sum.
• Adding a positive and a negative number involves subtracting and keeping the sign of the larger absolute value.
• Adding two negative numbers keeps the negative sign and sums the absolute values.

In this exercise, since all numbers are positive, straightforward addition is all that’s needed.