Question

Use a calculator to evaluate the expression. (Round to two decimal places.)\(3\left(-\frac{5}{12}+\frac{3}{8}\right)\)

Short answer

The value of the expression rounded to two decimal places is -0.13.

Step-by-step solution

Evaluate the Sum Inside the Brackets

Using the BIDMAS rule, the first operation to be performed is the sum inside the brackets. This involves adding two fractions. (-5/12 + 3/8). Which is equivalent to = -0.4167 + 0.3750 = -0.0417

Apply Multiplication

The next step is to multiply the result from the sum in Step 1 with 3. Hence, 3(-0.0417) = -0.1250.

Rounding to Two Decimal Places

The final step is to round the answer to 2 decimal places as instructed by the problem. Thus, -0.1250 rounded to two decimal places is -0.13.

Key concepts

BIDMAS Rule

In mathematics, the BIDMAS rule helps us understand the order in which operations should be carried out in a complex expression. BIDMAS is an acronym for Brackets, Indices, Division/Multiplication (from left to right), Addition/Subtraction (from left to right). It is crucial that operations are performed in this specific order to ensure accurate results. For instance, in the given expression \(3\left(-\frac{5}{12}+\frac{3}{8}\right)\), we first look at the sum inside the brackets, as per the BIDMAS rule. Clear understanding of this hierarchy can avoid common mistakes, like prematurely multiplying before addressing the addition or subtraction within brackets.

Adding Fractions

To add fractions, as seen in the expression \( -\frac{5}{12} + \frac{3}{8} \), the first step is to find a common denominator, which is a common multiple of both denominators. In this case, the common denominator is 24. The next step is to convert the fractions so that their denominators match this common number. The converted fractions become \( -\frac{10}{24} + \frac{9}{24} \). Afterwards, we simply add the numerators together and keep the common denominator thus: \( -\frac{10}{24} + \frac{9}{24} = \frac{-10 + 9}{24} \). This sum gives us \( \frac{-1}{24} \), which can be converted to a decimal for further operations.

Rounding Decimals

Rounding decimals is a method for simplifying a number while retaining its approximate value. For most practical purposes, numbers are rounded to a certain number of decimal places to make them easier to work with. In our example, the instruction was to round to two decimal places. To do this, we look at the third decimal place (if available) to determine whether to round the second decimal place up or leave it as it is. If the third decimal place is 5 or more, the second decimal place is rounded up; if it is less than 5, the second decimal place remains unchanged. Hence, \( -0.1250 \) is rounded to \( -0.13 \) as the third decimal place is 5 or greater, requiring an increase in the second decimal place from 2 to 3.