Problem 42 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. (Lesson 1.3) $$ 0.75 \div 2.5 \cdot 2+1 $$

Step-by-Step Solution

Answer

The solution to the given expression is 1.6.

Step 1: Perform Division First

Perform division first since according to BIDMAS/BODMAS/PEDMAS, division comes before multiplication and addition. So, divide 0.75 by 2.5 to get 0.3.

Step 2: Perform Multiplication

The next operation in line is multiplication. Multiply the result of step 1 by 2. This gives us \(0.3 \cdot 2 = 0.6\).

Step 3: Perform Addition

The last operation is addition. Add the result of step 2 to 1. So, \(0.6 + 1 = 1.6\) .

Key Concepts

Division

In the context of order of operations, division is an essential process that plays a significant role in calculating expressions accurately. When faced with expressions involving more than one operation, it's crucial to follow the principles of BIDMAS, BODMAS, or PEDMAS, which are acronyms for brackets, indices (or orders), division and multiplication, addition and subtraction.

• Division is prioritized over addition and subtraction, but is performed alongside multiplication left to right.
• In the given problem, the division involves dividing 0.75 by 2.5, and the answer is 0.3.

A helpful way to understand division is to relate it to real-life situations. For instance, if you have 0.75 of a cake and want to divide it into 2.5 equal parts, how much would each part be? Thinking about division in such a practical manner can make it easier to understand.
Remember, division is the inverse of multiplication, and both share equal precedence in the order of operations rules. Always remember to perform these operations from left to right when they appear consecutively in an expression.

Multiplication

Once division is performed, multiplication swiftly follows on our list of operations according to our order of operations rule. Again, remember: if multiplication and division appear in an expression, solve them as they appear from left to right.

• In the exercise provided, we multiply the result of our division step—0.3—by 2.
• This results in 0.6, showing how multiplication affects the current value moving forward in our calculations.

Understanding multiplication entails visualizing it as scaling or growing a number. For example, if you have 3 baskets each containing 2 apples, multiplying tells you how many apples you have in total (3 times 2 gives you 6 apples). Similarly, in the exercise, multiplication scales the result of the division (0.3) up by a factor of 2.

Addition

Addition is often one of the more straightforward operations, but it is equally crucial in solving expressions fully. After division and multiplication, we proceed to addition, as prescribed by the order of operations.

• In our problem, the step involves adding 1 to our previously calculated product, 0.6, resulting in a final total of 1.6.
• Addition is usually the concluding operation when following the BIDMAS/BODMAS/PEDMAS order.

This process can be likened to gathering objects together, such as adding more apples to your basket. If you already have a few apples (0.6) and pick one more (1), combining them gives you 1.6 apples (figuratively speaking).
Addition is the simplest arithmetic operation, merely moving quantities together, making it a natural and conceivable end to solving mathematical expressions.