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Sep12

Tricks to Solve Combined Operations

In today’s post we will learn some tricks to solve combined operations in a simpler way.

Example 1

Look at these two operations:

Have you finished it yet? Have you noticed that the two results are the same? Which of the two was easier to multiply?

Converting an operation to an equivalent one can help a lot when calculating the final result.

In the example above we have divided the first factor by two and multiplied the second factor by two. Thus the result does not change and we can calculate 86 * 5 by finding the result of 43 * 10, which is a much easier multiplication to perform.

Before proceeding, let us remember the order in which operations must be performed when an arithmetic expression involves addition, subtraction, multiplication, division and/or parentheses.

• Step 1: operations inside the parentheses
• Step 2: multiplications and divisions from left to right
• Step 3: addition and subtraction from left to right
Example 2

What is a simple way to resolve this operation?

In this case, as multiplication comes first, we can use the commutative property of multiplication to transform the operation into the following:

Now, choose the order of operations. We have a multiplication and division, we can choose either of the two. What will be easier? Multiplying 12 by 77 and then divide the result by 11? or to divide 77 by 11 and then multiply the result by 12? Think wisely! It will be much easier if you first divide and then multiply.

Example 3

Let’s look at one last example:

To solve this expression we can use the distributive property to transform the expression into the following:

Now, to not disobey the hierarchy of operations, we first conduct divisions:

Finally, we add! Did you find it easier to solve the expression in this way?

Do not forget that to learn, either combined operations or any other subject of mathematics, you have to practice!

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