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Chapter 2: Problem 56

Simplify. \(33 \div(3+8) \cdot 2\)

Short Answer

Expert verified
6

Step by step solution

01

Solve inside the Parentheses

First, solve the expression inside the parentheses. The expression is: \(3+8\) which simplifies to \(11\).
02

Substitute and Divide

Next, substitute the simplified value back into the original expression. Now perform the division. The expression becomes: \(33 \div 11\) which simplifies to \(3\).
03

Multiply the Result

Finally, take the result and perform the multiplication. The expression is: \(3 \cdot 2\) which simplifies to \(6\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplification
Simplification in math means making an expression easier to work with. It's like cleaning up a messy room! You take a complicated problem and break it down step-by-step.

In the given exercise, we simplified the expression \(33 \div (3+8) \cdot 2\). We did this by following a series of steps to make it easier to solve.

First, solve what's inside the parentheses. Then, move on to other operations like division and multiplication. Always work through the expression in a logical order.
Parentheses in Math
Parentheses are used in math to group certain parts of an expression. They tell us what to solve first. For instance, in our example \(33 \div (3+8) \cdot 2\), the \(3+8\) is inside parentheses.

When you see parentheses, always solve what's inside them first.
This method is called the 'order of operations'. Ignoring the parentheses might lead to a different, often incorrect answer.
For instance:
  • Without solving \(3+8\) first, you might divide or multiply the wrong number.
  • This could change the final outcome.
Dividing and Multiplying
Once you've handled any parentheses, move on to dividing and multiplying. These operations are of equal importance in the order of operations. You tackle them from left to right.

In our example, we simplified \(33 \div 11\) to get \(3\) before multiplying \(3 \cdot 2\). This left-to-right method ensures accuracy.

Remember these key points:
  • Always handle division or multiplication in the order they appear, from left to right.
  • Breaking the rules of the order of operations can significantly alter your results.
By following these steps, you make sure your math work is neat and correct.

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Most popular questions from this chapter

In the following exercises, translate the given sentence into an algebraic equation. Twice the difference of n and 10 gives 52.

In the following exercises, simplify, using the order of operations. $$ 5[2+7(9-8)] $$

In the following exercises, find the prime factorization of each number. $$ 165 $$

In the following exercises, find all the factors of each number. $$ 180 $$

In the following exercises, solve each equation using the addition property of equality. $$ y-3=19 $$
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