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Chapter 3: Problem 119

Simplify \(48 \div 12 \cdot 2\)

Short Answer

Expert verified
The expression simplifies to 8.

Step by step solution

01

Understand the Operation Order

Recognize that the expression involves both division and multiplication: \(48 \div 12 \cdot 2\). According to the order of operations (PEMDAS/BODMAS), division and multiplication are done from left to right as they appear.
02

Perform the Division

First, perform the division on the left part of the expression: \(48 \div 12\). Calculate this to get \(4\).
03

Execute the Multiplication

Next, multiply the result from the division by the remaining number in the expression: \(4 \cdot 2 = 8\). This completes the simplification of the original expression.

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Key Concepts

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

Division
Division is the process of determining how many times one number is contained within another. In our expression, we have the division problem: \(48 \div 12\). To "divide", you need to see how many groups of 12 fit into 48.
  • Think about it like sharing. If you have 48 apples and you want to share them evenly among 12 friends, each friend would get 4 apples.
  • This is why the division of 48 by 12 equals 4.
  • Remember, division can be seen as the opposite of multiplication.
Understanding division in this context helps you see that we are breaking a quantity into parts rather than combining them.
Multiplication
Multiplication involves combining equal groups. It's like adding the same number several times. After we have divided and found the result to be \(4\), our expression moves to multiplication: \(4 \cdot 2\).
  • Imagine having 4 bags with 2 items in each. By multiplying \(4 \times 2\), we find there are 8 items in total.
  • This operation shows how multiplication brings parts together to form a whole.
  • It's crucial to remember that multiplication can involve large numbers, but the concept remains root in repeated addition.
Understanding multiplication clearly helps in simplifying expressions accurately and seeing the scalability of numbers.
Simplifying Expressions
Simplifying expressions involves performing all operations according to the correct order to transform a complex expression into a more straightforward one. In our example, \(48 \div 12 \cdot 2\), we use the order of operations to simplify correctly.
  • We follow the left-to-right rule for operations of the same precedence, like division and multiplication.
  • It's like following a recipe: specific steps in order yield the correct dish, ensuring you don鈥檛 miss any flavor 鈥� or number, in math.
  • In this case, after dividing 48 by 12 and getting 4, we multiply 4 by 2 to get 8.
Remember that simplifying expressions is not just about finding the answer but understanding how operations transform numbers.

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Most popular questions from this chapter

Find the area of the triangle with base 13 inches and height 8 inches.

The following problems all involve the concept of borrowing. Subtract in case. \(12 \frac{3}{10}-5 \frac{7}{10}\)

The following problems all involve the concept of borrowing. Subtract in case. \(8-1 \frac{3}{4}\)

The following problems all involve the concept of borrowing. Subtract in case. \(24-10 \frac{5}{12}\)

These problems review the four basic operations with fractions from this chapter. Perform the indicated operations. $$\frac{7}{8} \div \frac{14}{24}$$
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