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Chapter 1: Problem 27

Find the value of each expression. $$ 64 \div 4 \cdot 2 $$

Short Answer

Expert verified
32

Step by step solution

01

Perform the Division

First, divide 64 by 4. This means calculating \( 64 \div 4 = 16 \).
02

Perform the Multiplication

Next, multiply the result from Step 1 by 2. So, \( 16 \cdot 2 = 32 \).

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Key Concepts

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

Division
Division is one of the basic operations in mathematics. It involves splitting a number into equivalent parts or groups. For instance, if you have 64 cookies and divide them into groups of 4, each group will have 16 cookies. This is the essence of the operation performed when you calculate \(64 \div 4 = 16\). Dividing essentially asks how many times one number fits into another. In our example, 4 fits into 64 exactly 16 times. When performing division in multi-step math problems, it鈥檚 essential to remember to follow the order of operations, where division and multiplication should be addressed from left to right.
Multiplication
Multiplication is another fundamental operation in arithmetic. It is essentially repeated addition. Instead of adding a number multiple times, you can use multiplication to simplify the math. For example, 16 multiplied by 2 means you have two groups of 16, which equals 32. In our exercise, after dividing 64 by 4 to get 16, we then need to multiply 16 by 2. This gives us: \(16 \cdot 2 = 32\). Multiplication, like division, is an operation that should follow the left-to-right rule if both division and multiplication are present in a single expression.
Step-by-Step Solution
Following a step-by-step solution ensures you get the correct results, especially when dealing with expressions involving multiple operations. Let's look at the problem: \(64 \div 4 \cdot 2\). The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), tells us that we should first handle multiplication and division from left to right. Here鈥檚 a breakdown:
  • Step 1: Start with the division: \(64 \div 4\). This gives \(16\).
  • Step 2: Next, perform the multiplication: \(16 \cdot 2\). This results in \(32\).
This process ensures that every operation is completed in the correct order, leading to a final answer of \(32\) for our given expression.

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Most popular questions from this chapter

Solve each problem. The top of Mt. Whitney, visible from Death Valley, has an altitude of \(14,494\) ft above sea level. The bottom of Death Valley is 282 ft below sea level. Using 0 as sea level, find the difference between these two elevations.

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. Show that (a) \(4,114,107\) is divisible by \(9 \quad\) and \(\quad\) (b) \(2,287,321\) is not divisible by \(9 .\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 12 if it is divisible by both 3 and \(4,\) and not otherwise. Show that (a) \(4,253,520\) is divisible by 12 and \((b) 4,249,474\) is not divisible by 12

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