Problem 47 - Fundamentals of Mathematics

Question

Combine the numbers as indicated. $$521+453-334+600$$

Step-by-Step Solution

Answer

1240

Step 1: Combining the Additions

Start by adding the numbers that need to be combined through addition: \[521 + 453\]Add the two numbers together: \[521 + 453 = 974\]

Step 2: Performing the Subtraction

Next, subtract 334 from the result obtained in Step 1:\[974 - 334\]Perform the subtraction to find:\[974 - 334 = 640\]

Step 3: Adding the Remaining Number

Finally, add 600 to the result obtained in Step 2:\[640 + 600\]After performing the calculation, you get:\[640 + 600 = 1240\]

Key Concepts

Addition

Addition is one of the basic arithmetic operations fundamental to many areas of math and real-life problem-solving. It's the process of calculating the total of two or more numbers or amounts. When you add numbers together, you're essentially combining them into a larger number, which represents the total. For instance, in the exercise's first step, you start by adding 521 and 453 together.

• 521 can be thought of as five hundreds, two tens, and one unit.
• 453 represents four hundreds, five tens, and three units.

By adding each place value individually, the sums are compiled starting from the units up to hundreds or more, ensuring you capture the complete total effectively. The final sum of 521 and 453 is 974, a straightforward computation: \[521 + 453 = 974\]Understanding addition helps in various real-world scenarios, from budgeting finances to mixing ingredients in recipes. It's essential to master this skill as a basis for more complex mathematical concepts.

Subtraction

Subtraction is another key arithmetic operation that involves taking one number away from another. It's used to find the difference between numbers, and is incredibly useful in determining what remains. In the exercise, subtraction is performed after the initial addition to subtract 334 from 974.

• Start with the larger number, which is 974 in this case.
• Subtract the smaller number, which is 334.

Breaking it down, you subtract each digit in place value, beginning with the units, followed by tens, and so forth: \[974 - 334 = 640\]Subtraction can help in many practical situations, like calculating change in a transaction or determining distance. Grasping how to subtract accurately ensures you can solve a variety of numerical challenges day-to-day.

Step by Step Solution

A step-by-step solution approach is designed to break down complex problems into simpler, more digestible tasks. This method is highly effective for learning and understanding arithmetic operations since it allows you to tackle each part independently.

• First, simplify the problem by performing addition, such as \(521 + 453 = 974\).
• Next, use subtraction on your result, \(974 - 334 = 640\).
• Finally, address any remaining operations, like adding \(640 + 600\) to reach the final answer of 1240.

This approach not only enhances your ability to solve problems logically but also ensures precision. Each step builds upon the previous one, creating a chain of operations that lead to the correct answer. Breaking the problem into parts makes it easier to identify errors and understand each operation's role within the entire process. This structured method is invaluable in honing problem-solving skills and gaining confidence in handling arithmetic tasks.