Problem 319 - Prealgebra

Question

In the following exercises, translate and simplify. the sum of 3,075 and 95

Step-by-Step Solution

Answer

3170

Step 1: Translate the problem into a mathematical expression

The phrase 'the sum of 3,075 and 95' translates to the mathematical expression: \( 3075 + 95 \)

Step 2: Simplify the expression

Add the two numbers together: \( 3075 + 95 = 3170 \)

Key Concepts

translation of phrases to expressions

Understanding how to translate phrases into mathematical expressions is crucial in prealgebra. Let's break it down. When a problem states 'the sum of 3,075 and 95,' the word 'sum' indicates addition. Here is how you can translate such phrases to an expression:

• Identify the key terms and what operation they imply (e.g., sum means addition).
• Replace the words with mathematical symbols. In this case, 'the sum of 3,075 and 95' becomes 3075 + 95.

Always proceed step-by-step to avoid missing out on any detail. This skill is fundamental for solving complex problems later on.

simplifying expressions

Simplifying expressions means making them easier to understand or solve. In our example, the expression is already quite simple: 3075 + 95. Here’s a strategy to simplify:

• First, recognize and perform the operations indicated by the symbols. Here, we need to add.
• Work systematically from left to right unless order of operations (PEMDAS/BODMAS) dictates otherwise.
• Combine the numbers to get a single result. For 3075 + 95, you directly add them to get 3170.

Through simplifying, you can clearly see your solution and verify its accuracy more easily.

addition

Addition is a fundamental arithmetic operation. When you see the word 'sum,' it tells you to add the numbers involved. Here’s a quick guide to performing addition correctly:

• Align the numbers vertically if you are doing it on paper, making sure that each digit is in the correct place value.
• Start adding from the rightmost digit (units place) and move leftwards, carrying over any value more than 9 to the next column.
• Ensure accuracy by double-checking your work

For example, adding 3075 and 95, you align and sum each column:
Units: 5 + 5 = 10 (write down 0, carry over 1)
Tens: 7 + 9 = 16, plus 1 carried over = 17 (write down 7, carry over 1)
Hundreds: 0 + 0 + 1 carried over = 1 (write down 1)
Thousands: 3 + 0 = 3 (write down 3).
The result is 3170, the sum of 3075 and 95. Always ensure each step is taken carefully to gain the correct result.