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Chapter 1: Problem 76

Translate the English phrase to a mathematical statement and simplify. The sum of 100 and 42

Short Answer

Expert verified
142

Step by step solution

01

Identify key terms in the phrase

The phrase 'The sum of 100 and 42' indicates addition.
02

Convert words to a mathematical expression

Translate the phrase into a mathematical expression. 'The sum of' means addition, so the expression becomes: 100 + 42
03

Perform the addition

Add the numbers: 100 + 42 = 142

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Key Concepts

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

Understanding Addition
Addition is one of the fundamental operations in mathematics. It involves combining two or more numbers to get a total. When you add numbers, you are essentially counting how many items you have in total. For instance, if you have 3 apples and someone gives you 2 more apples, you now have 5 apples in total.

In the exercise, the phrase 'The sum of 100 and 42' specifically uses the word 'sum.' This is a clear signal that addition is needed. Here's how addition works in general:
  • Identify the numbers you need to add.
  • Combine the values to get a total.
So, when we add 100 and 42, we align the numbers and proceed with the addition: 100 + 42 results in 142. This is how addition simplifies the process of understanding total amounts or counts.
Understanding a Mathematical Expression
A mathematical expression is a combination of numbers, variables, and operators (like addition and subtraction) that represents a value. In this exercise, we translated the English phrase into a mathematical expression to solve it. The phrase 'The sum of 100 and 42' was converted into 100 + 42.

When dealing with mathematical expressions:
  • Identify key terms that dictate the operation (like 'sum' for addition).
  • Translate those terms into symbols (such as + for addition).
  • Combine numbers and symbols to form the expression.
For example, in our exercise, 'The sum of' translates to '+', creating the expression 100 + 42.
Steps to Simplification
Simplification in mathematics means making an expression more straightforward or easier to work with. This often involves performing operations to reduce the expression to a single number or a simpler form. In our exercise, we simplified the mathematical expression 100 + 42 by simply performing the addition.

Simplification process involves:
  • Looking at the expression and identifying operations you can perform.
  • Carrying out those operations step by step.
  • Arriving at a simpler form or a single value.
In this case:
  • We saw the expression 100 + 42.
  • We performed the addition.
  • We got the simplified answer, which is 142.
Simplifying helps in solving problems more quickly and understanding results better.

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