Problem 27 - Fundamentals of Mathematics

Question

Write each expression in words. $$ 1+(-7) $$

Step-by-Step Solution

Answer

One plus negative seven.

Step 1: Identify Operation

First, identify the operation involved. We have a positive number, 1, and a negative number, -7, which are being added together.

Step 2: Write Positive Number in Words

Write the positive number in words. The number 1 is written as 'one'.

Step 3: Write Negative Number with Addition in Words

Write the negative number with the addition in words. 'Plus negative seven' represents the operation of adding a negative number.

Step 4: Combine into Full Sentence

Combine all parts into a full sentence. The expression \(1 + (-7)\) is written as 'one plus negative seven' in words.

Key Concepts

Addition

Addition is one of the fundamental operations in mathematics. It involves combining two or more numbers to get a new total, called the sum. In basic terms, it is like putting two collections of objects together to see how many there are in total. For instance, adding 2 and 3 gives you 5. In mathematical terms, addition follows this pattern: if you have two numbers, say 'a' and 'b', adding them is expressed as:

• \( a + b = c \)

where \( c \) is the sum of \( a \) and \( b \).
Addition is applicable in everyday situations, like calculating the total cost of groceries or determining the number of hours you've worked in a week. Recognizing addition symbols and expressions is crucial for solving problems efficiently.

Negative Numbers

Negative numbers are numbers that are less than zero. They are represented with a minus sign (-) preceding the actual number, like -7. These numbers can seem a bit tricky at first, but they are simply numbers on the opposite side of zero from the positive numbers.

• Negative numbers are often used to represent debts or temperatures below freezing.
• In a number line, negative numbers are placed to the left of zero.

Understanding negative numbers helps when dealing with real life situations. For instance, if you have \(10 and you owe \)7, you effectively have $3 left. In mathematical operations, adding a negative number is similar to subtracting a positive number. So when you see an expression like \( 1 + (-7) \), it is the same as \( 1 - 7 \), which equals -6. Being familiar with negative numbers will allow you to solve a wide array of problems with ease.

Writing Numbers in Words

Writing numbers in words involves expressing numerical values using words instead of digits. This skill is essential for clear communication, as it helps prevent misunderstandings, especially in complex mathematical expressions.

• The number 1 is written as 'one'.
• The number -7 is read as 'negative seven'.

When you encounter a mathematical expression, such as \( 1 + (-7) \), it helps to break it down into parts, converting each number into words and including the operation symbols like 'plus'.
For example, the expression \( 1 + (-7) \) translates to 'one plus negative seven'. This straightforward conversion ensures that the numbers are easily interpreted, providing a clear understanding of the mathematical operation being performed.