Problem 30 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. Find the difference of -19 and 7 .

Step-by-Step Solution

Answer

The difference is -26.

Step 1: Understanding the Vocabulary

The phrase 'the difference of' in mathematical terms refers to subtraction. We are finding the difference of two numbers here: -19 and 7.

Step 2: Translating the Sentence into an Equation

Translate the sentence 'the difference of -19 and 7' into a mathematical equation. The equation representing the difference of -19 and 7 is \(-19 - 7\).

Step 3: Simplifying the Equation

Now simplify the equation \(-19 - 7\). To do this, subtract 7 from -19. This can also be thought of as adding -7 to -19, which results in -26. Thus, \(-19 - 7 = -26\).

Key Concepts

Mathematical Statements

A mathematical statement is a way of expressing a mathematical idea using mathematical symbols, numbers, and operations. Just like sentences in English, mathematical statements convey complete thoughts or ideas that can be solved or evaluated. In this context, the phrase "Find the difference of -19 and 7" needs to be translated into a mathematical statement. This involves recognizing which numbers to use and the operation that connects them.

By understanding the key terms in the sentence and identifying the operation required, you can write a coherent mathematical equation. For instance, in this exercise, translating the sentence into a mathematical statement involves recognizing that "difference" indicates subtraction, resulting in the equation \(-19 - 7\).

Subtraction

Subtraction is one of the fundamental arithmetic operations. It involves finding the difference between two numbers by taking away one from the other. In our exercise, you are asked to subtract the two numbers -19 and 7.

When subtracting a positive number from a negative number, you essentially move further down on the number line. This can also be thought of as adding a negative to a negative. In this case, subtracting 7 from -19 can be seen as -19 plus the negative of 7, which results in -26.

Practicing subtraction with positive and negative numbers helps strengthen your understanding of number lines and operations.

Vocabulary in Math

In mathematics, understanding vocabulary is key to accurately interpreting problems and forming correct equations. Words such as 'difference', 'sum', 'product', and 'quotient' provide instructions for what operations to perform.

For example:

• 'Difference' means subtraction.
• 'Sum' pertains to addition.
• 'Product' refers to multiplication.
• 'Quotient' indicates division.

In our exercise, recognizing that "difference" translates to the subtraction operation was crucial to creating the mathematical statement -19 - 7.

Once you become familiar with these math-specific terms, tackling similar problems becomes much more intuitive.

Equation Simplification

Simplifying an equation involves performing operations to reduce it to its simplest form. In our problem, the equation was \(-19 - 7\). Starting with this expression, you subtract 7 from -19 to simplify. This leads to -26, which is the answer.

To simplify correctly, perform the operations as indicated by the expression or problem statement. Consider every number and sign carefully, especially when dealing with positives and negatives.

Simplifying equations can reveal solutions and help recognize patterns in numbers and operations. The simplified result is often easier to understand and is the final step in solving an algebraic problem. Practice helps make these simplifications second nature.