Problem 36 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. Five less than -10 .

Step-by-Step Solution

Answer

-15

Step 1: Translate the Sentence

To translate the sentence "Five less than -10" into a mathematical statement, identify the numbers and operation involved. "Five less than -10" implies subtraction of 5 from -10. So, the mathematical expression is: \[-10 - 5\]

Step 2: Simplify the Expression

Now, simplify the expression obtained in the previous step. Begin with the expression: \[-10 - 5\]Combine the numbers -10 and -5:\[-10 - 5 = -15\]

Key Concepts

Mathematical Translation

Mathematical translation involves converting words into mathematical symbols or expressions. This process requires understanding the language of mathematics and interpreting verbal statements accurately.
For example, the phrase "five less than -10" indicates that we are subtracting 5 from -10. The word "less" is a key indicator that prompts us to think about subtraction. It is crucial to recognize these keywords as they guide the translation.
Here are some common keywords for subtraction:

• "less than"
• "minus"
• "decreased by"

By identifying these terms, students can effectively translate verbal statements into mathematical expressions, making complex word problems more manageable.

Subtraction

Subtraction is one of the basic operations in mathematics. It involves finding the difference between numbers by taking one number away from another. The operation of subtraction is symbolized by the minus sign (-).
In the exercise, we are asked to find "five less than -10", which involves calculating \[-10 - 5\]. This means starting with -10 and moving 5 steps downwards on the number line.
When subtracting numbers, especially from a negative starting point, it is essential to visualize or draw a number line:

• Locate the starting number on the line (-10 in this case).
• Move left by the number you want to subtract (5 units in this example).

Subtraction becomes clearer with practice and by using mental math strategies or number lines to aid in understanding.

Negative Numbers

Negative numbers are numbers less than zero and they appear to the left of zero on a number line. They are denoted by a minus sign (-) before the number. Knowing how to work with negative numbers is vital as they often come up in real-life scenarios, like temperatures below zero or depths below sea level.
Here's what you need to know about negative numbers:

• Adding a negative number is the same as subtracting its absolute value.
• Subtracting a positive number from a negative results in a more negative number.
• Subtraction involving two negative numbers requires careful attention to their differences.

In our example, subtracting 5 from -10 results in -15, pushing further into the negative side of the number scale. Visualizing a number line can help understand how negative numbers interact in different operations.