Problem 43
Question
Write a true sentence using either \(< or >\) $$ -6 \square 6 $$
Step-by-Step Solution
Verified Answer
The true sentence is -6 < 6.
1Step 1: Understand the Symbols
The symbols '<' and '>' are used to compare two numbers. '<' means 'less than' and '>' means 'greater than'.
2Step 2: Identify the Numbers
Look at the numbers given in the problem. The first number is -6 and the second number is 6.
3Step 3: Compare the Numbers
Since -6 is on the left side of 0 on the number line and 6 is on the right side of 0, -6 is less than 6.
4Step 4: Choose the Correct Symbol
Since -6 is less than 6, the correct symbol to use is '<'.
5Step 5: Form the True Sentence
Combine the numbers with the correct symbol to form the true sentence: -6 < 6.
Key Concepts
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number line
A number line is a visual representation of numbers in a straight line. Each point on this line corresponds to a unique number.
It extends infinitely in both directions, with 0 usually placed at the center.
On a number line, numbers to the right of 0 are positive, while numbers to the left of 0 are negative. For example, -6 is to the left of 0, and 6 is to the right of 0.
This helps us visually see that -6 is indeed less than 6. Placing numbers on a number line is essential for understanding their relationships, such as which number is greater or lesser.
It extends infinitely in both directions, with 0 usually placed at the center.
On a number line, numbers to the right of 0 are positive, while numbers to the left of 0 are negative. For example, -6 is to the left of 0, and 6 is to the right of 0.
This helps us visually see that -6 is indeed less than 6. Placing numbers on a number line is essential for understanding their relationships, such as which number is greater or lesser.
less than
The symbol '<' means 'less than.' It is used to compare two numbers and shows that the first number is smaller than the second. For example, in the sentence -6 < 6, the '<' symbol correctly indicates that -6 is less than 6.
To remember it easily, think of the '<' symbol like the mouth of a hungry alligator that always wants to eat the larger number. Thus, its open end points towards the bigger number.
Whenever you see '<,' it shows the first number is smaller. This makes it clear that -6 being less than 6 is a true statement.
To remember it easily, think of the '<' symbol like the mouth of a hungry alligator that always wants to eat the larger number. Thus, its open end points towards the bigger number.
Whenever you see '<,' it shows the first number is smaller. This makes it clear that -6 being less than 6 is a true statement.
greater than
The symbol '>' means 'greater than.' Like '<,' it is used to compare two numbers, but shows the opposite relationship — that the first number is bigger than the second.
For instance, if you compare 7 and 3, you would write 7 > 3. This indicates that 7 is greater than 3.
Just like the '<' symbol, you can remember '>' as the mouth of an alligator. This time, it opens towards the larger number, indicating that the first number is bigger.
Be attentive to these symbols; using the wrong one can lead to incorrect conclusions. In our exercise, -6 is not greater than 6, so we use -6 < 6 instead.
For instance, if you compare 7 and 3, you would write 7 > 3. This indicates that 7 is greater than 3.
Just like the '<' symbol, you can remember '>' as the mouth of an alligator. This time, it opens towards the larger number, indicating that the first number is bigger.
Be attentive to these symbols; using the wrong one can lead to incorrect conclusions. In our exercise, -6 is not greater than 6, so we use -6 < 6 instead.
Other exercises in this chapter
Problem 43
Add. Do not use the number line except as a check. \(-3.6+1.9\)
View solution Problem 43
Multiply. $$ -2 \cdot(-5) \cdot(-3) \cdot(-5) $$
View solution Problem 43
Simplify. $$ \frac{19}{76} $$
View solution Problem 43
Translate to an algebraic expression. \(x\) divided by \(w\)
View solution