Solve Mixed Number Division: -7½ ÷ (+1) Step-by-Step

Q: Why is the answer still negative when I divide by a positive number?

When you divide a negative number by a positive number, the result is always negative! Think of it like sharing debt: if you owe $ 7\frac{1}{2} $ dollars and split it among 1 person, you still owe $ 7\frac{1}{2} $ dollars.

Q: Does dividing by 1 change the mixed number at all?

No! Dividing by 1 is like asking 'how many groups of 1 fit into this number?' The answer is always the original number. It's like cutting a pizza into 1 piece - you still have the whole pizza.

Q: What if I had to convert the mixed number to an improper fraction?

For this problem, you don't need to! Since we're dividing by 1, the mixed number stays exactly the same. Converting would just add unnecessary steps: $ -\frac{15}{2} ÷ 1 = -\frac{15}{2} = -7\frac{1}{2} $

Q: How do I remember the sign rules for division?

Use this simple pattern: same signs = positive, different signs = negative. Here we have negative ÷ positive (different signs), so the answer is negative.

Q: Is there ever a time when dividing by 1 would change the number?

Never! The identity property of division states that any number divided by 1 equals itself. This is one of the most reliable rules in math - $ \frac{x}{1} = x $ for any value of x.

Division by One with Mixed Numbers

Solve the following problem:

$(-7\frac{1}{2}):(+1)=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$(-7\frac{1}{2}):(+1)=$

Step-by-step solution

Note that we are dividing a negative number by a positive number, and therefore the result must be a negative number:

$-:+=-$

We will write the exercise in the following way:

$\frac{-7\frac{1}{2}}{1}=$

Let's remember the rule:

$\frac{x}{1}=x$

In other words, any number divided by 1 will be equal to itself.

Therefore, the answer is:

$-7\frac{1}{2}$

Final Answer

$-7\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Any number divided by 1 equals the number itself
Sign: Negative ÷ positive = negative, so $-7\frac{1}{2} ÷ 1 = -7\frac{1}{2}$
Check: Verify $-7\frac{1}{2} × 1 = -7\frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to keep the negative sign in the answer
Don't drop the negative sign and write $7\frac{1}{2}$ = positive answer! Dividing negative by positive must give negative. Always remember: negative ÷ positive = negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why is the answer still negative when I divide by a positive number?

When you divide a negative number by a positive number, the result is always negative! Think of it like sharing debt: if you owe $7\frac{1}{2}$ dollars and split it among 1 person, you still owe $7\frac{1}{2}$ dollars.

Does dividing by 1 change the mixed number at all?

No! Dividing by 1 is like asking 'how many groups of 1 fit into this number?' The answer is always the original number. It's like cutting a pizza into 1 piece - you still have the whole pizza.

What if I had to convert the mixed number to an improper fraction?

For this problem, you don't need to! Since we're dividing by 1, the mixed number stays exactly the same. Converting would just add unnecessary steps: $-\frac{15}{2} ÷ 1 = -\frac{15}{2} = -7\frac{1}{2}$

How do I remember the sign rules for division?

Use this simple pattern: same signs = positive, different signs = negative. Here we have negative ÷ positive (different signs), so the answer is negative.

Is there ever a time when dividing by 1 would change the number?

Never! The identity property of division states that any number divided by 1 equals itself. This is one of the most reliable rules in math - $\frac{x}{1} = x$ for any value of x.

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