Solve Division with Decimals: Evaluating -3.5 ÷ (-7) + 14

Q: Why does negative divided by negative equal positive?

Think of division as repeated subtraction. When you divide -3.5 by -7, you're asking "how many times does -7 go into -3.5?" Since both numbers have the same sign, the result is positive: $ \frac{-}{-} = + $

Q: How do I convert 0.5 to a mixed number with 14?

First recognize that 0.5 = $ \frac{1}{2} $. Then add: $ \frac{1}{2} + 14 = \frac{1}{2} + \frac{28}{2} = \frac{29}{2} = 14\frac{1}{2} $

Q: Do I have to follow order of operations with decimals too?

Yes, absolutely! Order of operations (PEMDAS/BODMAS) applies to all numbers - whole numbers, decimals, fractions, and mixed numbers. Division always comes before addition.

Q: What if I get confused by the negative signs?

Use the sign rules: same signs give positive, different signs give negative. Here we have $ (-3.5) ÷ (-7) $ - both negative, so the result is positive!

Q: Can I write the answer as just a decimal instead?

Yes! $ 14\frac{1}{2} = 14.5 $. Both forms are correct, but mixed numbers often show the relationship between whole and fractional parts more clearly.

Order of Operations with Mixed Number Results

$-3.5:-7+14=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together.

00:10 We'll use the correct order of operations.

00:14 Write the division as a fraction. This helps us see it clearly.

00:19 Remember, always do multiplication and division first, before addition and subtraction.

00:25 A negative divided by a negative equals a positive. Keep that in mind!

00:36 Break 7 into factors: 3 point 5 and 2.

00:42 Let's simplify what we can. We're getting close!

00:51 And that's how we solve this question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-3.5:-7+14=\text{ ?}$

Step-by-step solution

We must solve the exercise from left to right.

First, we will rewrite the division as a simple fraction in the following way:

$\frac{-3.5}{-7}+14=$

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

$\frac{-}{-}=+$

We will then break down 7 into a multiplication exercise:

$\frac{3.5}{3.5\times2}+14=$

Finally, we will reduce the 3.5 in both the numerator and denominator of the fraction to get our answer:

$\frac{1}{2}+14=14\frac{1}{2}$

Final Answer

$+14\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Negative divided by negative equals positive result
Technique: Simplify $\frac{3.5}{7} = \frac{1}{2}$ before adding 14
Check: Verify $\frac{1}{2} + 14 = 14\frac{1}{2}$ equals original expression ✓

Common Mistakes

Avoid these frequent errors

Forgetting to follow order of operations
Don't add 14 to -7 first to get (-3.5) ÷ 7 + 14 = 13.5! This ignores order of operations rules. Always complete division before addition, so (-3.5) ÷ (-7) = 0.5, then 0.5 + 14 = 14.5.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$(+6)\cdot(+9)=$

FAQ

Everything you need to know about this question

Why does negative divided by negative equal positive?

Think of division as repeated subtraction. When you divide -3.5 by -7, you're asking "how many times does -7 go into -3.5?" Since both numbers have the same sign, the result is positive: $\frac{-}{-} = +$

How do I convert 0.5 to a mixed number with 14?

First recognize that 0.5 = $\frac{1}{2}$ . Then add: $\frac{1}{2} + 14 = \frac{1}{2} + \frac{28}{2} = \frac{29}{2} = 14\frac{1}{2}$

Do I have to follow order of operations with decimals too?

Yes, absolutely! Order of operations (PEMDAS/BODMAS) applies to all numbers - whole numbers, decimals, fractions, and mixed numbers. Division always comes before addition.

What if I get confused by the negative signs?

Use the sign rules: same signs give positive, different signs give negative. Here we have $(-3.5) ÷ (-7)$ - both negative, so the result is positive!

Can I write the answer as just a decimal instead?

Yes! $14\frac{1}{2} = 14.5$ . Both forms are correct, but mixed numbers often show the relationship between whole and fractional parts more clearly.

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Solve Division with Decimals: Evaluating -3.5 ÷ (-7) + 14

Order of Operations with Mixed Number Results

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does negative divided by negative equal positive?

How do I convert 0.5 to a mixed number with 14?

Do I have to follow order of operations with decimals too?

What if I get confused by the negative signs?

Can I write the answer as just a decimal instead?

🌟 Unlock Your Math Potential

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