Solve -13×4÷(-8): Working with Negative Integer Operations

Q: Why do I get a positive answer when starting with negative numbers?

Great observation! Even though we start with $ -13 $, the signs follow specific rules. Negative × positive = negative ($ -52 $), but negative ÷ negative = positive ($ \frac{-52}{-8} = +6.5 $)!

Q: How do I convert the decimal 6.5 to a mixed number?

The decimal 6.5 means 6 and 5 tenths. Since 5 tenths = $ \frac{5}{10} = \frac{1}{2} $, we get $ 6\frac{1}{2} $. Always simplify fractions to lowest terms!

Q: Can I do this problem using just fractions instead of decimals?

Absolutely! Write it as $ \frac{-13 \times 4}{-8} = \frac{-52}{-8} = \frac{52}{8} = \frac{13}{2} = 6\frac{1}{2} $. Both methods work perfectly!

Q: What if I accidentally get -6.5 as my answer?

You probably made a sign error! Remember: when dividing two negative numbers, the result is positive. Double-check your sign rules: $ \frac{-52}{-8} = +6.5 $, not negative!

Q: Why does the order of operations matter so much here?

If you divide first, you get $ -13 \times (4 ÷ (-8)) = -13 \times (-0.5) = 6.5 $ - which happens to be the same! But this won't always work. Always follow PEMDAS/BODMAS to be safe.

Negative Integer Operations with Mixed Numbers

$-13\cdot4:-8=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem step by step.

00:09 Remember, negative times positive always equals negative.

00:15 Let's multiply the numbers and plug them into the exercise.

00:26 Express division as a fraction. Pause now if you need.

00:32 Remember, a negative divided by a negative is positive.

00:43 Calculate to find the whole number and the remainder.

00:49 Break down 8 into four and two. Keep it simple.

00:55 Simplify wherever possible and keep going.

00:59 And that's the solution! Great job.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-13\cdot4:-8=$

Step-by-step solution

Let's solve the exercise from left to right.

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

$-13\times4=-52$

Now we got the exercise:

$-52:-8=$

Let's write the exercise as a simple fraction:

$\frac{-52}{-8}=$

Note that we are dividing between two negative numbers, therefore the result must be a positive number:

$\frac{52}{8}=$

Let's convert it to an addition exercise:

$6+\frac{4}{8}=$

Let's break down the 8 into a multiplication exercise:

$6+\frac{4}{4\times2}=$

Let's reduce the 4 in both eight and the fraction's denominator:

$6+\frac{1}{2}=6\frac{1}{2}$

Final Answer

$6\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Follow order of operations: multiplication before division always
Technique: Track signs carefully: negative × positive = negative, negative ÷ negative = positive
Check: Convert back to improper fraction: $6\frac{1}{2} = \frac{13}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and dividing first
Don't solve -13×4÷(-8) by doing -13÷(-8)×4 first = wrong order gives 6.5! This violates the order of operations rules. Always multiply -13×4 = -52 first, then divide by -8.

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 do I get a positive answer when starting with negative numbers?

Great observation! Even though we start with $-13$ , the signs follow specific rules. Negative × positive = negative ( $-52$ ), but negative ÷ negative = positive ( $\frac{-52}{-8} = +6.5$ )!

How do I convert the decimal 6.5 to a mixed number?

The decimal 6.5 means 6 and 5 tenths. Since 5 tenths = $\frac{5}{10} = \frac{1}{2}$ , we get $6\frac{1}{2}$ . Always simplify fractions to lowest terms!

Can I do this problem using just fractions instead of decimals?

Absolutely! Write it as $\frac{-13 \times 4}{-8} = \frac{-52}{-8} = \frac{52}{8} = \frac{13}{2} = 6\frac{1}{2}$ . Both methods work perfectly!

What if I accidentally get -6.5 as my answer?

You probably made a sign error! Remember: when dividing two negative numbers, the result is positive. Double-check your sign rules: $\frac{-52}{-8} = +6.5$ , not negative!

Why does the order of operations matter so much here?

If you divide first, you get $-13 \times (4 ÷ (-8)) = -13 \times (-0.5) = 6.5$ - which happens to be the same! But this won't always work. Always follow PEMDAS/BODMAS to be safe.

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