Calculate -5.8 ÷ -3.4: Dividing Negative Decimals

Q: Why does negative divided by negative equal positive?

Think of it this way: if you're removing negative groups of something, you're actually adding! The two negative signs cancel each other out, just like in multiplication.

Q: Do I have to convert decimals to fractions?

Not always, but it helps with exact answers! You can divide decimals directly: -5.8 ÷ -3.4 ≈ 1.706, but converting gives the precise fraction $ \frac{29}{17} $.

Q: How do I convert division to multiplication with fractions?

When dividing fractions, multiply by the reciprocal! Flip the second fraction upside down: $ -\frac{58}{10} \div -\frac{34}{10} = -\frac{58}{10} \times -\frac{10}{34} $

Q: What does it mean to 'reduce' the fractions?

Look for common factors in numerator and denominator. Here, both 58 and 34 have factor 2, so $ \frac{58}{34} = \frac{29}{17} $ in simplest form.

Q: Can I use a calculator instead?

Yes, but be careful with rounding! Calculators give decimal approximations. The fraction $ \frac{29}{17} $ is the exact answer, while 1.706 is rounded.

Division Operations with Negative Decimal Numbers

Solve the following expression:

$-\text{5}.8:-3.4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Convert from decimal to fraction

00:10 Here too we'll convert from decimal to fraction

00:18 Let's set up our exercise

00:22 Division is also multiplication by the reciprocal

00:26 Let's swap between numerator and denominator

00:36 Let's reduce what we can

00:41 Negative times negative is always positive

00:50 Let's factor 58 into 2 and 29

00:53 Let's factor 34 into 2 and 17

00:56 Let's reduce what we can

00:59 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$-\text{5}.8:-3.4=$

Step-by-step solution

Let's begin by converting 5.8 into a simple fraction:

$-5.8=-\frac{58}{10}$

Let's proceed to convert 3.4 into a simple fraction:

$-3.4=-\frac{34}{10}$

Below is the resulting exercise

$-\frac{58}{10}:-\frac{34}{10}=$

Let's now convert the division exercise into a multiplication exercise, not forgetting to swap the numerator and denominator in the second fraction:

$-\frac{58}{10}\times-\frac{10}{34}=$

Let's reduce the 10 in both fractions in order to obtain the following:

$+\frac{58}{34}=$

Let's now break down the numerator and denominator into multiplication exercises:

$\frac{2\times29}{2\times17}=$

Finally let's reduce the 2 in both the numerator and denominator of the fraction and we should obtain:

$\frac{29}{17}$

Final Answer

$\frac{29}{17}$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative divided by negative always gives positive result
Technique: Convert to fractions: -5.8 = -58/10, -3.4 = -34/10
Check: $\frac{29}{17} \times (-3.4) = -5.8$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting sign rules for division
Don't assume negative ÷ negative = negative! This gives wrong signs in your answer. When dividing two negatives, the signs cancel out and become positive. Always remember: same signs give positive results.

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 does negative divided by negative equal positive?

Think of it this way: if you're removing negative groups of something, you're actually adding! The two negative signs cancel each other out, just like in multiplication.

Do I have to convert decimals to fractions?

Not always, but it helps with exact answers! You can divide decimals directly: -5.8 ÷ -3.4 ≈ 1.706, but converting gives the precise fraction $\frac{29}{17}$ .

How do I convert division to multiplication with fractions?

When dividing fractions, multiply by the reciprocal! Flip the second fraction upside down: $-\frac{58}{10} \div -\frac{34}{10} = -\frac{58}{10} \times -\frac{10}{34}$

What does it mean to 'reduce' the fractions?

Look for common factors in numerator and denominator. Here, both 58 and 34 have factor 2, so $\frac{58}{34} = \frac{29}{17}$ in simplest form.

Can I use a calculator instead?

Yes, but be careful with rounding! Calculators give decimal approximations. The fraction $\frac{29}{17}$ is the exact answer, while 1.706 is rounded.

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