Solve Integer Division: -19 ÷ -76 Step by Step

Q: Why does negative divided by negative give a positive answer?

Think of it this way: two negatives make a positive! When you divide -19 by -76, you're asking "how many -76s fit into -19?" The answer is a positive fraction because both numbers have the same sign.

Q: How do I know when to simplify the fraction?

Always look for common factors in the numerator and denominator. In this case, both 19 and 76 are divisible by 19, so $ \frac{19}{76} = \frac{19}{19 \times 4} = \frac{1}{4} $.

Q: What if I wrote the answer as a decimal instead?

That's fine too! $ \frac{1}{4} = 0.25 $. Both forms are correct, but fractions are often preferred in math problems unless specifically asked for decimals.

Q: Can I flip the fraction and multiply instead?

No! Division is not the same as multiplying by the reciprocal when you have negative numbers. Stick to the division method and apply sign rules correctly.

Q: How do I remember all the sign rules?

Same signs: positive ÷ positive = positive, negative ÷ negative = positiveDifferent signs: positive ÷ negative = negative, negative ÷ positive = negativeThink: "Same signs are friends (positive), different signs fight (negative)"

Division of Integers with Negative Signs

$-19:-76=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

00:08 First, we can write division as a fraction.

00:16 Remember, a negative number divided by another negative is always positive.

00:27 Now, let's split 76 into its factors: 19 and 4.

00:32 Let's simplify any common factors.

00:36 And that's how you find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-19:-76=\text{ ?}$

Step-by-step solution

First, let's rewrite the exercise in the form of a simple fraction:

$\frac{-19}{-76}=$

Since we have negative numbers in both the numerator and denominator of the fraction, the result of the fraction must be positive.

Now let's break down the 76 into a multiplication exercise:

$\frac{19}{19\times4}=$

We can then cancel out the 19s in the numerator and denominator of the fraction and get:

$+4$

Final Answer

$+\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by negative always gives positive result
Technique: Rewrite $-19 ÷ -76$ as $\frac{-19}{-76} = \frac{19}{76}$
Check: Factor and simplify: $\frac{19}{19 \times 4} = \frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rules for division
Don't just ignore the negative signs or assume the answer is negative = wrong result! When both numbers are negative, they cancel out to give a positive answer. Always remember: negative ÷ negative = positive.

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 give a positive answer?

Think of it this way: two negatives make a positive! When you divide -19 by -76, you're asking "how many -76s fit into -19?" The answer is a positive fraction because both numbers have the same sign.

How do I know when to simplify the fraction?

Always look for common factors in the numerator and denominator. In this case, both 19 and 76 are divisible by 19, so $\frac{19}{76} = \frac{19}{19 \times 4} = \frac{1}{4}$ .

What if I wrote the answer as a decimal instead?

That's fine too! $\frac{1}{4} = 0.25$ . Both forms are correct, but fractions are often preferred in math problems unless specifically asked for decimals.

Can I flip the fraction and multiply instead?

No! Division is not the same as multiplying by the reciprocal when you have negative numbers. Stick to the division method and apply sign rules correctly.

How do I remember all the sign rules?

Same signs: positive ÷ positive = positive, negative ÷ negative = positive
Different signs: positive ÷ negative = negative, negative ÷ positive = negative

Think: "Same signs are friends (positive), different signs fight (negative)"

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