Q. \( -1\dfrac{2}{3} \div \left(-2\dfrac{1}{5}\right) = \dfrac{25}{33}\).

Q: What is the rule for dividing fractions?

Invert the divisor and multiply: \frac{a}{b}\div\frac{c}{d} = \frac{a}{b}\cdot\frac{d}{c}. Apply to the improper fractions after conversion.

Q: What is the final simplified result?

Compute: -\frac{5}{3}\div -\frac{11}{5} = -\frac{5}{3}\cdot -\frac{5}{11} = \frac{25}{33}..

Q: How can I check my answer with decimals?

Convert: \,-1\frac{2}{3} = -1.666\ldots,\; -2\frac{1}{5} = -2.2.\, Then \,-1.666\ldots\div -2.2 \approx 0.757575\ldots,\, which matches \,\frac{25}{33}\approx 0.7576.\,

Answer

Short solution

Convert both mixed numbers to improper fractions.

\(-1\frac{2}{3}=-\frac{5}{3}\)

\(-2\frac{1}{5}=-\frac{11}{5}\)

Now divide by multiplying by the reciprocal.

\(\left(-\frac{5}{3}\right)\div\left(-\frac{11}{5}\right)=\left(-\frac{5}{3}\right)\cdot\left(-\frac{5}{11}\right)\)

Multiply across.

\(\left(-\frac{5}{3}\right)\cdot\left(-\frac{5}{11}\right)=\frac{25}{33}\)

Final result: \(\frac{25}{33}\)

Detailed Explanation

Step-by-step solution

Convert the mixed numbers to improper fractions. For a negative mixed number, convert the positive mixed number first, then apply the negative sign.\(-1\frac{2}{3}=-\left(1+\frac{2}{3}\right)\)
\(-1\frac{2}{3}=-\frac{1\cdot3+2}{3}\)

\(-1\frac{2}{3}=-\frac{5}{3}\)

\(-2\frac{1}{5}=-\left(2+\frac{1}{5}\right)\)

\(-2\frac{1}{5}=-\frac{2\cdot5+1}{5}\)

\(-2\frac{1}{5}=-\frac{11}{5}\)
Rewrite the division using the improper fractions.\(-1\frac{2}{3}\div\left(-2\frac{1}{5}\right)=-\frac{5}{3}\div\left(-\frac{11}{5}\right)\)
Change division into multiplication by the reciprocal.The reciprocal of \(-\frac{11}{5}\) is \(-\frac{5}{11}\).
\(-\frac{5}{3}\div\left(-\frac{11}{5}\right)=-\frac{5}{3}\cdot\left(-\frac{5}{11}\right)\)
Multiply the numerators and denominators.\(-\frac{5}{3}\cdot\left(-\frac{5}{11}\right)=\frac{(-5)\cdot(-5)}{3\cdot11}\)
\(\frac{(-5)\cdot(-5)}{3\cdot11}=\frac{25}{33}\)
The fraction \(\frac{25}{33}\) is already in simplest form because \(25\) and \(33\) have no common factor greater than \(1\).
Final answer:\(\frac{25}{33}\)

See full solution

Struggling with math? Get instant AI homework help today!

AI helper

Arithmetic FAQs

How do I convert the mixed numbers to improper fractions?

Convert by multiplying the whole by the denominator and adding the numerator, keeping the sign: \( -1\frac{2}{3} = -\frac{5}{3},\quad -2\frac{1}{5} = -\frac{11}{5}.\).

What is the rule for dividing fractions?

Invert the divisor and multiply: \( \frac{a}{b}\div\frac{c}{d} = \frac{a}{b}\cdot\frac{d}{c}.\) Apply to the improper fractions after conversion.

How do I handle the negative signs?

Negative divided by a negative is positive, so the result will be positive here: \( -\frac{5}{3}\div -\frac{11}{5}\) gives a positive product.

Can I simplify before multiplying?

Yes — cancel common factors between any numerator and any denominator before multiplying to keep numbers small. In this case \( -\frac{5}{3}\cdot -\frac{5}{11}\) has no cross common factors, so no cancellation applies.

What is the final simplified result?

Compute: \( -\frac{5}{3}\div -\frac{11}{5} = -\frac{5}{3}\cdot -\frac{5}{11} = \frac{25}{33}.\).

Should I convert the final answer to a mixed number?

How can I check my answer with decimals?

Convert: \(\,-1\frac{2}{3} = -1.666\ldots,\; -2\frac{1}{5} = -2.2.\,\) Then \(\,-1.666\ldots\div -2.2 \approx 0.757575\ldots,\)\, which matches \(\,\frac{25}{33}\approx 0.7576.\,\)

What are common mistakes to avoid?

Don’t forget to convert mixed numbers, invert the divisor, or handle signs. Also avoid cancelling terms incorrectly (only cancel factors across numerators and denominators).

AI tools for finance and economics.
Accounting help is also here.

252,312+ customers tried
Analytical, General, Biochemistry, etc.

Finance homework help Economics homework help Accounting homework help