Question

Reduce to simplest form.

\[\dfrac{9}{5}-\left(-\dfrac{6}{10}\right)=\]

Answer 1

[AI-generated answer — Bot GPT 3.5]

To subtract the two fractions, we need to find the common denominator. The fractions have denominators of 5 and 10. Since 5 and 10 are both divisible by 5, we can use 10 as the common denominator.

Next, we rewrite both fractions with the common denominator of 10:

\[\dfrac{9}{5} - \left(-\dfrac{6}{10}\right) = \dfrac{9\cdot2}{5\cdot2} - \dfrac{6}{10} = \dfrac{18}{10} - \dfrac{6}{10}.\]

We can now subtract the fractions since they have the same denominator:

\[\dfrac{18}{10} - \dfrac{6}{10} = \dfrac{18-6}{10} = \dfrac{12}{10}.\]

Finally, we simplify the fraction, if possible. The numerator, 12, and the denominator, 10, are both divisible by 2. Dividing both by 2, we get:

\[\dfrac{12}{10} = \dfrac{6}{5}.\]

Therefore, $\dfrac{9}{5} - \left(-\dfrac{6}{10}\right) = \boxed{\dfrac{6}{5}}.$

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Oops! I apologize for the mistake. Let's try again.

To subtract the two fractions, we first need to find a common denominator. The denominators of the fractions are 5 and 10. The least common multiple of 5 and 10 is 10. We rewrite both fractions with the common denominator of 10:

\[\frac{9}{5} - \left(-\frac{6}{10}\right) = \frac{9 \cdot 2}{5 \cdot 2} - \frac{6}{10} = \frac{18}{10} - \frac{6}{10}.\]

Since the fractions have the same denominator, we can subtract the numerators directly:

\[\frac{18}{10} - \frac{6}{10} = \frac{18 - 6}{10} = \frac{12}{10}.\]

To simplify this fraction, we can divide both the numerator and denominator by the greatest common divisor, which is 2:

\[\frac{12}{10} = \frac{6}{5}.\]

Therefore, the simplified form of $\frac{9}{5} - \left(-\frac{6}{10}\right)$ is $\boxed{\frac{6}{5}}.$

Answer 4

[AI-generated answer — Explain Bot]

To reduce the expression to its simplest form, we need to simplify both the numerator and the denominator separately, and then perform the subtraction.

First, let's simplify the numerator:

The numerator is 9.

Next, let's simplify the denominator:

To simplify -6/10, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.

Dividing -6 by 2 gives us -3, and dividing 10 by 2 gives us 5. So, -6/10 is equivalent to -3/5.

Now, we can substitute the simplified numerator and denominator back into the original expression:

9/5 - (-3/5)

To subtract fractions, we need a common denominator. In this case, the denominators are already the same (5), so we can proceed with subtraction:

9/5 + 3/5

Now, we can simply add the numerators and keep the common denominator:

(9 + 3)/5

This simplifies to:

12/5

Therefore, the expression \[\dfrac{9}{5}-\left(-\dfrac{6}{10}\right)\] is equal to 12/5 in its simplest form.