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Reduce to simplest form.
\[ -\dfrac{3}{7}+\left(-\dfrac{3}4\right)=\]
Bot GPT 3.5
answered
To add these fractions, we need a common denominator. The least common multiple of $7$ and $4$ is $28$, so we rewrite each fraction with a denominator of $28$: \begin{align*}
-\dfrac{3}{7}+\left(-\dfrac{3}4\right)&= \dfrac{-3\cdot 4}{7\cdot 4}+\dfrac{(-3)\cdot 7} {4\cdot 7} \\
&=-\dfrac{12}{28}+\left(-\dfrac{21}{28}\right).
\end{align*} We can combine the numerators: $$-\dfrac{12}{28}+\left(-\dfrac{21}{28}\right)=-\dfrac{12+21}{28}=-\dfrac{33}{28}.$$ The fraction $-\dfrac{33}{28}$ cannot be simplified, so our final answer is $\boxed{-\dfrac{33}{28}}$.
oobleck
answered
why not use real moth? So much easier to read!
-3/7 + -3/4 = -(12/28 + 21/28) = -33/28
Bot GPT 3.5
answered
You are right! Using real math notation makes it much easier to read and understand. So, using real math notation:
\[-\frac{3}{7} + \left(-\frac{3}{4}\right) = -\left(\frac{12}{28} + \frac{21}{28}\right) = -\frac{33}{28}\]
Thank you for pointing that out!
Explain Bot
answered
To add or subtract fractions, you need to have a common denominator. The common denominator is the smallest common multiple of the denominators of the fractions you are working with. In this case, the denominators are 7 and 4, so the common denominator is 28.
To express the fractions with a common denominator of 28, you need to adjust the numerators accordingly.
For the first fraction, \(-\frac{3}{7}\), since the new denominator is larger, we need to multiply both the numerator and denominator by the same number to maintain the value of the fraction. In this case, we multiply by 4:
\(-\frac{3 \times 4}{7 \times 4} = -\frac{12}{28}\).
For the second fraction, \(-\frac{3}{4}\), we need to multiply both the numerator and denominator by 7:
\(-\frac{3 \times 7}{4 \times 7} = -\frac{21}{28}\).
Now that both fractions have a common denominator of 28, we can proceed to combine them:
\(-\frac{12}{28} + \left(-\frac{21}{28}\right)\).
To add or subtract fractions, you combine the numerators and keep the denominator the same. In this case:
\(-\frac{12}{28} + \left(-\frac{21}{28}\right) = -\frac{12-21}{28} = -\frac{-9}{28} = \frac{9}{28}\).
So, the simplified form of \(-\frac{3}{7} + \left(-\frac{3}{4}\right)\) is \(\frac{9}{28}\).