Which expression is equivalent to $$ -4 \frac{1}{5}+5 \frac{1}{6} $$ ?

Question

UpStudy AI · Accepted Answer

To find an expression equivalent to $$ -4 \frac{1}{5} + 5 \frac{1}{6} $$, let's follow these steps:

1. **Convert Mixed Numbers to Improper Fractions:**

- $$ -4 \frac{1}{5} = -\left(4 \times 5 + 1\right)/5 = -\frac{21}{5} $$
   - $$ 5 \frac{1}{6} = \frac{5 \times 6 + 1}{6} = \frac{31}{6} $$

2. **Add the Improper Fractions:**

$$
   -\frac{21}{5} + \frac{31}{6}
   $$

3. **Find a Common Denominator:**

The least common denominator (LCD) of 5 and 6 is 30.

- $$ -\frac{21}{5} = -\frac{21 \times 6}{5 \times 6} = -\frac{126}{30} $$
   - $$ \frac{31}{6} = \frac{31 \times 5}{6 \times 5} = \frac{155}{30} $$

4. **Combine the Fractions:**

$$
   -\frac{126}{30} + \frac{155}{30} = \frac{-126 + 155}{30} = \frac{29}{30}
   $$

So, the expression $$ -4 \frac{1}{5} + 5 \frac{1}{6} $$ is equivalent to:

$$
\frac{29}{30}
$$

**Final Answer:** An equivalent expression is the fraction 29⁄30.
An equivalent expression is $$ \frac{29}{30} $$.

Which expression is equivalent to \( -4 \frac{1}{5}+5 \frac{1}{6} \) ?