Questions: Divide. Simplify, if necessary. -5/22 ÷ 25/77 -5/22 ÷ 25/77 =

Transcript text: Divide. Simplify, if necessary. \[ -\frac{5}{22} \div \frac{25}{77} \] $-\frac{5}{22} \div \frac{25}{77}=$ $\square$

Solution

Solution Steps

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction if possible.

Step 1: Set Up the Division of Fractions

We start with the expression: \[ -\frac{5}{22} \div \frac{25}{77} \] To divide by a fraction, we multiply by its reciprocal: \[ -\frac{5}{22} \times \frac{77}{25} \]

Step 2: Multiply the Fractions

Now we multiply the numerators and the denominators: \[ -\frac{5 \times 77}{22 \times 25} = -\frac{385}{550} \]

Step 3: Simplify the Result

Next, we simplify the fraction $-\frac{385}{550}$. The greatest common divisor (GCD) of 385 and 550 is 55. Thus, we divide both the numerator and the denominator by 55: \[ -\frac{385 \div 55}{550 \div 55} = -\frac{7}{10} \]