Questions: Add. 2/3 + 4/63 + 5/7 2/3 + 4/63 + 5/7 = (Type a whole number or a simplified fraction.)

Solution Steps

To add the fractions \(\frac{2}{3}\), \(\frac{4}{63}\), and \(\frac{5}{7}\), we need to find a common denominator. The least common multiple (LCM) of the denominators 3, 63, and 7 will be used as the common denominator. Once the fractions are expressed with this common denominator, we can add the numerators and simplify the result if necessary.

To add the fractions \( \frac{2}{3} \), \( \frac{4}{63} \), and \( \frac{5}{7} \), we first determine the least common multiple (LCM) of the denominators 3, 63, and 7. The LCM is found to be 63.

Next, we convert each fraction to have the common denominator of 63:

• For \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 21}{3 \times 21} = \frac{42}{63} \]
• For \( \frac{4}{63} \): \[ \frac{4}{63} = \frac{4}{63} \]
• For \( \frac{5}{7} \): \[ \frac{5}{7} = \frac{5 \times 9}{7 \times 9} = \frac{45}{63} \]

Now, we add the numerators of the converted fractions: \[ \frac{42}{63} + \frac{4}{63} + \frac{45}{63} = \frac{42 + 4 + 45}{63} = \frac{91}{63} \]

The fraction \( \frac{91}{63} \) can be simplified by finding the greatest common divisor (GCD) of 91 and 63, which is 7: \[ \frac{91 \div 7}{63 \div 7} = \frac{13}{9} \]

Final Answer