Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.

Question

1/4=

5/12=

1/4+ 5/12=__ =

Answer 1

To add the fractions \( \frac{1}{4} \) and \( \frac{5}{12} \) together, we first need to find the Least Common Denominator (LCD) of the denominators 4 and 12.

Step 1: Find the LCD

• The denominators are 4 and 12.
• The multiples of 4 are: 4, 8, 12, 16, ...
• The multiples of 12 are: 12, 24, 36, ...
• The smallest common multiple is 12.

So, the LCD of 4 and 12 is 12.

Step 2: Convert each fraction to an equivalent fraction with the LCD

1. Convert \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]

2. Convert \( \frac{5}{12} \):

   • This fraction already has the denominator of 12, so it remains: \[ \frac{5}{12} \]

Step 3: Add the equivalent fractions

Now we can add the converted fractions: \[ \frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12} \]

Step 4: Reduce the final sum

Now, we reduce \( \frac{8}{12} \):

• The greatest common divisor (GCD) of 8 and 12 is 4.
• Divide both the numerator and denominator by 4: \[ \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \]

Final Result

The sum of \( \frac{1}{4} + \frac{5}{12} \) is: \[ \frac{2}{3} \]

So, the final answer is: \[ 1/4 + 5/12 = \frac{2}{3} \]