Part B Find the sum of 1/6 and 5/8. Enter the numerator followed by the denominator separated by a comma. View Available Hint(s)
The Correct Answer and Explanation is:
To find the sum of 16\frac{1}{6}61 and 58\frac{5}{8}85, we follow these steps:
Step 1: Find a common denominator
The denominators are 6 and 8. The least common denominator (LCD) of 6 and 8 is 24.
Step 2: Convert the fractions to have the common denominator
Convert both fractions to equivalent fractions with denominator 24:
- 16=1×46×4=424\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}61=6×41×4=244
- 58=5×38×3=1524\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}85=8×35×3=2415
Step 3: Add the fractions
Now add the numerators:424+1524=1924\frac{4}{24} + \frac{15}{24} = \frac{19}{24}244+2415=2419
✅ Final Answer: 19,24
Explanation
Adding fractions is a fundamental operation in arithmetic and algebra. When two fractions have different denominators, you cannot add them directly. Instead, you must first find a common denominator so that the fractions represent parts of the same whole. This is similar to needing the same type of unit before combining quantities (like you can’t directly add 3 inches and 2 centimeters without converting one).
In this problem, the fractions are 16\frac{1}{6}61 and 58\frac{5}{8}85. Their denominators are different, so we need to find a least common denominator (LCD), which is the smallest number that both denominators divide evenly into. For 6 and 8, the smallest common multiple is 24. This becomes our new common denominator.
Once the common denominator is determined, each fraction is rewritten with that denominator. To convert a fraction to an equivalent fraction with a new denominator, multiply both its numerator and denominator by the same number. This maintains the value of the fraction while allowing it to be compared or combined with others.
So, 16\frac{1}{6}61 becomes 424\frac{4}{24}244 and 58\frac{5}{8}85 becomes 1524\frac{15}{24}2415. Now that both fractions have the same denominator, we simply add the numerators and keep the denominator: 4+15=194 + 15 = 194+15=19, giving the final answer 1924\frac{19}{24}2419.
This fraction is already in its simplest form, since 19 and 24 have no common factors other than 1. Therefore, the sum of 16\frac{1}{6}61 and 58\frac{5}{8}85 is 1924\frac{19}{24}2419.
