Bot GPT 4-o mini To find the sum of \( \frac{3}{6} + \frac{8}{9} \) and express it as a benchmark fraction, we first need to simplify \( \frac{3}{6} \):
\[ \frac{3}{6} = \frac{1}{2} \]
Now we need to add \( \frac{1}{2} + \frac{8}{9} \). To do this, we will find a common denominator. The least common multiple of 2 and 9 is 18.
Next, we convert both fractions to have a denominator of 18:
\[ \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \]
\[ \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18} \]
Now we can add the two fractions:
\[ \frac{9}{18} + \frac{16}{18} = \frac{9 + 16}{18} = \frac{25}{18} \]
Finally, we convert \( \frac{25}{18} \) to a mixed number:
\[ \frac{25}{18} = 1 \frac{7}{18} \]
The sum of \( \frac{3}{6} + \frac{8}{9} \) is \( \frac{25}{18} \) or \( 1 \frac{7}{18} \) when expressed as a mixed number. To express this as a benchmark fraction, we note that the whole number part (1) suggests it's just above \( 1 \).
Thus, \( \frac{25}{18} \) does not fall exactly on common benchmark fractions like \(\frac{1}{2}\), \(\frac{1}{4}\), or \(\frac{3}{4}\), etc. However, you can think of \( 1 \frac{7}{18} \) as slightly below \( 1 \frac{1}{2} \) since \( \frac{1}{2} = \frac{9}{18} \).
In conclusion, the sum of \( \frac{3}{6} + \frac{8}{9} \) is \( \frac{25}{18} \), which is a bit more than 1 but less than \( 1 \frac{1}{2} \).
1 answer