To solve the question of how much less Jose's sisters ate than his dad when considering fractional parts of the cake, we need to take the following steps:
1. Identify the fractions involved:
- Dad ate [tex]\(\frac{1}{8}\)[/tex] of the cake.
- Sisters ate [tex]\(\frac{2}{3}\)[/tex] of the cake.
2. Find a common denominator:
To compare these fractions, they must have a common denominator. The denominators are 8 and 3. The least common denominator (LCD) of these two numbers is found by looking for the least common multiple (LCM).
- The LCM of 8 and 3 is 24.
So, the least common denominator is 24.
3. Convert each fraction to the common denominator:
- Convert [tex]\(\frac{1}{8}\)[/tex] to a fraction with denominator 24:
[tex]\[
\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}
\][/tex]
- Convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with denominator 24:
[tex]\[
\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}
\][/tex]
4. Calculate the difference:
Now that both fractions have the same denominator, we can find out how much less the dad ate compared to the sisters.
[tex]\[
\frac{16}{24} - \frac{3}{24} = \frac{16 - 3}{24} = \frac{13}{24}
\][/tex]
5. Convert the fractional difference into a decimal, if needed:
- In decimal form, [tex]\(\frac{13}{24} = 0.5416666666666666\)[/tex].
Thus, Jose’s sisters ate approximately [tex]\(0.542\)[/tex] or exactly [tex]\(\frac{13}{24}\)[/tex] (which is 0.5416666666666666) more of the cake than his dad did.
