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Sagot :
Of course! Let's break down the problem step-by-step:
### Part (i) What parts of the cake did Pratik give to Bishwant?
1. Determine the total fraction of the cake eaten by Pratik, his mother, and his father:
- Pratik ate [tex]\(\frac{3}{10}\)[/tex] of the cake.
- Pratik's mother ate [tex]\(\frac{1}{4}\)[/tex] of the cake.
- Pratik's father ate [tex]\(\frac{1}{5}\)[/tex] of the cake.
To combine these fractions, we need to find a common denominator. The denominators are 10, 4, and 5. The least common multiple (LCM) of 10, 4, and 5 is 20.
2. Convert each fraction to have the common denominator of 20:
- [tex]\(\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}\)[/tex]
- [tex]\(\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}\)[/tex]
- [tex]\(\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}\)[/tex]
3. Sum the fractions to find the total amount of cake eaten:
- Total eaten = [tex]\(\frac{6}{20} + \frac{5}{20} + \frac{4}{20} = \frac{15}{20}\)[/tex]
4. Calculate the parts of the cake given to Bishwant:
- The entire cake is [tex]\(1\)[/tex], so the parts given to Bishwant is [tex]\(1 - \frac{15}{20}\)[/tex].
To simplify this:
- [tex]\(\frac{15}{20} = 0.75\)[/tex]
- Parts given to Bishwant = [tex]\(1 - 0.75 = 0.25\)[/tex].
Therefore, Pratik gave Bishwant [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex] parts of the cake.
### Part (ii) Who ate the greatest parts of the cake?
1. Compare the parts of the cake eaten by Pratik, his mother, and his father:
- Pratik: [tex]\(\frac{3}{10}\)[/tex] or [tex]\(0.30\)[/tex]
- Mother: [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex]
- Father: [tex]\(\frac{1}{5}\)[/tex] or [tex]\(0.20\)[/tex]
2. Determine the greatest part:
- Pratik's [tex]\(0.30\)[/tex] is greater than Mother's [tex]\(0.25\)[/tex] and Father's [tex]\(0.20\)[/tex].
Therefore, Pratik ate the greatest parts of the cake, which is [tex]\(\frac{3}{10}\)[/tex] or [tex]\(0.30\)[/tex].
### Summary:
(i) Pratik gave Bishwant [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex] parts of the cake.
(ii) Pratik ate the greatest parts of the cake, [tex]\(\frac{3}{10}\)[/tex] or [tex]\(0.30\)[/tex].
### Part (i) What parts of the cake did Pratik give to Bishwant?
1. Determine the total fraction of the cake eaten by Pratik, his mother, and his father:
- Pratik ate [tex]\(\frac{3}{10}\)[/tex] of the cake.
- Pratik's mother ate [tex]\(\frac{1}{4}\)[/tex] of the cake.
- Pratik's father ate [tex]\(\frac{1}{5}\)[/tex] of the cake.
To combine these fractions, we need to find a common denominator. The denominators are 10, 4, and 5. The least common multiple (LCM) of 10, 4, and 5 is 20.
2. Convert each fraction to have the common denominator of 20:
- [tex]\(\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}\)[/tex]
- [tex]\(\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}\)[/tex]
- [tex]\(\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}\)[/tex]
3. Sum the fractions to find the total amount of cake eaten:
- Total eaten = [tex]\(\frac{6}{20} + \frac{5}{20} + \frac{4}{20} = \frac{15}{20}\)[/tex]
4. Calculate the parts of the cake given to Bishwant:
- The entire cake is [tex]\(1\)[/tex], so the parts given to Bishwant is [tex]\(1 - \frac{15}{20}\)[/tex].
To simplify this:
- [tex]\(\frac{15}{20} = 0.75\)[/tex]
- Parts given to Bishwant = [tex]\(1 - 0.75 = 0.25\)[/tex].
Therefore, Pratik gave Bishwant [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex] parts of the cake.
### Part (ii) Who ate the greatest parts of the cake?
1. Compare the parts of the cake eaten by Pratik, his mother, and his father:
- Pratik: [tex]\(\frac{3}{10}\)[/tex] or [tex]\(0.30\)[/tex]
- Mother: [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex]
- Father: [tex]\(\frac{1}{5}\)[/tex] or [tex]\(0.20\)[/tex]
2. Determine the greatest part:
- Pratik's [tex]\(0.30\)[/tex] is greater than Mother's [tex]\(0.25\)[/tex] and Father's [tex]\(0.20\)[/tex].
Therefore, Pratik ate the greatest parts of the cake, which is [tex]\(\frac{3}{10}\)[/tex] or [tex]\(0.30\)[/tex].
### Summary:
(i) Pratik gave Bishwant [tex]\(\frac{1}{4}\)[/tex] or [tex]\(0.25\)[/tex] parts of the cake.
(ii) Pratik ate the greatest parts of the cake, [tex]\(\frac{3}{10}\)[/tex] or [tex]\(0.30\)[/tex].
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