Sure, let's solve these step by step!
### Part 11 a)
We are asked to find Elizabeth's share of the total pocket money when the total is £4.80.
Elizabeth's share is given as [tex]\(\frac{3}{8}\)[/tex] of the total.
1. Calculate [tex]\(\frac{3}{8}\)[/tex] of £4.80:
[tex]\[
\text{Elizabeth's share} = \frac{3}{8} \times 4.80
\][/tex]
2. Performing the multiplication:
[tex]\[
\text{Elizabeth's share} = \frac{3 \times 4.80}{8} = \frac{14.40}{8} = 1.80
\][/tex]
Thus, Elizabeth's share is £1.80.
### Part 11 b)
Next, we need to find the fraction of the total that Margaret receives each week. To do so, we must first determine the fractions of the total amount received by Angelica and Elizabeth, and then calculate the remaining fraction for Margaret.
Angelica's share is [tex]\(\frac{3}{10}\)[/tex] and Elizabeth's share is [tex]\(\frac{3}{8}\)[/tex]. We need to add these fractions together and subtract from 1.
1. First, find a common denominator for the two fractions (the least common multiple of 10 and 8, which is 40):
2. Convert [tex]\(\frac{3}{10}\)[/tex] to a fraction with a denominator of 40:
[tex]\[
\frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40}
\][/tex]
3. Convert [tex]\(\frac{3}{8}\)[/tex] to a fraction with a denominator of 40:
[tex]\[
\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}
\][/tex]
4. Add these fractions together:
[tex]\[
\frac{12}{40} + \frac{15}{40} = \frac{12 + 15}{40} = \frac{27}{40}
\][/tex]
5. Subtract this sum from 1 to find Margaret's share:
[tex]\[
\text{Margaret's share} = 1 - \frac{27}{40}
\][/tex]
Converting 1 to a fraction with the denominator 40:
[tex]\[
1 = \frac{40}{40}
\][/tex]
6. Subtract the fractions:
[tex]\[
\frac{40}{40} - \frac{27}{40} = \frac{40 - 27}{40} = \frac{13}{40}
\][/tex]
Thus, the fraction of the total that Margaret receives each week is [tex]\(\frac{13}{40}\)[/tex].
