BECE Mathematics 2024 Paper

Method IThe sum of all fractions should be 1Fraction of oranges + fraction of mangoes + fraction of pears $=1$Fraction of pears $=1$ - (fraction of oranges + fraction of mangoes) Fraction of pears $=1- \left( \frac{2}{5} + \frac{6}{25} \right)$Fraction of pears $=1- \left( \frac{5 \times 2 + 1 \times 6}{25} \right)$Fraction of pears $=1- \left( \frac{10+6}{25} \right)$Fraction of pears $=1- \left( \frac{16}{25} \right)$Every whole number is being divided by 1$1 = \frac{1}{1}$ Fraction of pears $= \frac{1}{1} - \frac{16}{25}$Fraction of pears $= \frac{25 \times 1 - 1 \times 16}{25}$Fraction of pears $= \frac{25-16}{25}$Fraction of pears $= \frac{9}{25}$The whole fraction is $100 \%$If $1 = 100 \%$$\frac{9}{25} = \frac{9}{25} \times 100 \% \div 1$Any number/fraction divided by 1 is the same number/fraction$\frac{9}{25} = \frac{9}{25} \times 100 \%$ Note:1. 25 divides itself 1 time and 100, 4 times2. $9 \times 4 = 36$$\frac{9}{25} = 36 \%$$\therefore$ Percentage of pears $= 36 \%$ Method IIFind the percentage of oranges and mangoes and subtract the sum from $100 \%$Percentage of orangesThe whole fraction is 1 which represents $100 \%$ Percentage of orangesThe whole fraction is 1 which represents $100 \%$$\; \; \text{ If } \; 1 = 100 \%$$\; \; \frac{2}{5} = \frac{2}{5} \times 100 \% \div 1$ Note:1. Any number/fraction divided by 1 is the same number/fraction2. 5 divides itself 1 time and 100, 20 times3. $2 \times 20 = 40$$\frac{2}{5} = 40 \%$$\therefore$ Percentage of the fruits which are oranges $= 40 \%$Percentage of mangoesIf 1 = 100\%$\frac{6}{25} = \frac{6}{25} \times 100 \% \div 1$ Note:1. Any number/fraction divided by 1 is the same number/fraction2. 25 divides itself 1 time and 100, 4 times3. $6 \times 4 = 24$$\frac{6}{25} = 24 \%$$\therefore$ Percentage of the fruits which are mangoes $= 24 \%$Percentage of fruits which are pears $= 100 \% - (40 \% + 24 \%)$Percentage of fruits which are pears $= 100 \% - 64 \%$Percentage of fruits which are pears $= 36 \%$