Study Mathematics notes on Arithmetic and Ratio. Useful for revision, homework, and exam preparation in Zimbabwe.
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1(a) Simplify $\left(3 \frac{1}{2}-1 \frac{3}{5}\right)+1 \frac{2}{3}$.
Convert mixed numbers to improper fractions:
\[
3 \frac{1}{2}=\frac{7}{2}, \quad 1 \frac{3}{5}=\frac{8}{5}, \quad 1 \frac{2}{3}=\frac{5}{3}
\]
Subtract the second term from the first:
\[
\frac{7}{2}-\frac{8}{5}=\frac{35}{10}-\frac{16}{10}=\frac{19}{10}
\]
Add the third term:
\[
\frac{19}{10}+\frac{5}{3}=\frac{57}{30}+\frac{50}{30}=\frac{107}{30}=3 \frac{17}{30}
\]
Answer: $3 \frac{17}{30}$
1(b) Find the exact value of
(i) $10.03 \times 0.17$
\[
10.03 \times 0.17=1.7051
\]
Answer: 1.7051
(ii) $7.2 \div 0.018$
\[
7.2 \div 0.018=\frac{7.2}{0.018}=400
\]
Answer: 400
1(c) Three farmers share $\mathbf{1 2 0}$ hectares of land in the ratio $3: 4: 5$. Calculate the area of the largest piece of land.
Total parts:
\[
3+4+5=12
\]
Area of the largest piece:
\[
\frac{5}{12} \times 120=50 \text { hectares }
\]
Answer: 50 hectares
1(d) Find the Highest Common Factor (H.C.F) of