Working with Fractions | IT

Question 5

Context: If we assume 1 gold dinar = 12 silver drammas, 1 silver dramma = 4 copper panas, 1 copper pana = 6 mashakas, and 1 pana = 30 cowrie shells,

Given: 1 copper pana = $\dfrac{1}{48}$ gold dinar $\left(\dfrac{1}{12} \times \dfrac{1}{4}\right)$

Fill in the blanks:

(i) 1 cowrie shell = ______ copper panas

(ii) 1 cowrie shell = ______ gold dinar.

Solution

Understand the Question

We are given conversion relationships between different units of currency:
- $1 \text{ copper pana} = 30 \text{ cowrie shells} \implies 1 \text{ cowrie shell} = \dfrac{1}{30} \text{ copper pana}$
- $1 \text{ copper pana} = \dfrac{1}{48} \text{ gold dinar}$
To convert cowrie shells into gold dinars, substitute the value of $1 \text{ copper pana}$ in terms of gold dinars into the fraction for $1 \text{ cowrie shell}$ .

(i) 1 cowrie shell = ______ copper panas

Step 1 · Convert Cowrie Shells to Copper Panas

Given $1 \text{ copper pana} = 30 \text{ cowrie shells}$ Diagram 1

Therefore $1 \text{ cowrie shell} = \dfrac{1}{30} \text{ copper panas}$

Answer

(i) $\dfrac{1}{30}$

(ii) 1 cowrie shell = ______ gold dinar.

Step 1 · Convert Cowrie Shells to Gold Dinars

From part (i), $1 \text{ cowrie shell} = \dfrac{1}{30} \text{ copper panas}$ .

Given that $1 \text{ copper pana} = \dfrac{1}{48} \text{ gold dinar}$ , substitute this into the expression:

\begin{aligned} 1 \text{ cowrie shell} &= \dfrac{1}{30} \times \left(\dfrac{1}{48} \text{ gold dinar}\right) \\[0.6em] &= \dfrac{1 \times 1}{30 \times 48} \text{ gold dinar} \\[0.6em] &= \dfrac{1}{1440} \text{ gold dinar} \end{aligned}

Answer

(ii) $\dfrac{1}{1440}$

Common Mistakes

Multiplying Instead of Dividing: Confusing the conversion direction by writing $1 \text{ cowrie shell} = 30 \text{ copper panas}$ instead of the reciprocal $\dfrac{1}{30}$ .
Multiplication Errors in the Denominator: Making an arithmetic mistake when calculating $30 \times 48 = 1440$ .

Question 5

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