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Calculate the least share for problem 19c, and the HCF, LCM, and their product for problem 20a.
Mathematics
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15 stepsHere are the solutions for problems 19c, 20a, 20b, and 20c.
:
Find the total number of parts in the ratio.
Calculate the value of one ratio part by dividing the total amount by the total parts.
The least share corresponds to the smallest number in the ratio, which is 3.
Multiply the value per part by 3.
The least share is .
:
Find the prime factorization of each number
- $9 = 3^2$ - $12 = 2^2 \times 3$ - $18 = 2 \times 3^2$Find the HCF (Highest Common Factor).
This is the product of the lowest powers of common prime factors. The only common prime factor is 3, and its lowest power is .
Find the LCM (Least Common Multiple).
This is the product of the highest powers of all prime factors present. - Highest power of 2 is . - Highest power of 3 is .
Find the product of the LCM and HCF
The product of the LCM and HCF is .
:
Identify the given values for simple interest
- Principal (P) = ₦30,000.00 - Time (T) = $3\frac{1}{2}$ years = 3.5 years - Rate (R) = 5% per annum = 0.05Use the formula for simple interest
Substitute the values into the formula
Perform the multiplication in the numerator
Perform the division
The simple interest is .
:
Calculate the loss amount.
Calculate the loss percentage using the formula
Substitute the values and calculate
The loss percent is .
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