Give the ratio $16 t o 40$ in the simplest form.

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Solution

Convert ratio in simplest form:
We can write $16 : 40$ as $\frac{16}{40}$ .
HCF of numerator $16$ and denominator $40$
By the method of prime factorisation,
$16 = 2^{4} \times 1$
$40 = 2^{3} \times 5 \times 1$
$H C F (16, 40) = 2^{3} \times 1 = 8 \times 1 = 8$
Divide both the numerator and denominator by HCF
$=$ $\frac{16 \div 8}{40 \div 8}$
$=$ $\frac{2}{5}$
Therefore, $16 : 40$ can be expressed in simplest form as $2 : 5$ .

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