Question

Find the ratio 15kg to 210g.

Answer 1

Hint: Use the fact that 1 kg = 1000g. Hence convert 15kg in grams. Use the fact that the ratio a:b can be converted in lowest terms by dividing a and b by HCF(a,b). Hence find the given ratio in lowest terms. Use Euclid’s division lemma to find the HCF of a and b.

Complete step-by-step answer:
We know that 1kg = 1000g
Hence 15kg = 15000g.
Hence the ratio 15kg to 210g is in proportion with 15000g to 210g
Finding HCF of 15000 to 210:
Euclid’s division algorithm:
Finding HCF using Euclid’s division lemma is an algorithmic process. We start by setting the two variables p and q equal to the given numbers, with q being equal to the smaller one. Then we repeat the following process:
Apply Euclid’s division lemma to the numbers p and q
i.e. p = aq+r where $0 \le r < q, a\in \mathbb{Z}$
if r = 0 then stop the process and we have HCF = q
Otherwise set p = q and q =r and repeat the process.
We start by taking p = 15000 and q = 210
$15000=210\times 71+90$ Here r = 90.
So we take p = 210 and q = 90.
Applying Euclid’s division lemma, we get
$210=90\,\times 2+30$
Here r = 30.
So we take p = 90 and q = 30
Applying Euclid’s division lemma, we get
$90=30\times 3+0$
Here r = 0. So HCF = q = 30.
Hence we have HCF(15000,210) = 30
Dividing 15000 by 30, we get
$\dfrac{15000}{30}=500$
Dividing 210 by 30, we get
$\dfrac{210}{30}=7$
Hence we have 15000:210:: 500:7
Hence the ratio of 15kg to 210g is 500:7

Note: [1] It is very important to keep the units of the terms the same. Many students forget to change the units and hence end up with an incorrect answer.