Question

find the ratio 15kg 100g to 210kg​

Answer 1

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Answer 2

• Find the ratio 15kg to 210g.



Answer

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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

• Use Euclid's division lemma to find the HCF of a and b. Hence 15kg = 15000g. Otherwise set p = q and q =r and repeat the process. 15000=210×71+90 Here r = 90.
• Step-by-step explanation:

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