Question

Find the ratio in its simplest form:
7 kg to 700 grams.

Answer 1

Hint: To solve this problem we need to know that the quantity 1 kg is equal to 1000 grams and also that the ratio a : b can also be expressed as $\dfrac{a}{b}$. Now we have to find the ratio 7 kg to 700 grams so, we will first convert 7 kgs to grams using the formula 1 kg = 1000 grams then after we will express it in the ratio form and we can apply all that operations on a : b which we can apply on $\dfrac{a}{b}$.

Complete step-by-step answer:
First we need to know that we can apply all those formulas or operations on a : b which we can apply on $\dfrac{a}{b}$.
Now we have to simplify the ratio 7 kg to 700 grams but before that we should convert 7 kg to grams using the condition that 1 kg = 1000 grams, so we get
1 kg = 1000 grams
Multiplying by 7 on both sides, we get
7 kg = 7000 grams
Now we will express it in ratio form and then after in fractional form we get, \[=7000\,grams:700\,grams\]
$=\dfrac{7000}{700}\,grams$
Now dividing both numerator and denominator by 700 we get
$=\dfrac{10}{1}\,grams$
Expressing the above expression back in ratio form we get,
$=10:1\,$
Hence the simplest ratio in which 7 kg and 700 grams can be expressed is 10 : 1.

Note: Usually these kinds of questions are asked in subjective exams so for that you have to show every step that you use in order to solve the question. And also some students do not express the fractional form back to the ratio form but his step is important so you need to be careful about that. There is another possibility where students can convert into terms of kg and then find the ratio, either way the ratio would remain the same.