Class Notes NCERT Solutions for CBSE Students
Ratio in the Lowest Terms
Of the three equal ratios 3 : 5, 6 : 10 and 9 : 15, 3 : 5 is in the lowest terms or simplest form.
We can find the simplest form of a ratio by reducing it to its lowest term just like we would do it in a fraction.
CHECKPOINT: A ratio is said to be its lowest form when the terms have an HCF of 1.
Preetam does yoga for 45 minutes every morning. His friend Subhash does yoga for 1 hour every morning.
The ration of the time that Preetam does yoga to the time that Subhash does yoga is not 45 : 1 as we cannot compare different units.
We convert 1 hour to 60 minutes and than the ratio is correctly written as 45 : 60.
45 ÷ 5 / 60 ÷ 5 = 9/12 = 9 ÷ 3 / 12 ÷ 3 = 3/4
In the lowest terms we can say that the ratio is 3 : 4. That is, for every 3 minutes that is, for every 3 minutes that Preetam does yoga, Subhash does 4 minutes of yoga.
CHECKPOINT: Quantities that are being compared should be in the same units, but we do not use unit while writing ratios.
Using Ratio
(a) Zaheeda and her friend Smita brought 35 pastries for the class party. If they had brought it in the ratio of 3 : 4, how many pastries did each bring?
Ratio of Zaheeda’s pastries to Smita’s pastries 3 : 4
Ration of Zaheeda’s pastries to all the pastries is 3 : 7 or 3/7
Ratio of Smita’s pastries to Zaheeda’s Pastries 4 : 3
Ratio of Smita’s pastries to all pasties is 4 : 7 or 4/7
There are 35 pastries in all.
So, Zaheeda brought 3/7 × 35 = 15 pastries.
And Smita brought 4/7 × 35 = 20 pastries.
(b) Sushmita and her brought Amar got new notebooks for the new school term in the ratio of 2 : 3. If Sushmita got new notebooks, how many notebooks did Amar get?
The ratio of Sushmita’s notebooks to Amar’s notebooks is 2 : 3 or 2/3
2 : 3 = 12 : ?
So, 2/3 = 12/?
2 × 6 / 3 × 6 = 12/18
Amar got 18 new notebooks.
