Question

4.
Find the ratios of the following in their simplest form.
(1)
45 seconds to 30 minutes
25 minutes to 55 minutes
(1)
4 m. 20 cm to 8 m. 40 cm (iv) 5 litres to 0.75 litre
(v) 4 weeks to 4 days
(vi) 5 dozen to 2 scores (1 scor​

Answer 1

Answer:

• 45 seconds to 30 minutes = 1 :  40
• 25 minutes to 55 minutes = 5 : 11
• 4 m 20 cm to 8 m 40 cm = 1 : 2
• 5 litres to 0.75 litres = 20 : 3
• 4 weeks to 4 days = 7 : 1
• 5 dozen to 2 score = 3 : 2

Step-by-step explanation:

i) 45 seconds to 30 minutes

We know that to write ratio we need to have both the quantities in same unit. So here, we first have to convert 30 minutes to seconds.

As we know that:

• 1 minute = 60 seconds

Therefore,

• 30 minutes = 30 × 60 = 1800 seconds

Now,

$\sf{\longrightarrow 45:1800}$

$\sf{\longrightarrow \dfrac{45}{1800}}$

$\sf{\longrightarrow \dfrac{45\div45}{1800\div45}}$

$\sf{\longrightarrow \dfrac{1}{40}}$

$\sf{\longrightarrow 1:40}$

ii) 25 minutes to 55 minutes

Here, we don't need to convert the quantities here as the units are same.

Now,

$\sf{\longrightarrow 25:55}$

$\sf{\longrightarrow \dfrac{25}{55}}$

$\sf{\longrightarrow \dfrac{25\div5}{55\div5}}$

$\sf{\longrightarrow \dfrac{5}{11}}$

$\sf{\longrightarrow 5:11}$

iii) 4 m 20 cm to 8 m 40 cm

Here, we need to convert both the quantities from metre to centimetre.

As we know that,

• 1 m = 100 cm

Therefore,

• 4 m 20 cm = (100 × 4) + 20 = 400 + 20 = 420 cm
• 8 m 40 cm = (100 × 8) + 40 = 800 + 40 = 840 cm

Now,

$\sf{\longrightarrow 420:840}$

$\sf{\longrightarrow \dfrac{420}{840}}$

$\sf{\longrightarrow \dfrac{420\div420}{840\div420}}$

$\sf{\longrightarrow \dfrac{1}{2}}$

$\sf{\longrightarrow 1:2}$

iv) 5 litres to 0.75 litres

Here, we have to convert both the quantities from litre to millilitre.

As we know that,

• 1 litre = 1000 millilitre

Therefore,

• 5 litres = 1000 × 5 = 5000 millilitres
• 0.75 litres = 1000 × 0.75 = 750 millilitres

Now,

$\sf{\longrightarrow 5000:750}$

$\sf{\longrightarrow \dfrac{5000}{750}}$

$\sf{\longrightarrow \dfrac{5000\div250}{750\div250}}$

$\sf{\longrightarrow \dfrac{20}{3}}$

$\sf{\longrightarrow 20:3}$

v) 4 weeks to 4 days

Here, we need to convert 4 weeks to days.

As we know that:

• 1 week = 7 days

Therefore,

• 4 weeks = 4 × 7 = 28 days

Now,

$\sf{\longrightarrow 28:4}$

$\sf{\longrightarrow \dfrac{28}{4}}$

$\sf{\longrightarrow \dfrac{28\div4}{4\div4}}$

$\sf{\longrightarrow \dfrac{7}{1}}$

$\sf{\longrightarrow 7:1}$

vi) 5 dozens to 2 scores

Here, we need to convert both the units in numbers.

As we know that,

• 1 dozen = 12
• 1 score = 20

Therefore,

• 5 dozens = 5 × 12 = 60
• 2 scores = 2 × 20 = 40

Now,

$\sf{\longrightarrow 60:40}$

$\sf{\longrightarrow \dfrac{60}{40}}$

$\sf{\longrightarrow \dfrac{60\div20}{40\div20}}$

$\sf{\longrightarrow \dfrac{3}{2}}$

$\sf{\longrightarrow 3:2}$

Answer 2

Answer:

Step-by-step explanation:

1 min = 60 sec

45 to 30 min

=45 : 1800

(dividing both terms by 5)

(dividing both terms by 9)

= 1:40