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Simplifying ratios with units

Simplifying ratios with units. Steps for same units Step1: If the given quantity is in the same units then write the quantity in ratio form Step2: Write the given ratio in the fractional form Step3: Simplify the fraction Step4: Finally write the simplified answer in Ratio.

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Simplifying ratios with units

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  1. Simplifying ratios with units

  2. Steps for same units Step1: If the given quantity is in the same units then write the quantity in ratio form Step2: Write the given ratio in the fractional form Step3: Simplify the fraction Step4: Finally write the simplified answer in Ratio Steps for different units Step1: If the given quantity is in the different units Step2: Convert the quantities to the same units and then write the quantity in ratio form. Step3: Write the given ratio in the fractional form Step 4: Simplify the fraction Step5: Finally write the simplified answer in Ratio TIP : Try dividing the fraction by the numbers given below to simplify it 2 , 3 , 5 ,7 , 10

  3. Example 1: Find the simplified ratio of 21kg to 7kg Solution The given units are in same units(i.e., kg) Step1: Write the quantity in ratio form Ratio of 21kg to 7kg is 21 : 7 Step2 : Write 21:7 into fractional form Step3: Simplify the fraction Rule :Divide fraction using the numbers 2, 3, 5, 7, 10 21 and 7 are divisible by common number 7 3 and 1 are further not divisible by any common number. Hence fraction is said to be in simplified form Step 4: Write the simplified fraction in Ratio

  4. Example 2: Find the simplified ratio of 150cm to 200cm Solution: The given units are in same units(i.e., cm) Step1: Write the quantity in ratio form Ratio of 150cm to 200cm is 150 : 200 Step2 : Write 150:200 into fractional form Step3: Simplify the fraction Rule :Divide fraction using the numbers 2, 3, 5, 7, 10 150 and 200 are divisible by common number 10 15 and 20 are divisible by common number 5 3 and 4 are further not divisible by any common number. Hence fraction is said to be in simplified form Step 4: Write the simplified fraction in Ratio

  5. Different units Conversion Time conversions: 1 hour = 60 minutes Length conversions: 1 m = 100 cm 1 km = 1000 m Distance conversions: Weight conversions: 1 kg = 1000 g 1 l = 1000 ml Quantity conversions: Money conversions: Re. 1= 100 paise Year conversions: 1 year = 12 months

  6. Time conversions: Example 1: Convert 2 hours to minutes Solution: We know that 1 hour = 60 minutes 2 hours = 2 x 60 = 120 minutes Example 2: Convert 3 hours 15 minutes to minutes Solution: We know that 1 hour = 60 minutes 3 hours = 3 x 60 = 180 minutes 3 hours 15 minutes = 180 minutes + 15 minutes =195 minutes Year conversions: Example 1: Convert 3 years to months Solution: We know that 1 year = 12 months 3 years = 3 x 12 = 36 months Example 2: Convert 2 years 6 months to months Solution: We know that 1 year = 12 months 2 years = 2 x 12 = 24 months 2 years 6 months = 24 months + 6 months =30 months

  7. Length conversions: Example 1: Convert 4m to cm Solution: We know that 1 m = 100 cm 4 m = 4 x 100 = 400 cm Example 2: Convert 2 m 30 cm to cm Solution: We know that 1 m = 100 cm 2 m = 2 x 100 = 200 cm 2 m 30cm = 200 cm + 30cm =230 cm Distance conversions: Example 1: Convert 7km to m Solution: We know that 1 km = 1000 m 7km = 7 x 1000 = 7000 m Example 2: Convert 3 km 400m to m Solution: We know that 1 km = 1000 m 3km = 3 x 1000 = 3000 m 3km 400m = 3000 m + 400m =3400 m

  8. Weight conversions: Example 1: Convert 6kg to g Solution: We know that 1 kg = 1000 g 6kg = 6 x 1000 = 6000g Example 2: Convert 2 kg 750g to g Solution: We know that 1 kg = 1000g 2kg = 2 x 1000 = 2000g 2 kg 750g = 2000g + 750g =2750g Quantity conversions: Example 1: Convert 7L to ml Solution: We know that 1 L = 1000 ml 7L= 7 x 1000 = 7000 ml Example 2: Convert 3L 250ml to ml Solution: We know that 1 l = 1000 ml 3L= 3 x 1000 = 3000 ml 3L 250ml = 3000 ml + 250ml = 3250 ml

  9. Year conversions: Example 1: Convert 3 year to months Solution: We know that 1 year = 12 months 3 year= 3 x 12 = 36 months Example 2: Convert 2 years 5 months to months Solution: We know that 1 year = 12 months 2 year= 2 x 12 = 24 months 2 years 5 months = 24 months + 5 months = 29 months

  10. Example 1: Ratio of 60 paises to 1 rupee Solution: The given units are in different units Step 1: Convert the quantities to the same units We know that 1 rupee = 100 paises Thus, 60 paises to 1 rupee = 60 paises to 100 paises and write the quantity in ratio form Ratio of 60 paisesto 100 paises is 60 : 100 Step2: Write 60:10 into fractional form Step3: Simplify the fraction Rule :Divide fraction using the numbers 2,3,5,7,10 60 and 10 are divisible by common number 10 6 and 10 are divisible by common number 2 3 and 5 are further not divisible by any common number. Hence fraction is said to be in simplified form Step 4: Write the simplified fraction in Ratio

  11. Example 2: Ratio of 55 minutes to 2 hours Solution: The given units are in different units Step 1: Convert the quantities to the same units We know that 1 hour = 60 minutes ∴ 2 hour = 2 x 60 =120 min Thus, 55 minutes to 2 hours = 55 minutes to 120 minutes and write the quantity in ratio form Ratio of 55 minutes to 120 minutes is 55 : 120 Step2: Write 55:120 into fractional form Step3: Simplify the fraction Rule :Divide fraction using the numbers 2,3,5,7,10 55 and 120 are divisible by common number 5 11 and 24 are further not divisible by any common number. Hence fraction is said to be in simplified form Step 4: Write the simplified fraction in Ratio

  12. Example 3: Ratio of 3m to 330cm Solution: The given units are in different units Step 1: Convert the quantities to the same units We know that 1 metre = 100 cm ∴ 3 metre = 3 x 100 =300 cm Thus, 3m to 330cm = 300cm to 330cm and write the quantity in ratio form Ratio of 300cm to 330cm is 300 : 330 Step2: Write 300 : 330 into fractional form Step3: Simplify the fraction Rule :Divide fraction using the numbers 2,3,5,7,10 300 and 330 are divisible by common number 10 30 and 33 are divisible by common number 3 10 and 11 are further not divisible by any common number. Hence fraction is said to be in simplified form Step 4: Write the simplified fraction in Ratio

  13. Example 4: Ratio of 3km 300m to 5km Solution: The given units are in different units Step 1: Convert the quantities to the same units We know that 1 km = 1000 m ∴ 5 km = 5 x 1000 =5000 m ∴ 3 km = 3 x 1000 =3000 m , 3km 300m =3000 + 300 = 3300m Thus, 3km 300m to 5km = 3300m to 5000m and write the quantity in ratio form Ratio of 3300m to 5000m is 3300 : 5000 Step2: Write 3300 : 5000 into fractional form Step3: Simplify the fraction Rule :Divide fraction using the numbers 2,3,5,7,10 3300 and 5000 are divisible by common number 10 330 and 500 are divisible by common number 10 33 and 50 are further not divisible by any common number. Hence fraction is said to be in simplified form Step 4: Write the simplified fraction in Ratio

  14. Try these • Simplified Ratio of 30kgs to 70kgs • Simplified Ratio of 3litres to 650ml • Simplified Ratio of 2m 25cm to 350cm

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