# EXPRESS A NUMBER AS A PERCENTAGE OF ANOTHER

To express the given quantity as a percentage of other, we have to consider the following.

Are they in same unit or different units.

• If they are in the same unit, express the first as a fractional part of the second.
• If they are in different units, convert them into same unit and write it as fraction.
• To convert the fraction as a percentage, we have to multiply it by 100%.

Express the first quantity as a percentage of the second :

Problem 1 :

10 km, 50 km

Solution :

Expressing 10 km of 50 km as fraction :

= 10/50

Converting as percentage :

= (10/50) × 100

= 20%

Problem 2 :

€2, €8

Solution :

Expressing €2 of €8 as fraction :

= 2/8

Converting as percentage :

= (2/8) × 100

= (1/4) × 100

= 25%

Problem 3 :

300 m, 0.7 km

Solution :

1 km = 1000 m

0.7 km = 0.7 ×1000 = 700 m

Expressing 300 m of 700 m as fraction :

= 300/700

Converting as percentage :

= (300/700) × 100

= 42.9%

Problem 4 :

60 cents, \$2

Solution :

\$1 = 100 cents

\$2 = 200 cents

Expressing 60 cents of 200 cents as fraction :

= 60/200

Converting as percentage :

= (60/200) × 100

= 30%

Problem 5 :

8 months, 2 years

Solution :

1 year = 12 months

2 year = 24 months

Expressing 8 months of 24 months as fraction :

= 8/24

= 1/3

Converting as percentage :

= (1/3) × 100

= 33%

Problem 6 :

50 g, 1.2 kg

Solution :

1 kg = 1000 g

1.2 kg = 1.2 × 1000 = 1200 g

Expressing 50 g of 1200 g as fraction :

= 50/1200

Converting as percentage :

= (50/1200) × 100

= 4.2%

Problem 7 :

24 min, 2 hours

Solution :

1 hour = 60 minutes

2 hour = 120 minutes

Expressing 24 minutes of 120 minutes as fraction :

= 24/120

Converting as percentage :

= (24/120) × 100

= 20%

Problem 8 :

0.5 m, 25 cm

Solution :

1 m = 100 cm

0.5 m = 50 cm

Expressing 50 cm of 25 cm as fraction :

= 50/25

Converting as percentage :

= (50/25) × 100

= 200%

Problem 9 :

5 mg, 2 g

Solution :

1 mg = 0.001 g

5 mg = 0.005 g

Expressing 0.005 g of 2 g as fraction :

= 0.005/2

Converting as percentage :

= (0.005/2) × 100

= 0.25%

Problem 10 :

3 weeks, 15 days

Solution :

1 week = 7 days

3 weeks = 7 × 3 = 21 days

Expressing 21 days of 15 days as fraction :

= 21/15

= 7/5

Converting as percentage :

= (7/5) × 100

= 140%

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