Friday, December 7, 2012

CBSE Class 7 - Maths - CH8 - Comparing Quantities (Ratio and NCERT Ex 8.1)

Comparing Quantities(Ratio)
Ratio of Circumference: Diameter = π
image credits: openclipart

Important Points

1. In the ratio x:y (called as x is to y), x is called the first term or antecedent. y is called the second term or consequent.

2. While comparing two quantities, the units must be the same.

3. A ratio remains unchanged if both its terms are multiplied or divided by same non-zero number.

 

4. The ratio (p:q) is said to be in simplest form when HCF of p and q is 1.

NCERT Exercise 8.1

Q1: Find the ratio of:
(a) ₹ 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours



Answer:
(a) ₹ 5 to 50 paise
Since units are not same, we need to convert both to same units.
 ₹ 1 = 100 paise     ∴ ₹ 5 = 5 × 100 = 500 paise
∴ ₹ 5 to 50 paise = 500 paise: 50 paise = 500/50 = 10:1

(b) 15 kg to 210 g
Since units are not same, we need to convert both to same units.
∵ 1 kg  = 1000g   ∴ 15kg = 15 × 1000 = 15000g
∴ 15 kg to 210 g = 15000g : 210g = 15000/210 = 500:7

(c) 9 m to 27 cm
Converting both terms to same units.
∵ 1m = 100 cm   ∴ 9m = 9 × 100cm = 900cm
 ∴ 9m to 27cm = 900cm : 27cm = 900 / 27 = 100/3 = 100:3

(d)  30 days to 36 hours
Converting both terms to same units.
∵ 1 day = 24 hours
∴ 30 days = 30 × 24 hours = 720 hours
 ∴ 30 days to 36 hours = 720 hours : 36 hours =720/36 = 20/1 = 20:1


Q2: In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

Answer:







Q3:Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.
Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.
(i) How many people are there per km2 in both these States?
(ii) Which State is less populated?

Answer:
Let us calculate ratio as population per area.
Population of Rajasthan per 3 lakh km2 = 570 lakh
Population of Rajasthan per 1 lakh km2 =570/3 = 190 lakh      ... (I)

Population of UP per 2 lakh km2 = 1660 lakh
Population of UP per 1 lakh km2 = 1660/2 = 830 lakh             ...(II)

Comparing values I and II, we can say population ratio per area of  Rajasthan is less.

Other Questions on Ratio

Q4: Express 24:30 in its simplest form.


Answer: Ratio in simplest form is when HCF of two terms is 1 i.e. there is no common factor except one.

∴ 24 : 30 = 4 × 2 × 3 : 5 × 2 × 3 = 4 : 5


Q5: Express ratio 1m 5cm : 63 cm in simplest form.


Answer: Converting into same units.
∵ 1m = 100 cm
∴ 1m 5cm = 100 cm + 5 cm = 105 cm
∴ 1m 5cm : 63 cm = 105 cm : 63 cm = 7 × 5 × 3 : 7 × 3 × 3 = 5 : 3

Q6: Divide ₹ 360 in the ratio 7:8.

Answer:  Let the two values after division is 7x and 8x.
Sum of these values = 7x + 8x = 15x = ₹ 360
⇒ x = 360/15 = 24

∴ First value = 7x = 7 × 24 = ₹ 168
and the second value = 8x = 8 × 24 = ₹ 192

Thus  ₹360 is divided into ₹168 and ₹192 as per the given ratio (7:8)


Q7: Two numbers are in the ratio of 7:11. If 7 is added to each of the numbers the ratio becomes 2:3. Find the numbers.

Answer:
  Let the first number = 7p
  and the second number = 11p

After adding 7, the first number becomes = 7p + 7
After adding 7, the second number becomes = 11p + 7

The new ratio is,










 Thus numbers are 49 and 77.

Q8: If 15 oranges cost Rs 70, what do 39 oranges cost?

Answer: Cost of 15 oranges = ₹70
              Cost of 1 orange     = 70/15
              Cost of 39 oranges = 70 × 39 /15 = 14 × 13 = ₹182


Q9: Fill in the blanks:
  1. The comparison of two quantities of the same kind by means of division is termed as_____________.
  2. The two quantities to be compared are called the ________ of the ratio.
  3. The first term of the ratio is called the _________ and the second term is called the _______.
  4. Equality of two ratios is called a __________. If a,b;c,d are in proportion,then a:b::c:d .
  5. In a proportion, the product of extremes =___________
Answer
  1. ratio
  2. terms
  3. antecedent, consequent
  4. proportion
  5. product of means
.

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