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Continued proportion

Mean proportion

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**Proportion:**

**a) Introduction of Proportion:**

Bhavika has 28 marbles and Vini has 180 flowers. They want to share these among themselves. Bhavika gave 14 marbles to Vini and Vini gave 90 flowers to Bhavika. But Vini was not satisfied. She felt that she had given more flowers to Bhavika than the marbles given by Bhavika to her. What do you think? Is Vini correct?

To solve this problem both went to Vini’s mother Pooja. Pooja explained that out of 28 marbles, Bhavika gave 14 marbles to Vini. Therefore, the ratio is 14: 28 = 1: 2.And out of 180 flowers, Vini had given 90 flowers to Bhavika. Therefore, the ratio is 90: 180 = 1: 2.Since both the ratios are the same, so the distribution is fair.

**b) Proportion:**

- If two ratios are equal, then they are said to be in proportion.
- If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios.
- For example, we can say 2, 4, 180, and 360 are in the proportion which is written as 2: 4:: 180: 360 and is read as 2 is to 4 as 180 is to 360.
- If two ratios are not equal, then we say that they are not in proportion.

For example, the two ratios 2: 5 and 180: 45 are not equal, i.e. 2: 5 ≠ 180: 45. Therefore, the four quantities 2, 5, 180 and 45 are not in proportion - In a statement of proportion, the four quantities involved when taken in order are known as respective terms. The first and fourth terms are known as extreme terms. Second and third terms are known as middle terms.

1) Are the ratios 25g: 30g and 40 kg: 48 kg in proportion?

**Solution:**

25 g: 30 g = `25/30 `= 5: 6

40 kg: 48 kg = `40/48` = 5: 6

So, 25: 30 = 40: 48.

Therefore, the ratios 25 g: 30 g and 40 kg: 48 kg are in proportion, i.e. 25: 30:: 40: 48

The middle terms in this are 30, 40 and the extreme terms are 25, 48.

2) Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?

**Solution: **

Ratio of 15 cm to 2 m = 15: 2 × 100 (1 m = 100 cm)

= 3: 40

Ratio of 10 sec to 3 min = 10: 3 × 60 (1 min = 60 sec)

=1: 18

Since, 3: 40 ≠ 1: 18, therefore, the given ratios do not form a proportion.