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Example 4: School Ratio

Question: In my school, ratio is 5 teachers : 170 students. Is your school ratio proportional? Solution for Sample School:

My School Ratio: $5 : 170 \rightarrow 1 : 34$ (Dividing by 5).
Suppose your school has 10 teachers and 340 students.
- Ratio: $10 : 340 \rightarrow 1 : 34$ .
- Yes, they are proportional.
Suppose your school has 20 teachers and 500 students.
- Ratio: $20 : 500 \rightarrow 1 : 25$ .
- No, they are not proportional.

Question: Measure board, find ratio, draw proportional rectangle.

Assume Board Width = 120 cm, Height = 90 cm.
Ratio: $120 : 90 \rightarrow 4 : 3$ .
To draw in notebook:
- Scale down by factor of 10: Width 12 cm, Height 9 cm.
- Or scale down by factor of 20: Width 6 cm, Height 4.5 cm.

The base ratio is 15 : 35 (Coffee : Milk) $\approx$ 0.42 coffee per milk unit. Or simplified: 3 : 7.

Coffee	Milk	Ratio	Simplified	Strength
300	600	300:600	1 : 2	Stronger (1:2 > 3:7)
150	500	150:500	3 : 10	Lighter (3:10 < 3:7)
200	400	200:400	1 : 2	Stronger
24	56	24:56	3 : 7	Regular
100	300	100:300	1 : 3	Lighter

1. True/False Proportions:

(i) $4:7 :: 12:21 \rightarrow 4 \times 3 = 12, 7 \times 3 = 21$ . True.
(ii) $8:3 :: 24:6 \rightarrow 8 \times 3 = 24, 3 \times 2 = 6$ . Factors differ. False.
(vi) $24:8 :: 9:3 \rightarrow 3:1 :: 3:1$ . True.

2. Ratios proportional to 4:9 Multiply by 2, 3, 10:

3. Missing Numbers (18:24 $\rightarrow$ 3:4)