1. Determine if the following are in proportion:
a) 40, 50, 100, 125
C) 2kg : 500 g :: 400 g : 1600g
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in
proportion.
Answers
Answer:
proportion = product of extremes / product of means
Step-by-step explanation:
40:50::100:125 are in prortion because 40×125 = 5000 and 50×100 = 5000
40, 50, 100, 125 are in proportion
2kg : 500 g :: 400 g : 1600g are not in proportion
Given:
- 40, 50, 100, 125
- 2kg : 500 g :: 400 g : 1600g
To Find:
- Which are in proportion:
Solution:
- a : b :: c : d are in proportion if
- Product of Extremes = Product of Middle terms
- ad = bc
Step 1:
Check 40, 50, 100, 125
Product of Extremes = 40 x 125 = 5000
Product of Middles = 50 x 100 = 5000
5000 = 5000
Product of Extremes = Product of Middle terms
Hence, 40, 50, 100, 125 are in proportion
Step 2:
Check 2kg : 500 g :: 400 g : 1600g
First convert 2 kg in grams so that all have same units
2 kg = 2000 g
2000g : 500 g :: 400 g : 1600g
As all have same units so units can be ignored
2000 : 500 :: 400 : 1600
Product of Extremes = 2000 x 1600 = 3200000
Product of Middles = 500 x 400 = 200000
3200000 ≠ 200000
Product of Extremes ≠ Product of Middle terms
Hence, 2000 : 500 :: 400 : 1600 are not in proportion
=> 2kg : 500 g :: 400 g : 1600g are not in proportion
40, 50, 100, 125 are in proportion
2kg : 500 g :: 400 g : 1600g are not in proportion