Geometric proportion and Laws of Proportion

Learn about geometric proportion and laws of proportion

1. Geometric
proportion
©
Ma. Guadalupe Robles
[email protected]

2. ratio
comparison of two numbers with
the same units or different units

a:b= a (first number)
b (second number)

3. proportion
equality of two ratios

a:b=c:d

4. proportion
*number in a proportion= TERM

a(first term) = c(third term)
b(second term) d(fourth term)

5. proportion
a:b=c:d

6. proportion
a:b=c:d

MEANS

7. proportion
a:b=c:d

EXTREMES

8. Laws of
proportion

9. First law of proportion
Means-Extremes Product Law
of Proportions

If a = c , then ad=bc,
b d
where b≠0, d≠0

10. Means-Extremes Product Law of
Proportions

Example:

4= 2
x 6

11. Means-Extremes Product Law of
Proportions

Example:

2x = 4(6)
2x = 24

12. Means-Extremes Product Law of
Proportions

Example:

2x = 4(6)
2x = 24
2 2

13. Means-Extremes Product Law of
Proportions

Answer:


X=12

14. Second law of proportions
Switch Means-Switch Extremes law of
Proportions

If a = c , then a = b and d = c
b d c d b a

Where a, b, c, and d are nonzero real
numbers

15. Switch Means-Switch Extremes law of
Proportions

a:b=c:d a = c
b d
Switch of Means:
a:b=c:d

MEANS

16. Switch Means-Switch Extremes law of
Proportions

a:c=b:d
a = b
c d

17. Switch Means-Switch Extremes law of
Proportions


Switch of Extremes:
a:b=c:d
EXTREMES

d:b= c:a d = c
b a

18. Third law of proportions
Invert-Both-Sides Law of Proportions
If a = c , then b = d
b d a c

Where a, b, c, and d are nonzero real
numbers

19. fourth law of proportions
Denominator-Addition Law of Proportions
If a+b = c+d
b d

Where b≠0, d≠0

20. fifth law of proportions
Denominator-Substraction Law of
Proportions
If a-b = c-d
b d

Where b≠0, d≠0

21. Sixth law of proportions
Numerator-Denominator Sum Law of
Proportions
If a = c = e … then, a+c+e = a = c =e
b d f b+d+f b d f