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| Ratios and Proportions
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Ratio
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Proportion
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Ratios
and proportion properties
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Direct proportion
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Cross product, means and extremes
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| Ratio |
| A ratio is a comparison of two similar quantities obtained by dividing
one quantity by the other. |
| A ratio can be written as,
a
:
b
or as a fraction a/b
or by the phrase ' a to
b '. |
| A ratio is a way in which
quantities can be divided or shared. It shows how much bigger one
thing is than
another. |
| Make
the numbers in ratios smaller so that they are easier to
compare. Do this by dividing each side of the ratio
by the same number, the highest common factor. |
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| Proportion |
| A proportion is
a statement of the equality of two ratios. If the fractions both reduce
to the same value, the proportion is true. |
| Example: |
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9
: 6 = 3/2
and, 21
: 14 = 3/2,
follows,
9 :
6 = 21 : 14. |
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| Ratios and proportion properties
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| A ratio's value is not altered if both the first and second term are
multiplied or divided by the same number different from zero. |
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a
:
b =
(a · c)
:
(b ·
c) |
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| Two quantities are in
direct proportion when they increase or decrease in the same ratio. |
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| When two ratios are equal, then the
cross products of the ratios are equal. |
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That is, |
a
:
b = c
:
d |
or |
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| the
product of the means is equal to the product of the extremes.
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| The
first and last term in a proportion are called the extremes, the
second and third terms are called the means.
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| If any three terms in
a proportion are given, the fourth may be found. |
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the
extremes |
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the
means |
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| Examples: |
a)
2
:
x =
6 :
15 |
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b)
8
:
(x
-
1)
= 2 :
7 |
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c)
(7
-
x)
:
3 =
4x :
9 |
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9 · (7
-
x) =
3 ·
4x |
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63
-
9x
= 12x |
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x = 5 |
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x = 29 |
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21x = 63
| ¸
21 |
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x = 3 |
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| The first and third terms, and the second and the fourth terms in a
proportion are the corresponding terms. |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
