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Section Topics
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Products of
Fractions
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| 1 N |
× | P×N Q |
= | P Q |
(II) M one N-th of P× N Q- ths will be M times one
one N-th of P×N Q- ths
or M × P Q-ths or (M × P) Q-ths
| M N |
× | P×N Q |
= | M × |
P |
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| that gives | ||||||
| M N |
× | P×N Q |
= | M×P Q |
Step II: Multiplication of Fractions without simplification
Let us start with an example:
| 5 7 |
× | 11 6 |
= | 5 7 |
× | 11 × 7 7 ×6 |
Note how we replace the second factor by an equivalent one by raising terms to introduce a factor of 7 into the numerator of the second factor. |
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| = | 5 × 11 7 ×6 |
Follow the pattern for the easy case |
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| = | 55 42 |
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| = |
1 |
13 |
Motivation: For the raising of terms, we assume 11 one sixths of an object (say a length) is the same as 11 × 7 multiples of one 7 ×6 ths of the object. Then the question what is five sevenths of 11 one sixths of an object is identical to the the question of what is five sevenths of 11 × 7 multiples of one 7 ×6 ths of the object.. Thus raising terms is just rephrasing the question, so that the easy case applies.
The General Method for the calculating the product
| M N |
× | P B |
? |
is very similar. We raise terms in the second factor, so that its numerator is a multiple of the denominator of the first. We are taking one fraction of another.
| M N |
× | P B |
= | M N |
× | P × N N ×B |
Raise Terms |
| = | M × P N ×B |
Follow the Easy Case Pattern |
Thus the product is obtained by raising terms and then using the easy case calculation. After that the calculation can be combined with simplification of the result. That leads to multiplication with simplification. Student may be introduced for efficient methods for that via the introduction of cancellation of common factors to lower the product numerator and M × P and denominator N × B. The foregoing process suggests the product formula
| M N |
× | P B |
= | M × P N ×B |
for computing a fraction of a fraction without simplification.
Motivation: For the raising of terms, we assume P multiplies of one Bth of an object (say a length) is the same as P × N multiples of one N ×B th of the object. Then the question what is M/N times P multiples of one Bth of the object is identical to the the question of what is the fraction M multiples of one Nth of P × N multiples of one N ×B th of the object. Thus raising terms is just rephrasing the question, so that the easy case applies.
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Road
Safety Message Do not walk on a road with your back to the
traffic - rule of thumb
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