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Section Topics
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Fractions involving Units
Saying or showing how to do operations defines them.The following pages provide more example and more explanation of operations with units in expressions that are written like fractions. We call these expressions, fractions with units. Whole number or fraction Multiples:
Factoring:
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| 5 hour2 7 |
+ | 4 hour2 7 |
= [ |
5 |
+ | 4 7 |
] | hour2 |
= |
9 |
hour2 |
= | 9 hour2 7 |
and
| 3 cm2 5 gm5 |
+ | 9 cm2 5gm5 |
= [ |
3 |
+ | 9 5 |
] | cm2 gm5 |
= |
12 |
cm2 gm5 |
= | 12 cm2 5 gm5 |
terms need not be identical: any pair of terms can be multiplied.
| 7 cm2
sec3 3 gm5 |
× | 9 gm9 sec4 25 cm5 |
= |
7×9 |
gm9-5 sec3+4 cm5-2 |
= | 21 25 |
gm4 sec7 cm3 |
| 1 | = |
25 cm5 9 gm9 sec4 |
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| 9 gm9 sec4 25 cm5 |
Division by a "fraction" is given by multiplication by the reciprocal of the fraction.
| 72
sec3 3 gm5 |
= | 72
sec3 3 gm5 |
× |
25 cm5 9 gm9 sec4 |
= |
175 |
cm7 |
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| 9 gm9 sec4 25 cm5 |
The following
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15 |
cm2 gm5 |
= | 15 cm2 5 gm5 |
show how a fraction with units may be written with numerical coefficients as a factor (here a fraction) or with numerical coefficients included in the numerators and denominators. In general, we take
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a |
× | unit1 unit2 |
= | a unit1 b unit2 |
to be equivalent - to have the same value. We declare raising or lower terms by multiplying nd dividing numerators and denominators by the same number or quantity gives an equivalent fraction. (Here a numerical quantity is given by a number times a unit).
Above we may replace the 15/5 by 3 to get a simpler fraction-like expression:
| 15 cm2 5 gm5 |
= | 15 5 |
cm2 gm5 |
| = | 3 | cm2 gm5 |
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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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