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Saturday, March 5, 2016

On 6:50 AM by MATH CHANNEL in    1 comment
\boxed{\text {Is this true: }\dfrac{9}{4} = 2\dfrac{1}{4} = 2.25 = 225\%  \text { ? }}
I. MIXED NUMBERS
Example: 7 divided by 4 is 1 with remainder 3.
Then, we write: \boxed{\dfrac{7}{4} = 1 + \dfrac{3}{4} = 1\dfrac{3}{4}}. The number 1\dfrac{3}{4} is a mixed number, where 1 is the integer part and \dfrac{3}{4} is the fraction part of \dfrac{7}{4}.
Covert mixed numbers to fractions
    5\dfrac{1}{7} = \dfrac{{5.7 + 1}}{7} = \dfrac{{36}}{7}
     - 4\dfrac{3}{5}\bf-\dfrac{{4.5 + 3}}{5}\bf-\dfrac{{23}}{5}
 Covert fractions to mixed numbers
    \dfrac{7}{3} = 2\dfrac{1}{3} (7 divided by 3 is 2 with remainder 1)
    \dfrac{ - 7}{4}\bf-\dfrac{7}{4} = \bf- 1 \dfrac{3}{4}

II. DECIMAL NUMBERS
- A decimal fraction is a fraction where the denominator is a power of 10 (such as: \dfrac{3}{{10}}, \dfrac{{ - 152}}{{100}}, \dfrac{{73}}{{1000}}, etc).
- The decimal fractions can be written as decimal numbers.
- A decimal number includes two parts:
      + Integer part is written on the left of the decimal separator,
      + Decimal part is written on the right of the decimal separator.
Example: \dfrac{3}{{10}} = \color{black}{0.3}\dfrac{-152}{{100}} = \color{black}{-1.52}\dfrac{73}{{1000}} = \color{black}{0.073}; etc are fractions.
- The number of digits in the decimal part is exactly equal to the number of 0 digits in the denominator of the decimal fraction.
 Covert decimal fractions to decimal numbers:
    \dfrac{{27}}{{100}} = 0.27
    \dfrac{{ - 13}}{{1000}} =  - 0.013
    \dfrac{{261}}{{100000}} = 0.00261
 Covert decimal numbers to decimal fractions:
    1.21 = \dfrac{{121}}{{100}}
    0.07 = \dfrac{{7}}{{100}}
    -2.013 = \dfrac{{-2013}}{{1000}}

III. PERCENTAGES
Fractions with denominator 100 are written as percentages with the symbol %.
Example: \dfrac{3}{{100}} = 3\%
               \dfrac{107}{{100}} = 107\%
               \dfrac{7}{{25}} = \dfrac{{28}}{{100}} = 28\%
               \dfrac{{26}}{{65}} = \dfrac{2}{5} = \dfrac{{40}}{{100}} = 40\%
               3.7 = \dfrac{{37}}{{10}} = \dfrac{{370}}{{100}} = 370\%
               0.34 = \dfrac{{34}}{{100}} = 34\%
 Covert percentages to decimal numbers
    7\%  = 0.07
    45\%  = 0.45
    216\%  = 2.16

1 comment:

  1. Bài toán này rất hay, các em học sinh nên nghiên cứu

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