Respuesta :
For Commutative Property of Addition
Let us take a decimal number [tex]2.14[/tex] and a fraction [tex]\frac{5}{20}[/tex]
Now, according to the Commutative property of Addition:
For any two numbers [tex]a[/tex] and [tex]b[/tex] :
[tex]a+b = b+a[/tex]
So, for [tex]2.14[/tex] and [tex]\frac{5}{20}[/tex]
Let us add
[tex]2.14+\frac{5}{20} = \frac{214}{100} +\frac{5}{20}[/tex]
[tex]=\frac{214}{100} + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100} + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39[/tex]
Also,
[tex]\frac{5}{20} + 2.14 = \frac{5}{20} + \frac{214}{100}[/tex]
[tex]= \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100} + \frac{214}{100} \\ \\= 0.25 + 2.14 \\ \\ = 2.39[/tex]
Therefore, [tex]2.14+\frac{5}{20} = \frac{5}{20} + 2.14[/tex]
Hence, Commutative Property of Addition is satisfied.
For Associated Property of Addition
Let us take two same decimal numbers [tex]2.14[/tex] , [tex]7.25[/tex] and a fraction [tex]\frac{5}{20}[/tex]
Now, according to the Associated property of Addition:
For any three numbers [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex]
[tex]a + (b+c) =(a+b) + c[/tex]
So, for [tex]2.14[/tex] , [tex]7.25[/tex] and [tex]\frac{5}{20}[/tex]
The Left hand side:
[tex]a + (b+c) [/tex]
[tex]2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})[/tex]
[tex]= 2.14 + (\frac{725}{100} + \frac{25 }{100})[/tex]
[tex]= 2.14 + (\frac{750}{100} )[/tex]
[tex]= \frac{214}{100} + \frac{750}{100}[/tex]
[tex]= \frac{964}{100}[/tex]
[tex]=9.64[/tex]
The Right hand side:
[tex](a + b )+c[/tex]
[tex](2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}[/tex]
[tex]= 9.39 + \frac{5 \times 5 }{20 \times 5}[/tex]
[tex]= 9.39 + \frac{25}{100}[/tex]
[tex]= 9.39 + 0.25[/tex]
[tex]= 9.64[/tex]
Thus,
[tex](2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}[/tex]
Therefore, [tex]2.14+\frac{5}{20} = \frac{5}{20} + 2.14[/tex]
Hence, Associative Property of Addition is satisfied.
