Respuesta :
Answer:
We see adding mixed number is easier by using the Commutative and Associative Properties of Addition.
Step-by-step explanation:
We have to show how the Commutative and Associative Properties of Addition can make adding mixed numbers easier.
For given numbers a , b and c , we have,
Commutative property of addition:
[tex]a+b=b+a[/tex]
Associative property of addition,
[tex]a+(b+c)=(a+b)+c[/tex]
Let us show it by using example,
Consider the addition of numbers having fractions,
[tex]\frac{2}{3}+(2+\frac{4}{3})[/tex]
it is easy to find the sum by first combining fraction term and then adding 2 to it.
We first apply commutative property,
[tex]\frac{2}{3}+(2+\frac{4}{3})=\frac{2}{3}+(\frac{4}{3}+2)[/tex]
Now we apply associative property,
[tex]\frac{2}{3}+(\frac{4}{3}+2)=(\frac{2}{3}+\frac{4}{3})+2[/tex]
On solving , we get,
[tex](\frac{2}{3}+\frac{4}{3})+2=\frac{2+4}{3}+2=\frac{6}{3}+2[/tex]
Solving we get,
[tex]\frac{6}{3}+2=2+2=4[/tex]
We see adding mixed number is easier by using the Commutative and Associative Properties of Addition.
It is prove that, the Commutative and Associative Properties of Addition make adding mixed numbers easier.
Properties of Addition :
The associative and commutative properties are laws applied to addition and multiplication that always exist.
Commutative property of addition is,
[tex]a+b=b+a[/tex]
Associative property of addition is,
[tex]a+(b+c)=(a+b)+c[/tex]
For example,
[tex]2+(3+7)=(2+3)+7\\\\2+10=5+7\\\\12=12[/tex]
Thus, the Commutative and Associative Properties of Addition can make adding mixed numbers easier.
Learn more about the Commutative and Associative Properties here:
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