Question

Which of the following number sentences is an example of the associative property? Select all that apply.

$(1\frac{2}{5}*3\frac{1}{2} )*4=1\frac{2}{5} (3\frac{1}{2} *4)$

$2.5*(1.8+6.3)=(2.5*1.8)+(2.5*6.3)$

10(4.6 × 3) = (10 × 4.6) × 3

6.3 × 1 = 6.3

Answer 1

Associative property:-

• a+(b+c)=(a+b)+c

Lets check one by one

#1

Here the rule is

• (ab)c=a(bc)

Hence Yes associative property

#2

Here the rule is

• a(b+c)=ab+ac

Hence no it's distributive property

#3

• a(bc)=(ab)c

Yes

#4

• ab=ba

No

Answer 2

Associative property meaning rearranging the parentheses in an expression which will not change the result.

✔A)

$\rightarrow \sf (1\dfrac{2}{5} \ x \ 3\dfrac{1}{2} ) \ x \ 4 = 1\dfrac{2}{5} (3\dfrac{1}{2} \ x \ 4 )$

$\rightarrow \sf \dfrac{98}{5} = \dfrac{98}{5}$

This uses associate property as it is rearranged in a different way and result same.

B)

$\rightarrow \sf 2.5 \ x \ (1.8 +6.3) = (2.5 \ x \ 1.8)+(2.5 \ x \ 6.3 )$

This property is called distributive property. a(b + c) = a(b) + a(c)

✔C)

$\sf \rightarrow 10(4.6 \ x \ 3) = (10 \ x \ 4.6) \ x \ 3$

$\sf \rightarrow 138 = 138$

associate property as the following is rearranged inside the parentheses

D)

$\rightarrow \sf 6.3 \ x \ 1 = 6.3$

This does not fall under any method or else multiplicative identity property.