Question

4 puzzle time how can you share five apples with seven friends answers

Answer 1

Part 1:

Identify the algebraic properties of equality that are represented.
1.

Given

If
`a=b`, then
`a\cdot c=b\cdot c, c\\eq0`

The algebraic property of equality that is represented by the above expression is the multiplication property.


2.

Given

If
`a=b`, then
`a- c=b- c,`

The algebraic property of equality that is represented by the above expression is the subtraction property.


3.

Given

If a = b, then a can be substituted for b (or b for a) in any equation or expression.
The algebraic property of equality that is represented by the above expression is the substitution property.


4.

Given

If
`a=b`, then
`(a)/(c) = (b)/(c),\ c\\eq0`.

The algebraic property of equality that is represented by the above expression is the division property.


5.

Given

If
`a=b`, then
`a+ c=b+ c,`

The algebraic property of equality that is represented by the above expression is the addition property.


6.

Given

sum:
`a(b+c)=ab+ac`,
difference:
`a(b-c)=ab-ac`

The algebraic property of equality that is represented by the above expression is the distributive property.


7.

Given

If a = b and b = c, then a = c. If AB = CD and CD = EF, then AB = EF. If m<A = m<B and m<B = m<C, then m<A = m<C.

The algebraic property of equality that are represented by the above expression is the transitive property.


8.

Given

If a = b, then b = a. If AB = CD, then CD = AB. If m<A = m<B, then m<B = m<A.
The algebraic property of equality that are represented by the above expression is the symmetric property.

9.

Given

a = a, AB = AB, m<A = m<A
The algebraic property of equality that are represented by the above expression is the refrexive property.


10.

Given

If x = y, then 6x = 6y.
The algebraic property of equality that are represented by the above expression is the multiplication property.

11.

Given

If AB = BC, then AB - 2 = BC - 2.
The algebraic property of equality that are represented by the above expression is the subtraction property.

12.

Given

m<A = m<A

The algebraic property of equality that are represented by the above expression is the refrexive property.


13.

Given

If AB = CD and CD = 6, then AB = 6
The algebraic property of equality that are represented by the above expression is the transitive property.


14.

Given

If a = b, then b = a.
The algebraic property of equality that are represented by the above expression is the symmetric property.