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MATH RELATIONSHIPS

Properties of Addition

http://www.aaamath.com/B/pro74ax2.htm

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.

 multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4

Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)

Multiplicative Identity Property: The product of any number and one is that number. For example 5 * 1 = 5.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3

Multiplying by Repeated Addition

http://www.aaamath.com/B/pro39_x2.htm

The result of multiplication is the total number (product) that would be obtained by combining several (multiplier) groups of similar size (multiplicand). The same result can be obtained by repeated addition. If we are combining 7 groups with 4 objects in each group, we could arrive at the same answer by addition. For example, 4+4+4+4+4+4+4=28 is equivalent to the multiplication equation 7*4=28.

Dividing by Repeated Subtractions

http://www.aaamath.com/B/pro41_x3.htm

The result of division is to separate a group of objects into several equal smaller groups. The starting group is called the dividend. The number of groups that are separated out is called the divisor. The number of objects in each smaller group is called the quotient.

The results of division can be obtained by repeated subtraction. If we are separating 24 objects into 6 equal groups of four, we would take (or subtract) four objects at a time from the large group and place them in 6 equal groups. In mathematical terms this would be: 24-4-4-4-4-4-4.

Subtraction and Addition Relationship

http://www.aaamath.com/B/pro34bx2.htm

There is an inverse relationship between addition and subtraction.

Example: Since 3 + 7 = 10 then the following are also true:

• 10 - 3 = 7
• 10 - 7 = 3

Similar relationships exist for subtraction.
Example: Since 10 - 3 = 7 then the following are also true:

• 3 + 7 = 10
• 7 + 3 = 10

An equation is balanced or the same on either side of the equals (=) sign. If exactly the same thing is done to both sides of the equation, it will still be balanced or equal.

In the example above we start with the equation 3 + 7 = 10:

• Subtract the same number from both sides
  3 + 7 - 3 = 10 - 3
• On the left side the 3 and -3 produce 0 which leaves
  7 = 10 - 3
• Turning the equation around to be in more normal form
  10 - 3 = 7

Multiplication and Division Relationship

http://www.aaamath.com/B/pro34cx2.htm

There is an inverse relationship between multiplication and division just like there was between addition and subtraction.

The equation 3 * 7 = 21 has the inverse relationships:
21 ÷ 3 = 7
21 ÷ 7 = 3

Similar relationships exist for division. The equation 45 ÷ 5 = 9 has the inverse relationships:
5 * 9 = 45
9 * 5 = 45

Division and Multiplication Relationship

http://www.aaamath.com/B/pro34dx2.htm

The There is an inverse relationship between multiplication and division.

The equation 45 ÷ 5 = 9 has the inverse relationships following are also true:
5 * 9 = 45
9 * 5 = 45

Similar relationships exist for multiplication. The equation 3 * 7 = 21 has the relationships:
21 ÷ 3 = 7
21 ÷ 7 = 3