Help Understanding this definition(Basic Algebra)(10 points)?

Question

Product of an expression of two or more terms multiplied by a single factor is equal to the sum of the product of each term of the expression mutiplied by a single factor...

This is the the definition of distrubitive law in my aglebra book. I'm having trouble understanding distrubitive law so if any one can explain it in a down to earth way I would be very greatful

Answer 1

Sure. It means that if you have one number times a sum of numbers: a(b+c+d+e+...), then all you have to do is multiply the first number by each number in sequence, and add them all together....

ab+ac+ad+ae+...

Answer 2

Try thinking of it in terms of coins.

Your parents give you an allowance of $10 a week plus an amount equal to the allowance you have left from the last $10. Let's say you have 1 quarter, 2 dimes and 2 pennies. You can figure how much extra they will give you in two different ways:

2 times (1 quarter, 2 dimes and 2 pennies) equals 2 times 47¢ equals 94¢.

or:

2 times (1 quarter, 2 dimes and 2 pennies) equals 2 times 1 quarter + 2 times 2 dimes + 2 times 2 pennies equals 2 quarters + 4 dimes + 4 pennies equals 50¢ + 40¢ + 4¢ equals 94¢.

The second way shows the distributive property (of multiplication). The nice thing is, since they are, by this property, identical ways of solving, we do not have to worry about which we choose to use. We can pick either one.

Answer 3

In a class there are 10 boys and 15 girls.

The teacher decides to give two pens to each student.

How many pens are needed?

The number can be determined in these two ways.

First we find the number of students.

Number of boys and number of girls is 10 + 15 = 25.

Since each has to be given 2 pens total pens needed is

2 x 25 = 50.

The other way of calculating this is:

We distribute the pens separately for boys and girls.

For the 10 boys the number of pens needed is 2 x 10 = 20.

20 pens are distributed to the boys.

For the 15 girls the number of pens needed is 2 x 15 = 30

30 pens are distributed to the girls.

Total number of pens distributed is 20 + 30 = 50.

In the second method we distribute the pens separately for boys and girls.

In the first method we distribute the pens irrespective of the sex of the students.

In both case the total number remains the same.

This is the distributive property.

Answer 4

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Answer 5

Let a_1, a_2, ..., a_n be n arbitrary terms: numbers, expressions, etc. Let k be a number, expression, etc. Then,

k * (a_1 + a_2 + ... + a_n) = (k * a_1) + (k * a_2) + ... + (k * a_n).

The distributive property appears in several numeric sets, and many non-numerical sets; it is part of the definition of a ring. More information at the sources.

Answer 6

it means:
2*(5+10) = 2*5+2*10
either one will get you the same answer but the earlier one is easier to do