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We have discussed about addition of integers and its representation as chips. Recall in our previous discussion that a single positive chip added up to a single negative chip is equal to 0. The addition below as we have discussed will give us a notion of how to add signed numbers.
Now let us discuss on how use signed chips can be used as a strategy to subtract integers. Let us represent the following using chips. » Read more
Introduction
The set of integers is composed of the negative integers, zero, and the positive integers. The integers can be visualized using the number line (see first figure), a horizontal line, where, by convention (agreed upon by mathematicians), the negative numbers are located at the left of zero, and the positive integers at the right of 0. In the number line, the number a is greater than the number b if a is at the right of b. Therefore, -2 is greater than -3, -1 is less than 1, 0 is greater than -4.
As shown in the figure above, each integer has a specific location (coordinate) on the number line. Aside from being a coordinate on the number line, each integer can also be considered as movement from 0. For example, +2 means moving 2 units to the right of 0, while -3 is moving 3 units to the left of 0.
Given numbers a, b, and c, we are familiar since elementary grades that a(b+c) = ab + ac. This is what we call the distributive property of multiplication over addition. From commutative property, we also know that xy = yx; therefore, (b + c)a = a(b+c).
Knowing this property, we can do a lot of mathematical operations. For example, we do not need to memorize FOIL (First-Outside-Inside-Last) , one of the rote strategies (no need to memorize) in multiplying binomials. That is, in (a + b)(x + y), we multiply a(x + y), multiply b(x + y), and then add both terms giving us a(x + y) + b(x +y) which is equal to ax + ay + bx + by. If we have solved this, we can definitely solve (a + b)(x + y + z) and also (a + b + c)(x + y + z) and multiplication of polynomials of many terms. » Read more