Multiplying Greater Numbers
Let’s go back to the question posed at the opening of this topic of study. How can you use multiplication to figure out the total cost of 6 baseball caps that cost $14 each? (You do not have to pay sales tax). You can figure out the cost by multiplying ( 14 cdot 6).
One way to do this computation is to break 14 down into parts and multiply each part by 6.
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( begin{aligned} 14 &=10+4 quad text { So, } 14 cdot 6 &=10 cdot 6+4 cdot 6 &=60+24 &=84 end{aligned})
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You may recall the multiplication computed as ( 14 cdot 6):
( begin{array}{r} 2 14 times quad 6 hline 84 end{array})
In this notation, some of the steps are written down with special notation. The product of 6 and 4(24) is written by putting the 4 in the ones place and writing a 2 up above the 1. This 2 actually stands for 20. Then, 6 is multiplied by 1. We are actually multiplying 6 by 1 ten and adding 20 to get the 80 in 84.
An example of multiplying two two-digit numbers is shown below. When performing this multiplication, each part of each number is multiplied by the other number. The numeric notation and an accompanying description are provided.
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Notice that you are multiplying each of the parts of each number by the parts of the other number. You are doing so in a systematic way, from ones places to tens places. You are also using notation to keep track of what you have regrouped. These are shown with raised numbers.
To keep your columns straight and your work organized, consider using grid paper or lined paper turned sideways so the lines form columns. Here is an example of a problem written on grid paper:
( begin{array}{|l|l|l|l|} hline & & 2 & 3 hline & mathrm{x} & 1 & 2 hline & & color{blue}4 & color{blue}6 hline+ & color{blue}2 & color{blue}3 & color{blue}0 hline & color{red}2 & color{red}7 & color{red}6 hline end{array})
When you are multiplying whole numbers, be sure to line up the digits by their place values. In the example above, the digits in the ones place are lined up: the 2 in 12 is directly below the 3 in 23.
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