Multiplication sums usually fall in to the categories of either “SHORT” multiplication or “LONG” multiplication.
SHORT multiplication is done when one of the numbers involved in a multiplication sum is a smaller single number.
A multiplication sum such as, 26 × 3.
LONG multiplication is used when multiplying larger numbers together.
A sum such as, 27 × 36
This page will introduce the short multiplication method and how it can be used to solve some multiplication sums.
Along with touching on the commutative property of multiplication.
Short Multiplication Method
Let’s look at the multiplication sum 21 × 4.With the short multiplication method we first set up the sum with columns in the same way as we do with addition and subtraction.
\begin{array}{r} &2\space1\\ \times &\space\space\space4\\ \hline \end{array}
Then we work from right to left performing the multiplication, writing each result below each column.
The 3 from the bottom line, will multiply both the 2 and the 3 from the top line.
1 × 4 = 4, 2 × 4 = 8
Giving us the following.
\begin{array}{r} &2\space1\\ \times &\space\space\space4\\ \hline &8\space4 \end{array} 21 × 4 = 84
Commutative Property of Multiplication:
One thing to mention before looking at more examples of short multiplication, is the commutative property of multiplication.Which is that is doesn’t matter which order you perform a multiplication sum in, the answer will be the same.
3 × 4 = 12 , 4 × 3 = 12
So technically it doesn’t matter where you place each number in a short multiplication sum.
But it is generally better practice to place the larger number above.
Examples
1.1
32 × 2
Solution
\begin{array}{r} &3\space2\\ \times &\space\space\space2\\ \hline &6\space4 \end{array}
1.2
25 × 3
Solution
\begin{array}{r} &2\space5\\ \times &\space\space\space3\\ \hline \end{array}
With this short multiplication method example the first multiplication we get is 5 × 3 = 15.
Now in this situation we place the 5 in the answer section.
While carrying the 1 over to the next “TENS” column, it can be written above or below.
\begin{array}{r} &{\tiny{1}}\space\space\\ &2\space5\\ \times &\space\space\space3\\ \hline &\space\space\space5 \end{array}
Now the 1 gets added on to the “TENS” column after the next multiplication has been done.
Adding on before would result in doing 3 × 3 again, resulting in a final answer of 95 which is incorrect.
So we carry out the next multiplication in the “TENS” column as it sits: 2 × 3 = 6.
Then adding the extra 1 on from the 15 that was worked out first, giving 7.
\begin{array}{r} &2\space5\\ \times &\space\space\space3\\ \hline &7\space5 \end{array}
1.3
174 × 3
Solution
This is a bit of a larger multiplication, but the method is the same as before with example (1.2).
Though now we have a “HUNDREDS” column.
H T U
\begin{array}{r} &{\tiny{2}}\space\space{\tiny{1}}\space\space\space\\ &1\space7\space4\\ \times &\space\space\space\space\space\space3\\ \hline &5\space2\space2 \end{array}
Units: 3 × 4 = 12, 2 placed in answer, 1 carried left.
Tens: 3 × 7 + 1 = 22, 2 placed in answer, 2 carried left.
Hund: 3 × 1 + 2 = 5
1.4
4 × 32
Solution
Here 3 × 4 in the “TENS” column gives 12.
This just means that the 1 gets carried over to create a new “HUNDREDS” column in the answer.
\begin{array}{r} &{\tiny{1}}\space\space\space\space\space\space\\ &\space\space\space3\space2\\ \times &\space\space\space\space\space\space4\\ \hline &1\space2\space8 \end{array}
1.5
4 × 416
Solution
Here a new “THOUSANDS” column in the answer will be created with the 4 × 4 multiplication.
\begin{array}{r} &{\space\tiny{1}}\space\space\space\space\space{\tiny{2}}\space\space\space\space\space\space\\ &\space4\space1\space6\\ \times &\space\space\space\space\space\space\space4\\ \hline &1\space6\space6\space4\space\space \end{array}
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