Multiplication sums in Math are generally sums involving either “SHORT” multiplication or “LONG” multiplication.
SHORT multiplication is performed when one of the numbers contained in a multiplication sum is a single digit number.
For example a multiplication sum such as, 26 × 3.
LONG multiplication is performed when we want to multiply larger numbers together.
For example a sum such as, 27 × 36
This page looks to give a good introduction to the short multiplication method, and how it can be used to answer different multiplication sums.
Short Multiplication Method
We can look at the multiplication sum 23 × 3.Using the short multiplication method we initially write out the sum with columns, in the same way as with addition and subtraction.
\begin{array}{r} &2\space3\\ \times &\space\space\space3\\ \hline \end{array}
We then work from the right to the left performing multiplication, placing each result below each column.
The 3 from the bottom line, will multiply both the 2 and the 3 from the top line.
3 × 2 = 6, 3 × 3 = 9
To give us the following.
\begin{array}{r} &2\space3\\ \times &\space\space\space3\\ \hline &6\space9 \end{array} 23 × 3 = 69
Examples
(1.1)
41 × 2
Solution
\begin{array}{r} &4\space1\\ \times &\space\space\space2\\ \hline &8\space2 \end{array}
(1.2)
46 × 2
Solution
\begin{array}{r} &4\space6\\ \times &\space\space\space2\\ \hline \end{array}
In this short multiplication method example the first multiplication obtained is 2 × 6 = 12.
Now for examples like this we place the 2 in the answer section.
Then we carry the 1 over left to the next “TENS” column, this digit can be written above or below.
\begin{array}{r} &{\tiny{1}}\space\space\\ &4\space6\\ \times &\space\space\space2\\ \hline &\space\space\space6 \end{array}
Now the 1 then gets added in the “TENS” column, but only after the next “TENS” multiplication has been completed.
So we perform the next multiplication in the “TENS” column as is: 3 × 4 = 8.
Then we add on the carried 1 on from the 12 that was worked out first, giving a total of 9.
\begin{array}{r} &{\tiny{1}}\space\space\\ &4\space6\\ \times &\space\space\space2\\ \hline &9\space2 \end{array}
(1.3)
186 × 3
Solution
This is a slightly larger multiplication sum, however the main approach is the same as before with example (1.2).
But here there is also a “HUNDREDS” column.
H T U
\begin{array}{r} &{\tiny{2}}\space\space{\tiny{1}}\space\space\space\\ &1\space8\space6\\ \times &\space\space\space\space\space\space3\\ \hline &5\space5\space8 \end{array}
Units: 3 × 6 = 18, 8 placed in answer, 1 carried over left.
Tens: 3 × 8 + 1 = 25, 2 placed in answer, 5 carried over left.
Hund: 3 × 1 + 2 = 5
(1.4)
3 × 43
Solution
Here 4 × 3 in the “TENS” column results in 12.
What happens is that the 1 digit gets carried left to create a new “HUNDREDS” column in the answer.
\begin{array}{r} &{\tiny{1}}\space\space\space\space\space\space\\ &\space\space\space4\space3\\ \times &\space\space\space\space\space\space3\\ \hline &1\space2\space9 \end{array}
(1.5)
3 × 423
Solution
In this case a new “THOUSANDS” column in the answer is created with the 3 × 4 multiplication in the “HUNDREDS” column.
\begin{array}{r} &{\space\tiny{1}}\space\space\space\space\space\space\space\space\space\space\space\\ &\space4\space2\space3\\ \times &\space\space\space\space\space\space\space3\\ \hline &1\space2\space6\space9\space\space \end{array}
Units: 3 × 3 = 9, 9 placed in answer.
Tens: 3 × 2 + = 6, 6 placed in answer.
Hund: 3 × 4 = 12, 2 placed in answer, 1 carried over left.
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