To multiply 13.75 by 2.25, set them up as shown by arranging the two numbers in columns. We usually put the number with the smaller number of digits at the bottom.
It is not necessary to line up any decimal points in long multiplication as these are dealt with in another way.
Step 1: Firstly, work out 5 × 1375. As mentioned before, we can ignore the decimal point for now. The smaller figures in green are the tens figures carried over. Working from right to left:
5 × 5 = 25
Put the 5 in the appropriate column and carry the 2.
5 × 7 + 2(carried) = 37
Put the 7 in the appropriate column and carry the 3.
5 × 3 + 3(carried) = 18
Put the 8 in the appropriate column and carry the 1.
5 × 1 + 1(carried) = 6
Step 2: We now work out 20 × 1375.
This can be written as 2 × 1375 × 10.
Because we are multiplying by 10, we place 1 zero to the right and then work out 2 × 1375.
2 × 5 = 10
Put the 0 in the appropriate column and carry the 1.
2 × 7 + 1(carried) = 15
Put the 5 in the appropriate column and carry the 1.
2 × 3 + 1(carried) = 7
2 × 1 = 2
Step 3: Lastly, work out 200 × 1375.
This can be written as 2 × 1375 × 100.
Because we are multiplying by 100, we place 2 zeroes to the right and then work out 2 × 1375.
2 × 5 = 10
Put the 0 in the appropriate column and carry the 1.
2 × 7 + 1(carried) = 15
Put the 5 in the appropriate column and carry the 1.
2 × 3 + 1(carried) = 7
2 × 1 = 2
Step 4: Finally the 3 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.
0 + 0 + 5 = 5
0 + 0 + 7 = 7
0 + 5 + 8 = 13
Put the 3 in the appropriate column and carry the 1.
5 + 7 + 6 + 1(carried) = 19
Put the 9 in the appropriate column and carry the 1.
7 + 2 + 1(carried) = 10
Put the 0 in the appropriate column and carry the 1.
2 + 1(carried) = 3
How is the decimal point positioned? 13.75 has 2 digits after the decimal point and 2.25 also has 2 digits after the decimal point making a total of 4 digits after the decimal point.
The final answer must also have 4 digits after the decimal point.
So: 13.75 × 2.25 = 30.9375
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