We must learn NEVER to be influenced by what things look like: the meaning of dividing by
2, dividing by 5, etc. is clear: the concept of dividing by a quarter is, however, less
straightforward and requires more thought.
Think of 3
1
4
¸ as 'the number of
1
4
's that fit into 3'.
There are 4 quarters in 1, so in 3 there are 3 ´ 4 quarters in 3 as can be seen in the diagram
below.
So 3
1
4
¸ (or
3
1
4
) = 3 ´ 4 = 12 .
Generally n
m
¸ = n ´ m 1
or
n
n m
m ( 1 )= ´
Hence, for example, 5
1
2
¸ = 5 ´ 2 = 10.
The value of 3
1
4
¸ is equivalent to 3 ¸ 4 The division 3
1
4
¸ means how many
1
4
and hence has value
3
4
or 0.75 are there in the number 3. Clearly there are
4 quarters in 1 and hence 3 ´ 4(=12) in 3.
Similarly 5
1
2
¸ is equivalent to 5 ¸ 2 and So 3
1
4
¸ = 12
hence has value 2.5 or 2
1
2
We must learn NEVER to be influenced by what things look like: the meaning of dividing by2, dividing by 5, etc. is clear: the concept of dividing by a quarter is, however, lessstraightforward and requires more thought.Think of 314¸ as 'the number of14's that fit into 3'.There are 4 quarters in 1, so in 3 there are 3 ´ 4 quarters in 3 as can be seen in the diagrambelow.So 314¸ (or314) = 3 ´ 4 = 12 .Generally nm¸ = n ´ m 1ornn mm ( 1 )= ´Hence, for example, 512¸ = 5 ´ 2 = 10.The value of 314¸ is equivalent to 3 ¸ 4 The division 314¸ means how many14and hence has value34or 0.75 are there in the number 3. Clearly there are4 quarters in 1 and hence 3 ´ 4(=12) in 3.Similarly 512¸ is equivalent to 5 ¸ 2 and So 314¸ = 12hence has value 2.5 or 212
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