See whole-number multiplication as repeated fractional lots
This is a self-guided version of the lesson: rebuild the meaning, reconnect it to the rule you may remember, then test whether the idea is genuinely secure.
Start with repeated addition
4 × 2/3 means four lots of two thirds: 2/3 + 2/3 + 2/3 + 2/3.
The denominator stays 3 because the pieces are still thirds. Only the number of third-pieces changes.
Diagnostic: if you instinctively multiply the denominator as well, rebuild the repeated-addition picture.
Why only the numerator changes
The whole number counts how many identical lots you have; the numerator counts how many fraction-pieces are in each lot. So 4 lots of 2 thirds gives 8 thirds.
The denominator is not part of the count of lots. It names the size of each piece.
Money makes the structure obvious
Three lots of 1/4 of £1 are 25p + 25p + 25p = 75p. The same with $1 gives 75¢.
Use money whenever the notation feels less intuitive than the arithmetic.
Reconnect answers greater than one
4 × 2/3 = 8/3, and 8 thirds regroup as 2 2/3. This links directly back to mixed numbers.
Move on when…
You can explain the multiplication as repeated addition, justify why the denominator stays fixed, and regroup an improper result when useful.
Use the interactive learner lesson when useful
Use the learner page for the visual examples and interactive practice. Return here for the explanation, diagnostic prompts and bigger-picture connections.
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