Final answer:
To increase the size of the fencing 'f' by 20%, you multiply the original size by 1.2, resulting in 'f × 1.2', which reflects 120% of the original fence size.
Step-by-step explanation:
If Josh wants to increase the size of the fencing, 'f', by 20%, the new size of the fence after the increase can be calculated by multiplying the original size 'f' by 120% (or 1.2 in decimal form). This is because the original fence is 100%, and increasing it by 20% results in 120% of the original length. The expression to show the size of the fence after the increase would be f × 1.2. This calculation represents a 20% increase, not a multiplication by a factor of two, four, six or eight as suggested in other examples.
To show the size of the fence after a 20% increase, you can use the expression:
f + 0.2f = 1.2f
This expression represents adding 20% of the original size (0.2f) to the original size (f) to get the new size of the fence (1.2f). For example, if the original fence size is 10 units, the increased size would be 1.2 times that, which is 12 units.