A period of time is \(w\) weeks and \(d\) days. Write down an expression, in terms of \(w\) and \(d\), for the total number of days in this period.
Question 1 Report
A period of time is \(w\) weeks and \(d\) days.
Write down an expression, in terms of \(w\) and \(d\), for the total number of days in this period.
Answer Details
To build an expression, convert everything to the same unit first. The answer is wanted in days, so the weeks must be turned into days.
One week is \(7\) days, so \(w\) weeks is
\[ 7\times w=7w \text{ days} \] [B1]
The extra \(d\) days are already in days, so they are simply added on:
\[ 7w+d \] [B1]
Test the expression with numbers to see that it behaves: \(3\) weeks and \(2\) days should be \(23\) days, and \(7\times 3+2=23\).
Two common errors are worth naming. Writing \(w+d\) forgets the conversion entirely, and writing \(7(w+d)\) wrongly multiplies the loose days by \(7\) as well. Only the quantity measured in weeks is multiplied by \(7\). The terms \(7w\) and \(d\) are unlike, so the expression cannot be simplified any further.
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