Question 4.1.7

1. I’ve taken a number, multiplied it by $5$, and got $35$. What was the original number? Show answer

   To reverse the multiplication by $5$, we need to divide by $5$: \[35\div 5 = 7\] (this is equivalent to asking, ‘What number multiplied by $5$ gives $35$?) Therefore $7$ was the original number.

   

2. I’ve taken a number, added $13$, then divided by $6$, and got $3$. What was the original number? Show answer

   In this case there were two steps: adding $13$, then dividing by $6$. We need to reverse the last step first by multiplying by $6$: \[3\times6 = 18\] (this is equivalent to asking the question, ‘What number divided by $6$ gives $3$?’) Then we reverse the addition by subtracting: \[18 - 13 = 5\] (‘What number added to $13$ gives $18$?’) Therefore the original number was $5$.

   

3. I’ve taken a number, multiplied by $4$, subtracted $8$, and got $4$. What was the original number? Show answer

   To reverse the subtraction of $8$, we add $8$: \[4 + 8 = 12\] (‘What number gives $4$ when $8$ is subtracted from it?’) Then we divide by $4$ to reverse the multiplication: \[12\div 4=3\] (‘What number multiplied by $4$ gives $12$?’) Therefore $3$ was the original number.