Division with Remainders (Area Models) — Let's Practice!

Division with Remainders (Area Models) — Let's Practice! exercise

• Find the remainder of a division problem.

  Hints

  To complete the first section of the division diagram, we multiply $6 \times 4$ to get $24$, subtract this from $35$ to get a remainder of $11$, which carries over to the next box in the diagram.

  In the second box on the diagram, there is a ?. What is $11 - 6$? This is the number which should be where the ? is.

  Once you've figured out what $11-6$ is for the first ?, you should notice you cannot divide this by a multiple of $6$ any more so this is also the remainder for the overall calculation.

  Solution

  The remainder for $35 \div 6$ is $5$. Look at the complete area model to see how $6$ divides into $35$, $5$ times and leaves a remainder of $5$.

• Complete the calculation.

  Hints

  For the first box, what is $5 \times 4$? You could also figure out this box by working out the answer to the problem $27 -$? = $7$.

  How many whole multiples of $4$ will divide into 7? This will help you with the box at the top of the area model diagram.

  For the missing box closest to the bottom of the area model diagram, what is $7-4$? It is also the same number as the overall remainder for this problem.

  How many whole multiples of $4$ will fit into $27$? This number will be your answer for the final box on the right side of the area model diagram.

  Solution

  Look at the worked solution of the area model to help with the division problem. $27 \div 4 = 6r3$.

• Match the division sums with their corresponding answers and remainders.

  Hints

  Have a look at the completed area model for the calculation $25 \div 7$ to give you a place to start. You'll notice that $2$ lots of $7$ were subtracted out first and then another single multiple of $7$ was able to be divided out giving a final solution of $3$ r $4$.

  Here is another worked solution for the sum $18 \div 4$ to help you solve this question. In this question, $4$ lots of $4$ can be divided out leaving a remainder of $2$ which cannot have any more multiples of $4$ divided out any further.

  This is another worked example of the sum $32 \div 6$ to help you find the matching pairs. $5$ multiples of $6$ can be divided out leaving us a remainder of $2$.

  Solution

  The correct matching pairs are as follows;

  • $18 \div 4 = 4 r 2$
  • $25 \div 7 = 3 r 4$
  • $31 \div 6 = 5 r 2$
  • $28 \div 5 = 5 r 3$

• Sort the steps into the correct order.

  Hints

  We use area models to help us with division calculations and working out remainders but also to help us break calculations down into smaller, more manageable steps.

  When calculating a division, you would look for how many whole multiples divide into the number. The amount left over is the remainder.

  Solution

  The correct order for the steps is;

  1.) When completing the calculation $38 \div 9$ you can use a method such as an area model to help you break the problem down into smaller, more manageable steps.

  2.) Find a multiple of $9$ that divides $38$ a whole number of times. For example, choose $3$, since $9 \times 3 = 27$ and $38 - 27 = 11$. Show this in the first box of the area model diagram.

  3.) Next, focus on the current remainder, which is $11$ in this example. Notice that you can divide this by another multiple of $9$. This calculation goes into the second box of the area model, showing $9 \times 1 = 9$, so $11 - 9 = 2$.

  4.) There are $4$ multiples of $9$ in $38$ with a remainder of $2$. Thus, $38 \div 9 = 4 $, r $2$.

• Choose the correct answer.

  Hints

  By adding the two digits on the top of the area model diagram, $5+2$ you will get how many whole multiples of $6$ divide into $47$ and the first whole number to add to the diagram.

  If you focus on the second box of the area model diagram and figure out the subtraction, $17-12$, this will be the remainder of the overall division sum and the second missing number.

  Sometimes it can help to do the calculation from scratch, following the area diagram model method, instead of trying to pick it up midway from someone else's work.

  Solution

  The correct solution for $47 \div 6$ is $7$ r $5$.

• Sort the calculations.

  Hints

  There are two approaches to this task: either go through each calculation one by one or scan for those that are part of common times tables and won't result in a remainder.

  Use an area model diagram, like we've done before, to determine which questions have remainders. Look at this example to see how.

  Is it easier to start with the smaller divisor questions like $27 \div 5$ or $20 \div 4$?

  Solution

  The calculations which have a remainder are;

  • $27 \div 5$ as the answer is $5$ r $2$.
  • $38 \div 9$ as the answer is $4$ r $2$.
  • $50 \div 7$ as the answer is $7$ r $1$.

  and the calculations that have no remainder are;

  • $20 \div 4$ as the answer is $5$.
  • $36 \div 6$ as the answer is $6$.
  • $45 \div 9$ as the answer is $5$.