Use Their Knowledge of the Order of Operations to Carry Out Calculations Involving the Four Operations 3 - Reasoning

In this reasoning task, students are required to apply their understanding of the order of operations to solve a problem involving the four basic arithmetic operations: addition, subtraction, multiplication, and division. The problem presents a scenario where the cost of six notebooks is 41p less than the cost of 13 pencils, and the cost of one pencil is given as 83p. To determine the price of one notebook, students must first calculate the total cost of 13 pencils by multiplying the number of pencils (13) by the cost per pencil (83p), resulting in a product of 1,079p. Following this, they subtract the 41p difference to find the cost of six notebooks, which equals 1,038p. Finally, to find the cost of one notebook, they divide this total by the number of notebooks (6), arriving at a quotient of 173p, which is equivalent to £1.73.

The calculation is set out clearly using the order of operations, also known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). The students first multiply, then subtract, and finally divide, without the need for brackets in this instance. The solution is methodically reached by breaking down the problem into smaller, manageable steps and using the correct sequence of operations to ensure accuracy. This exercise not only tests the students' arithmetic skills but also their ability to understand and solve multi-step problems.