Operations with Integers | A

Question 1

A Magic Grid of Integers

A grid containing some numbers is given below. Follow the steps as shown until no number is left.

When there are no more unstruck numbers, stop. Multiply the circled numbers. An example is shown below.

Solution

Understand the Question

In this activity, we select numbers from a grid one by one.
Whenever a number is circled, all other numbers in its row and column are struck out so they cannot be picked again.
We continue this process until every row and column has contributed one number, and then find the product of all the circled numbers.

Step 1 · Identify the Circled Numbers

Following the example rounds: Diagram 1

The circled numbers are $-6$ , $14$ , $20$ , and $18$ .

Step 2 · Multiply the Circled Numbers

Multiply the four circled numbers step by step:

First, multiply $-6$ by $14$

\begin{aligned} (-6) \times 14 &= -(6 \times 14) \\[0.6em] &= -84 \end{aligned}

Next, multiply $-84$ by $20$

\begin{aligned} (-84) \times 20 &= -(84 \times 20) \\[0.6em] &= -(84 \times 2 \times 10) \\[0.6em] &= -(168 \times 10) \\[0.6em] &= -1680 \end{aligned}

Finally, multiply $-1680$ by $18$

\begin{aligned} (-1680) \times 18 &= -(1680 \times 18) \\[0.6em] &= -(1680 \times (10 + 8)) \\[0.6em] &= -(1680 \times 10 + 1680 \times 8) \\[0.6em] &= -(16800 + 13440) \\[0.6em] &= -30240 \end{aligned}

Answer

$-30240$

Common Mistakes

Sign Error: Since there is one negative integer ( $-6$ ) and three positive integers, the final product must be negative. Missing the negative sign results in $+30240$ .
Row/Column Overlap: Forgetting to strike out the entire row and column of a circled number can result in incorrectly selecting two numbers from the same row or column.

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