Questions: Fill in the blanks and complete the equations for each array.

Fill in the blanks and complete the equations for each array.
Transcript text: Fill in the blanks and complete the equations for each array.
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Solution

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Solution Steps

Step 1: Finding the missing value in the first array

The first array shows 4 x 10 = 40, and 2 x 4 = 8. Then, 10 + 2 = 12 and 40 + 8 = 48, which can be expressed as 12 x 4 = 48 or 12 x (10 + 2) = (4 x 10) + (4 x 2) = 4 x 12

Step 2: Filling the blanks in the equation corresponding to the first array

We found that 12 x 4 = 48 in the previous step, but we are given that the final answer is 96. 96 is the double of 48, so we must have 12 x 8 = 96.

Step 3: Finding the missing values in the second array

We have 10 x 10 = 100 in the second array. Then, for the second row we need a number that multiplied by 10 gives 70, which is 7. Similarly, for the last column, we have 10 x 3 = 30. Adding the rows or the columns, 10 + 7 = 17 and 10 + 3 = 13. In the first array, we had the following equation: 12 x 8 = 96 or 12 x (10 + 2) = (4 x 10) + (4 x 2) = 4 x 12. Since we have 10 x 10 = 100 and 7 x 10 = 70, then 3 x 10 = 30.

Step 4: Filling the blanks in the equation corresponding to the second array

From the previous steps, we found that 10 + 3 = 13 and 10 + 7 = 17. Also 10 x 10 = 100, 10 x 3 = 30, 10 x 7 = 70. Following the logic of the first array, we must have 13 x 7 = (10 + 3) x 7 = 70 + 21 = 91 or 17 x 3 = (10+7)x3 = 30+21 = 51. So, the last equation must be 3 x 17 = 21. This does not seem to be right, because we should have gotten something greater or equal than 91 + something or 51 + something. Let's review what we did.

Following the first array, we have that 10 x 10 = 100 and 3 x 10 = 30. Then 7 x 10 = 70 and 3 x 7 = 21. Then (10+7) x (10+3) = 17 x 13 = 221 = 100 + 70 + 30 + 21, then the equation should be 13 x 17 = 221.

Final Answer:

First array missing values: 10, 8. Equation: 12 x 8 = 96

Second array missing values: 30, 7, 21. Equation: 13 x 17 = 221

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