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Numerical grid with values arranged in three rows and three columns.

A 3x3 grid with numbers: 50 and 2 in the top row, 20, 1000, and 40 in the middle row, and 3, 150, and 6 in the bottom row.

A 3x3 grid with numbers: 50 and 2 in the top row, 20, 1000, and 40 in the middle row, and 3, 150, and 6 in the bottom row.

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Show Answer Key & Explanations Step-by-step solution for: Choose the correct answer by solving the given multiplication by ...
Looking at the grid, I need to find the missing number in the top-left cell.

Let me examine the relationships between the numbers.

First, let's look at the middle row: 20, 1000, 40
Notice that 20 × 40 = 800, but we have 1000. That doesn't match directly.

What if I consider multiplication with a factor?
20 × 50 = 1000 — oh! And 50 is in the top row, middle column.

Let me check the bottom row: 3, 150, 6
3 × 50 = 150 — yes! Again, 50 is involved.

And the top row: ?, 50, 2
If the pattern holds, then ? × 50 should equal something related to the rightmost number.

Wait — let me think differently.

Look at each column:

Top row: [?], 50, 2
Middle row: 20, 1000, 40
Bottom row: 3, 150, 6

Check if the middle number in each row is the product of the left and right numbers multiplied by 50?

Middle row: 20 × 40 = 800 → 800 × ? = 1000 → not quite.

But 20 × 50 = 1000 — and 50 is above it.

Similarly, 3 × 50 = 150 — again, 50 is above.

So perhaps for each row, the middle number equals the left number times 50?

Middle row: 20 × 50 = 1000 ✓
Bottom row: 3 × 50 = 150 ✓
Top row: ? × 50 = 2? → That would mean ? = 2/50 = 0.04 — unlikely.

Alternative idea: Maybe the middle number is left × right × something?

Middle row: 20 × 40 = 800; 1000 / 800 = 1.25 — not nice.

Another approach: Look at columns.

Column 1: ?, 20, 3
Column 2: 50, 1000, 150
Column 3: 2, 40, 6

In column 2: 50, 1000, 150
1000 ÷ 50 = 20
150 ÷ 50 = 3

Oh! So 1000 = 50 × 20, and 150 = 50 × 3

That means the middle number in each row is 50 times the left number.

So for top row: middle number is 50, which should be 50 × left number → so left number = 50 ÷ 50 = 1

Let me verify with other rows.

Middle row: left = 20, middle = 1000 → 20 × 50 = 1000 ✓
Bottom row: left = 3, middle = 150 → 3 × 50 = 150 ✓
Top row: left = ?, middle = 50 → ? × 50 = 50 → ? = 1

Perfect!

Also, check the right column: 2, 40, 6
Is there a pattern? 2 × 20 = 40, 2 × 3 = 6 — oh! The right number is 2 times the left number of the same row.

Top row: left = 1, right = 2 → 1 × 2 = 2 ✓
Middle row: left = 20, right = 40 → 20 × 2 = 40 ✓
Bottom row: left = 3, right = 6 → 3 × 2 = 6 ✓

Everything checks out!

So the missing number is 1.

Final Answer:
1
Parent Tip: Review the logic above to help your child master the concept of lattice method of multiplication.
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