Problem

Complete addition and multiplication tables

These are parts of an addition table and a multiplication table. In the addition table the header row reads 2, 4, 6 and the left column reads 2, 4, 6, 8, and the cell where left number 4 meets top number 6 is left blank as A. In the multiplication table both the header row and left column read 1, 3, 5, and the cell where left number 3 meets top number 3 is left blank as B, while the cell where left number 5 meets top number 5 is left blank as C. Find the rule for how the numbers change across a row and down a column, then find the numbers for A, B, and C.

Operations

Your answer

How to solve

Strategy Look for a Pattern — Each table cell follows a simple rule — sum or product of its row and column heads — and reading along a row shows a constant step, so I find the pattern and fill each blank from its heads.

1STEP 1

Fill in A in the addition table

A is where left number 4 meets top number 6, so A = 4 + 6 = 10.

4 + 6 = 10

2STEP 2

Set the multiplication rule and fill B

Each multiplication cell is left number x top number, so B (left 3, top 3) is 9.

3 × 3 = 9

3STEP 3

Fill in C

The same rule gives C, where left 5 meets top 5: 5 x 5 = 25.

5 × 5 = 25

Answer

A = 10, B = 9, C = 25

4 + 6 = 10, 3 × 3 = 9, 5 × 5 = 25

Check — in the addition table, 8 then 10 keeps the step-of-2 rule, and in the multiplication table 9 = 3 x 3 and 25 = 5 x 5 both match the left-times-top rule.

Takeaway

Every table cell is set by its left and top numbers. Add for the addition table, multiply for the multiplication table — the same rule gives A=10, B=9, C=25.

Addition table A = 4 + 6 = 10
Multiplication table B = 3 x 3 = 9
Multiplication table C = 5 x 5 = 25

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