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# Modular Arithmetic Operations

Considering the remainder "modulo" an integer is a powerful, foundational tool in Number Theory. You already use in clocks and work modulo 12.

# Modular Arithmetic Operations Warmup

If all integers are colored in the same pattern as the numbers in this grid, what color is 1234?

If you multiply a blue number by an orange number, what color will the product be?

Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.

If you add a blue number to a yellow number, what color will the sum be?

Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.

If you multiply a green number by a yellow number, what color will the product be?

Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.

What color is $$8 \times 17 \, ?$$

Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.

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