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# The Number System

## Undefined Quotient with Fraction Division

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create at least two different examples where the quotient is undefined. Source: Daniel Luevanos

## Multiply to Make -64

Directions: Find three numbers whose product is -64. You may use integers from -10 to 10. You may not use the same absolute value twice. Find all possible combinations. Source: Nathan Charlton and Daniel Martinez

## Subtracting Decimals (Middle School)

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) difference. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

## Dividing Two-Digit Numbers (Middle School)

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) quotient. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

## Adding Two-Digit Numbers (Middle School)

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) sum. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

## Subtracting Two-Digit Numbers (Middle School)

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) difference. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky