Question

identifying differences between multiplication and division sort each tile according to whether it describes multiplication or division. whole number multiplication joining groups of equal size the same as repeated addition the inverse of multiplication whole number division splitting into equal - sized groups the inverse of division the same as repeated subtraction

Explanation:

Step1: Analyze Whole Number Multiplication

Multiplication is about combining equal groups. Repeated addition is a way to understand multiplication (e.g., \(3\times4 = 4 + 4 + 4\)). The inverse of multiplication is division, but for multiplication's own descriptions: "joining groups of equal size" and "the same as repeated addition" fit. Also, "the inverse of multiplication" is for division, so we exclude that. So for Whole Number Multiplication, the tiles should be "joining groups of equal size" and "the same as repeated addition".

Step2: Analyze Whole Number Division

Division is splitting into equal - sized groups or is repeated subtraction (e.g., \(12\div3\) can be thought of as how many times 3 can be subtracted from 12). The inverse of division is multiplication, so "the inverse of division" is for multiplication, we exclude that. So for Whole Number Division, the tiles should be "splitting into equal - sized groups" and "the same as repeated subtraction". Also, "the inverse of multiplication" is division (since multiplication and division are inverses), so "the inverse of multiplication" goes to Whole Number Division, and "the inverse of division" goes to Whole Number Multiplication.

Let's match each tile:

• "joining groups of equal size": Multiplication (combining groups)
• "the same as repeated addition": Multiplication (as \(a\times b=\underbrace{b + b+\cdots + b}_{a\text{ times}}\))
• "splitting into equal - sized groups": Division (breaking into groups)
• "the same as repeated subtraction": Division (like \(10\div2\) is how many times 2 is subtracted from 10)
• "the inverse of multiplication": Division (since division undoes multiplication, e.g., if \(3\times4 = 12\), then \(12\div3 = 4\))
• "the inverse of division": Multiplication (since multiplication undoes division, e.g., if \(12\div3 = 4\), then \(3\times4 = 12\))

Answer:

For Whole Number Multiplication: "joining groups of equal size", "the same as repeated addition", "the inverse of division"

For Whole Number Division: "splitting into equal - sized groups", "the same as repeated subtraction", "the inverse of multiplication"