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Row 1 has orange beads followed by blue beads. Row 2 starts with the blue beads and must have the same total number of beads. How many orange beads go in the ? part, and which property of addition does this show?

Class 6Whole NumbersWhole Numbers
  • A6, associative property
  • B6, commutative property
  • C15, commutative property
  • D3, commutative property

Step-by-Step Solution

Row 1 has beads. Row 2 has 9 blue beads, so it needs orange ones: . Changing the ORDER of the numbers does not change the sum: this is the commutative property. (3 is ; 15 is the whole row.)
Answer: B) 6, commutative property

Key idea: Closure: when an operation 'stays inside' the whole numbers

Adding two whole numbers always gives a whole number — addition is **closed** on whole numbers. Multiplying two whole numbers always gives a whole number — multiplication is **closed** too. But subtraction is **not** closed: 5 − 7 = −2, which is not a whole number. Division is also not closed: 7 ÷ 2 = 3.5, not a whole number. Closure is the property that lets us trust an operation never to take us 'outside' the world of whole numbers.

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