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Why Is a Product of Odd Numbers Always Odd?

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Number Play · Parity of products · 3:13

You'll learn: A product of odd numbers is always odd, because no factor of 2 appears.

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Why Is a Product of Odd Numbers Always Odd?

3:13

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Why Is a Product of Odd Numbers Always Odd?

You'll learn: A product of odd numbers is always odd, because no factor of 2 appears.

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Parity of products

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Why Does One Even Factor Make a Product Even?
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Why Does One Even Factor Make a Product Even?
You'll learn: Counting grid squares shows that one even factor makes the whole product even.

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Parity of expressions

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Use 2n and 2n + 1 to Explain an Expression's Parity
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Use 2n and 2n + 1 to Explain an Expression's Parity
You'll learn: Write numbers as 2n or 2n + 1 to see when an expression is even or odd for every input.
Can an Incomplete Sequence Support a Parity Claim?
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Can an Incomplete Sequence Support a Parity Claim?
You'll learn: Checking a few cases is not enough; a parity claim needs the complete sequence or a general argument.

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Number-grid constraints

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Use Grid Totals and Bounds to Find Missing Numbers
3:05
Use Grid Totals and Bounds to Find Missing Numbers
You'll learn: Use row and column totals and the possible ranges of values to fill a grid's missing numbers.
Check Whether a Number Grid's Clues Can All Be True
3:10
Check Whether a Number Grid's Clues Can All Be True
You'll learn: Check whether all of a grid's clues can be true at once before solving.

Next topic

Constructing magic squares

2

What Do the Magic Sum and Centre Tell Us About a Magic Square?
3:08
What Do the Magic Sum and Centre Tell Us About a Magic Square?
You'll learn: The magic sum and the centre place strong limits on which numbers can go in the corners.
Complete a Magic Square Systematically and Compare Arrangements
3:14
Complete a Magic Square Systematically and Compare Arrangements
You'll learn: One complete magic-square construction needs time for the constraints and completion steps.

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Generalising magic squares

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Why Is a 3×3 Magic Square's Sum 3 Times Its Centre?
2:58
Why Is a 3×3 Magic Square's Sum 3 Times Its Centre?
You'll learn: One general magic-square relationship needs a labelled algebraic grid.
Transform a Magic Square by Adding or Scaling Its Entries
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Transform a Magic Square by Adding or Scaling Its Entries
You'll learn: Adding the same number to every entry, or multiplying every entry, keeps a magic square magic.
Build a Magic Square with Sum Zero Using Negative Numbers
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Build a Magic Square with Sum Zero Using Negative Numbers
You'll learn: Use negative numbers to build a magic square whose rows, columns and diagonals all sum to zero.

Next topic

Fractions multiplied by whole numbers

1

Multiply a Fraction by a Whole Number Using Repeated Groups
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Multiply a Fraction by a Whole Number Using Repeated Groups
You'll learn: A whole number times a fraction is repeated groups of that fraction.

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Working with Fractions

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Multiplying a Fraction by a Whole Number: Repeated Equal Quantities
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Multiplying a Fraction by a Whole Number: Repeated Equal Quantities
You'll learn: Multiplying a Fraction by a Whole Number: Repeated Equal Quantities
Taking One-Fifth of a Whole-Number Quantity
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Taking One-Fifth of a Whole-Number Quantity
You'll learn: Taking One-Fifth of a Whole-Number Quantity
Taking Two-Fifths: Divide First, Then Take the Required Parts
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Taking Two-Fifths: Divide First, Then Take the Required Parts
You'll learn: Taking Two-Fifths: Divide First, Then Take the Required Parts
Multiplication with Mixed Fractions in Sharing and Cost Problems
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