4.1 Divisibility and Mental Math

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4.1 Divisibility and Mental Math
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Mental Math

• Is 56 divisible by 7? Think!
• 56 8 x 7
• Is 56 divisible by 4? Think!
• 56 8 x 7, and 4 x 2 8, 56 is divisible by 4.

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Mental Math

• Is 64 divisible by 6?
• No
• Is 93 divisible by 3?
• Yes

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Divisibility Rules

• A whole number is divisible by
• 2, if the number ends in 0, 2, 4, 6, or 8.
• 3, if the sum of the numbers digits is divisible
  by 3.
• 5, if the number ends in 0 or 5
• 9, if the sum of the numbers digits is divisible
  by 9
• 10, if the number ends in 0.

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Divisibility by 2, 5, 10

• Ends in
• Test each number for divisibility by 2, 5, 10
• 150
• 1,021
• 2,112
• 65
• 100

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Divisibility by 3

• Sum of numbers digits is divisible by 3
• 715
• 7 1 5 13
• 13 is not divisible by 3
• 150
• 1 5 0 6
• 6 is divisible by 3

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Divisibility by 9

• sum of numbers digits is divisible by 9
• 163
• 1 6 3 10
• 10 is not divisible by 9
• 126
• 1 2 6 9
• 9 is divisible by 9

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Try it!

• Test each number for divisibility of 2, 3, 5, 9,
  and 10
• 60
• 48
• 81