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7’s

7’s. Properties of Number. Divisibility tests. 9’s. 8’s. Chris Clements. <date>. Learning Objective:. <Steps to success>. Divisibility Tests. In this lesson you will learn divisibility tests for multiples of 7, 8 and 9. Do you remember the divisibility test for multiples of 4?.

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7’s

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  1. 7’s Properties of Number Divisibility tests 9’s 8’s Chris Clements

  2. <date> Learning Objective: <Steps to success>

  3. Divisibility Tests In this lesson you will learn divisibility tests for multiples of 7, 8 and 9. Do you remember the divisibility test for multiples of 4? Divisibility test for multiples of 4 Look at the last 2 digits; are they even; if so when you half them are they still even.

  4. Divisibility Tests for multiples of 8 Divisibility test for multiples of 4 Look at the last 2 digits; are they even; if so when you half them are they still even. The test for multiples of 8 is similar. Do you know what changes must be made?

  5. If we wanted to test if 1272 is a multiple of 8 First look at the last 3 digits; 1272 *8 does not go exactly into 100 but does go into a 1000 272 It’s even (so it is definitely a multiple of 2) It’s still even so it must be a multiple of 8 If we half it; If we half it again; It’s still even so it must be a multiple of 4 68 136

  6. Divisibility Tests Divisibility test for multiples of 8 Look at the last 3 digits; are they even; if you half it, is it still even; if so, half it again, the answer must be even. Give it a go; 157 157 176 1,936 848 2,680 1,050 1,050 712 364 364 9,992

  7. Divisibility Tests for multiples of 9 Lets have a look at the first ten multiples of 9. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 What do you notice? 9, 1+8=9, 2+7=9, 3+6=9, 4+5=9, 5+4=9, 6+3=9, 7+2=9, 8+1=9, 9+0=9 The digits add up to 9!

  8. This pattern continues; 9+9=9, 1+0+8=9, 1+1+7=9, 1+2+6=9, 1+3+5=9, 1+4+4=9… Lets find multiples of 9 by doing the divisibility test; sum of the digits = 9. 601 601 2, 256, 075 2,556 1, 458 92, 475 180, 000 18, 000 945 3, 535 3, 535 1,602 5,099 5,099

  9. Divisibility Tests This is the test for multiples of 7 First double the last digit Subtract the rest of the number Answer must be a multiple of 7 • Is 343 divisible by 7; • 343 double the last digit = 6 • 34 – 6 =28 • 28 is a multiple of 7 so 343 is too

  10. Divisibility Tests First double the last digit Subtract the rest of the number Answer must be a multiple of 7 728 182 608 608 2, 142 7, 189 588 721 406 1, 400 801 801 1,4000

  11. Divisibility tests Steps to success Divisibility test for multiples of 8 Look at the last 3 digits; are they even; if you half it, is it still even; if so, half it again, the answer must be even. Divisibility test for multiples of 9 Sum of the digits add up to 9. Divisibility test for multiples of 7 First double the last digit. Subtract the rest of the number. Answer must be a multiple of 7

  12. Activity <type here>

  13. Plenary 40 80 120 160 200 240 280 If this number sequence is extended will the number 2140 be in it. Give reasons. 2 9 4 Write another Three-digit number that as factors of 2 and 7. This three digit number as factors of 2 and 7

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