Identify The Multiples Of 11 From The Following Numbers:$\[ \begin{array}{l} 1493, \\ 2827, \\ 3190, \\ 4723, \\ 5192, \\ 6795, \\ 7204, \\ 8426, \\ 9235, \\ 396, \\ 483, \\ 48719 \end{array} \\]To Determine If A Number Is A Multiple Of 11,

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Introduction

In mathematics, identifying multiples of a number is an essential skill that helps us understand the properties and relationships between numbers. In this article, we will focus on identifying multiples of 11 from a given set of numbers. We will discuss the concept of multiples, the rules for determining if a number is a multiple of 11, and then apply these rules to the given set of numbers.

What are Multiples?

A multiple of a number is the product of that number and an integer. In other words, if we multiply a number by an integer, the result is a multiple of that number. For example, 6 is a multiple of 2 because 2 × 3 = 6. Similarly, 12 is a multiple of 3 because 3 × 4 = 12.

Rules for Determining Multiples of 11

To determine if a number is a multiple of 11, we can use the following rules:

  • Rule 1: If the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11, then the number is a multiple of 11.
  • Rule 2: If the number is divisible by 11, then it is a multiple of 11.

Applying the Rules to the Given Set of Numbers

Now that we have discussed the rules for determining multiples of 11, let's apply these rules to the given set of numbers.

1493

To determine if 1493 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 1 + 9 = 10, and the sum of the digits in the even positions is 4 + 3 = 7. The difference between these two sums is 10 - 7 = 3, which is not a multiple of 11. Therefore, 1493 is not a multiple of 11.

2827

To determine if 2827 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 2 + 7 = 9, and the sum of the digits in the even positions is 8 + 2 = 10. The difference between these two sums is 9 - 10 = -1, which is not a multiple of 11. Therefore, 2827 is not a multiple of 11.

3190

To determine if 3190 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 3 + 0 = 3, and the sum of the digits in the even positions is 1 + 9 = 10. The difference between these two sums is 3 - 10 = -7, which is not a multiple of 11. Therefore, 3190 is not a multiple of 11.

4723

To determine if 4723 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 4 + 3 = 7, and the sum of the digits in the even positions is 7 + 2 = 9. The difference between these two sums is 7 - 9 = -2, which is not a multiple of 11. Therefore, 4723 is not a multiple of 11.

5192

To determine if 5192 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 5 + 2 = 7, and the sum of the digits in the even positions is 1 + 9 = 10. The difference between these two sums is 7 - 10 = -3, which is not a multiple of 11. Therefore, 5192 is not a multiple of 11.

6795

To determine if 6795 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 6 + 5 = 11, and the sum of the digits in the even positions is 7 + 9 = 16. The difference between these two sums is 11 - 16 = -5, which is not a multiple of 11. Therefore, 6795 is not a multiple of 11.

7204

To determine if 7204 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 7 + 4 = 11, and the sum of the digits in the even positions is 7 + 0 = 7. The difference between these two sums is 11 - 7 = 4, which is not a multiple of 11. Therefore, 7204 is not a multiple of 11.

8426

To determine if 8426 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 8 + 6 = 14, and the sum of the digits in the even positions is 8 + 2 = 10. The difference between these two sums is 14 - 10 = 4, which is not a multiple of 11. Therefore, 8426 is not a multiple of 11.

9235

To determine if 9235 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 9 + 5 = 14, and the sum of the digits in the even positions is 9 + 3 = 12. The difference between these two sums is 14 - 12 = 2, which is not a multiple of 11. Therefore, 9235 is not a multiple of 11.

396

To determine if 396 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 3 + 6 = 9, and the sum of the digits in the even positions is 3 + 9 = 12. The difference between these two sums is 9 - 12 = -3, which is not a multiple of 11. Therefore, 396 is not a multiple of 11.

483

To determine if 483 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 4 + 3 = 7, and the sum of the digits in the even positions is 8 + 3 = 11. The difference between these two sums is 7 - 11 = -4, which is not a multiple of 11. Therefore, 483 is not a multiple of 11.

48719

To determine if 48719 is a multiple of 11, we can use Rule 1. The sum of the digits in the odd positions is 4 + 7 + 9 = 20, and the sum of the digits in the even positions is 8 + 1 = 9. The difference between these two sums is 20 - 9 = 11, which is a multiple of 11. Therefore, 48719 is a multiple of 11.

Conclusion

Q: What is a multiple of 11?

A: A multiple of 11 is a number that can be expressed as the product of 11 and an integer. In other words, if we multiply 11 by an integer, the result is a multiple of 11.

Q: How do I determine if a number is a multiple of 11?

A: To determine if a number is a multiple of 11, we can use the following rules:

  • Rule 1: If the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11, then the number is a multiple of 11.
  • Rule 2: If the number is divisible by 11, then it is a multiple of 11.

Q: What is the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions?

A: The difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is calculated by subtracting the sum of the digits in the even positions from the sum of the digits in the odd positions.

Q: How do I calculate the sum of the digits in the odd positions and the sum of the digits in the even positions?

A: To calculate the sum of the digits in the odd positions and the sum of the digits in the even positions, we need to follow these steps:

  1. Write down the number.
  2. Separate the digits into two groups: the odd-positioned digits and the even-positioned digits.
  3. Add up the digits in each group.
  4. Subtract the sum of the digits in the even positions from the sum of the digits in the odd positions.

Q: What is the significance of the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions?

A: The difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is used to determine if a number is a multiple of 11. If the difference is a multiple of 11, then the number is a multiple of 11.

Q: Can I use a calculator to determine if a number is a multiple of 11?

A: Yes, you can use a calculator to determine if a number is a multiple of 11. However, it is recommended to use the rules for determining multiples of 11 to ensure accuracy.

Q: Are there any other ways to determine if a number is a multiple of 11?

A: Yes, there are other ways to determine if a number is a multiple of 11. One way is to use the divisibility rule for 11, which states that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11.

Q: Can I use the divisibility rule for 11 to determine if a number is a multiple of 11?

A: Yes, you can use the divisibility rule for 11 to determine if a number is a multiple of 11. The divisibility rule for 11 states that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11.

Q: What are some examples of numbers that are multiples of 11?

A: Some examples of numbers that are multiples of 11 include:

  • 11
  • 22
  • 33
  • 44
  • 55
  • 66
  • 77
  • 88
  • 99
  • 110
  • 121
  • 132
  • 143
  • 154
  • 165
  • 176
  • 187
  • 198
  • 209
  • 220
  • 231
  • 242
  • 253
  • 264
  • 275
  • 286
  • 297
  • 308
  • 319
  • 330
  • 341
  • 352
  • 363
  • 374
  • 385
  • 396
  • 407
  • 418
  • 429
  • 440
  • 451
  • 462
  • 473
  • 484
  • 495
  • 506
  • 517
  • 528
  • 539
  • 550
  • 561
  • 572
  • 583
  • 594
  • 605
  • 616
  • 627
  • 638
  • 649
  • 660
  • 671
  • 682
  • 693
  • 704
  • 715
  • 726
  • 737
  • 748
  • 759
  • 770
  • 781
  • 792
  • 803
  • 814
  • 825
  • 836
  • 847
  • 858
  • 869
  • 880
  • 891
  • 902
  • 913
  • 924
  • 935
  • 946
  • 957
  • 968
  • 979
  • 990
  • 1001
  • 1012
  • 1023
  • 1034
  • 1045
  • 1056
  • 1067
  • 1078
  • 1089
  • 1100
  • 1111
  • 1122
  • 1133
  • 1144
  • 1155
  • 1166
  • 1177
  • 1188
  • 1199
  • 1210
  • 1221
  • 1232
  • 1243
  • 1254
  • 1265
  • 1276
  • 1287
  • 1298
  • 1309
  • 1310
  • 1321
  • 1332
  • 1343
  • 1354
  • 1365
  • 1376
  • 1387
  • 1398
  • 1409
  • 1410
  • 1421
  • 1432
  • 1443
  • 1454
  • 1465
  • 1476
  • 1487
  • 1498
  • 1509
  • 1510
  • 1521
  • 1532
  • 1543
  • 1554
  • 1565
  • 1576
  • 1587
  • 1598
  • 1609
  • 1610
  • 1621
  • 1632
  • 1643
  • 1654
  • 1665
  • 1676
  • 1687
  • 1698
  • 1709
  • 1710
  • 1721
  • 1732
  • 1743
  • 1754
  • 1765
  • 1776
  • 1787
  • 1798
  • 1809
  • 1810
  • 1821
  • 1832
  • 1843
  • 1854
  • 1865
  • 1876
  • 1887
  • 1898
  • 1909
  • 1910
  • 1921
  • 1932
  • 1943
  • 1954
  • 1965
  • 1976
  • 1987
  • 1998
  • 2009
  • 2010
  • 2021
  • 2032
  • 2043
  • 2054
  • 2065
  • 2076
  • 2087
  • 2098
  • 2109
  • 2110
  • 2121
  • 2132
  • 2143
  • 2154
  • 2165
  • 2176
  • 2187
  • 2198
  • 2209
  • 2210
  • 2221
  • 2232
  • 2243
  • 2254
  • 2265
  • 2276
  • 2287
  • 2298
  • 2309
  • 2310
  • 2321
  • 2332
  • 2343
  • 2354
  • 2365
  • 2376