Is 30/3 A Whole Number
Whole Numbers
Whole Numbers and Their Bones Properties
Using Whole Numbers
Whole numbers
Place value
Expanded form
Ordering
Rounding whole numbers
Divisibility tests
Operations and Their Backdrop
Commutative property of add-on and multiplication
Associative property
Distributive property
The zero property of addition
The nix property of multiplication
Multiplicative identity
Order of operations
West pigsty Numbers
The whole numbers are the counting numbers and 0. The whole numbers are 0, 1, ii, 3, 4, 5, ...
P lace Value
The position, or place , of a digit in a number written in standard form determines the actual value the digit represents. This table shows the place value for various positions:
| Place (underlined) | Proper noun of Position |
| 1 00 0 | Ones (units) position |
| 1 0 0 0 | Tens |
| 1 0 00 | Hundreds |
| 1 000 | Thousands |
| 1 0 0 0 000 | 10 thousands |
| 1 0 00 000 | Hundred Thousands |
| i 000 000 | Millions |
| 1 0 0 0 000 000 | Ten Millions |
| one 0 00 000 000 | Hundred millions |
| i 000 000 000 | Billions |
E xample:
The number 721040 has a 7 in the hundred thousands place, a 2 in the ten thousands identify, a one in the thousands place, a iv in the tens place, and a 0 in both the hundreds and ones place.
Expanded Form
The expanded form of a number is the sum of its various place values.
Example:
9836 = 9000 + 800 + 30 + vi.
Ordering
Symbols are used to show how the size of 1 number compares to another. These symbols are < (less than), > (greater than), and = (equals.) For example, since ii is smaller than 4 and iv is larger than 2, nosotros can write: two < 4, which says the same equally 4 > 2 and of form, 4 = four.
To compare ii whole numbers, first put them in standard form. The 1 with more digits is greater than the other. If they have the same number of digits, compare the virtually significant digits (the leftmost digit of each number). The 1 having the larger significant digit is greater than the other. If the most pregnant digits are the same, compare the next pair of digits from the left. Repeat this until the pair of digits is dissimilar. The number with the larger digit is greater than the other.
Case: 402 has more digits than 42, so 402 > 42.
Case: 402 and 412 have the same number of digits. We compare the leftmost digit of each number: four in each case. Moving to the right, we compare the next two numbers: 0 and i. Since 0 < i, 402 < 412.
Rounding Whole Numbers
To round to the nearest x means to detect the closest number having all zeros to the correct of the tens identify. Note: when the digit 5, 6, 7, 8, or 9 appears in the ones identify, round upwardly; when the digit 0, 1, 2, three, or 4 appears in the ones place, round down.
Examples:
Rounding 119 to the nearest ten gives 120.
Rounding 155 to the nearest 10 gives 160.
Rounding 102 to the nearest ten gives 100.
Similarly, to circular a number to any place value, we find the number with zeros in all of the places to the right of the place value beingness rounded to that is closest in value to the original number.
Examples:
Rounding 180 to the nearest hundred gives 200.
Rounding 150090 to the nearest hundred thou gives 200000.
Rounding 1234 to the nearest thousand gives 1000.
Rounding is useful in making estimates of sums, differences, etc.
Example:
To estimate the sum 119360 + 500 to the nearest thousand, first round each number in the sum, resulting in a new sum of 119000 + 1000.. So add to go the gauge of 120000.
Divisibility Tests
There are many quick ways of telling whether or not a whole number is divisible by certain basic whole numbers. These can be useful tricks, especially for large numbers.
Commutative Holding of Addition and Multiplication
Addition and Multiplication are commutative: switching the lodge of two numbers being added or multiplied does not alter the result.
Examples:
100 + 8 = 8 + 100
100 × 8 = viii × 100
Associative Property
Addition and multiplication are associative: the order that numbers are grouped in addition and multiplication does not affect the event.
Examples:
(2 + 10) + vi = two + (10 + 6) = xviii
2 × (ten × vi) = (two × 10) × six =120
Distributive Property
The distributive holding of multiplication over addition: multiplication may be distributed over addition.
Examples:
10 × (50 + 3) = (ten × 50) + (x × 3)
3 × (12+99) = (three × 12) + (iii × 99)
The Nada Property of Addition
Calculation 0 to a number leaves information technology unchanged. We call 0 the condiment identity.
Example:
88 + 0 = 88
The Zero Property of Multiplication
Multiplying whatsoever number by 0 gives 0.
Example:
88 × 0 = 0
0 × 1003 = 0
The Multiplicative Identity
We call 1 the multiplicative identity. Multiplying any number by 1 leaves the number unchanged.
Example:
88 × 1 = 88
Club of Operations
The club of operations for complicated calculations is every bit follows:
i) Perform operations within parentheses.
2) Multiply and divide, whichever comes first, from left to correct.
3) Add and subtract, whichever comes first, from left to right.
Instance:
1 + 20 × (half-dozen + 2) ÷ 2 =
ane + 20 × 8 ÷ 2 =
1 + 160 ÷ ii =
1 + fourscore =
81.
Divisibility by 2
A whole number is divisible by ii if the digit in its units position is even, (either 0, 2, 4, 6, or 8).
Examples:
The number 84 is divisible by 2 since the digit in the units position is 4, which is even.
The number 333336 is divisible by 2 since the digit in the units position is 6, which is fifty-fifty.
The number 1297000 is divisible by two since the digit in the units position is 0, which is even.
Divisibility by iii
A whole number is divisible by 3 if the sum of all its digits is divisible past 3.
Examples:
The number 177 is divisible past iii, since the sum of its digits is 15, which is divisible by 3.
The number 8882151 is divisible by three, since the sum of its digits is 33, which is divisible by 3.
The number 162345 is divisible by three, since the sum of its digits is 21, which is divisible by 3.
If a number is not divisible by iii, the remainder when it is divided past 3 is the same as the residue when the sum of its digits is divided by iii.
Examples:
The number 3248 is not divisible by 3, since the sum of its digits is 17, which is not divisible by three. When 3248 is divided by iii, the remainder is 2, since when 17, the sum of its digits, is divided by 3, the remainder is 2.
The number 172345 is not divisible past 3, since the sum of its digits is 22, which is non divisible by 3. When 172345 is divided by 3, the remainder is ane, since when 22, the sum of its digits, is divided by three, the remainder is i.
Divisibility past four
A whole number is divisible by 4 if the number formed past the terminal two digits is divisible by iv.
Examples:
The number 3124 is divisible past 4 since the number formed by its last two digits, 24, is divisible by iv.
The number 1333336 is divisible by 4 since the number formed by its concluding two digits, 36, is divisible by 4.
The number 1297000 is divisible by 4 since the number formed past its last 2 digits, 0, is divisible by four.
If a number is not divisible by 4, the remainder when the number is divided by 4 is the same as the remainder when the concluding 2 digits are divided by 4.
Example:
The number 172345 is not divisible by 4, since the number formed by its concluding ii digits, 45, is not divisible by 4. When 172345 is divided past 4, the remainder is 1, since when 45 is divided by iv, the remainder is ane.
Divisibility by five
A whole number is divisible by 5 if the digit in its units position is 0 or 5.
Examples:
The number 95 is divisible by 5 since the last digit is 5.
The number 343370 is divisible by 5 since the terminal digit is 0.
The number 129700195 is divisible by five since the last digit is five.
If a number is not divisible by 5, the residual when information technology is divided by 5 is the same as the remainder when the last digit is divided by 5.
Instance:
The number 145632 is not divisible by 5, since the last digit is 2. When 145632 is divided by v, the remainder is ii, since two divided by 5 is 0 with a remainder of 2.
The number 7332899 is not divisible by 5, since the concluding digit is ix. When 7332899 is divided by five, the residual is iv, since 9 divided by 5 is 1 with a residuum of four.
Divisibility by 6
A number is divisible by half dozen if it is divisible by two and divisible by 3. We can use each of the divisibility tests to cheque if a number is divisible by 6: its units digit is fifty-fifty and the sum of its digits is divisible past three.
Examples:
The number 714558 is divisible by half dozen, since its units digit is even, and the sum of its digits is thirty, which is divisible by 3.
The number 297663 is not divisible by half dozen, since its units digit is not even.
The number 367942 is not divisible by 6, since it is non divisible past iii. The sum of its digits is 31, which is not divisible past 3, and then the number 367942 is not divisible past three.
Divisibility by 8
A whole number is divisible by viii if the number formed past the last three digits is divisible by 8.
Examples:
The number 88863024 is divisible past 8 since the number formed past its last iii digits, 24, is divisible by viii.
The number 17723000 is divisible by 8 since the number formed by its last three digits, 0, is divisible past 8.
The number 339122483984 is divisible past eight since the number formed past its last 3 digits, 984, is divisible by 8.
If a number is not divisible past viii, the remainder when the number is divided past 8 is the same as the balance when the last three digits are divided by 8.
Instance:
The number 172045 is non divisible by eight, since the number formed by its last 3 digits, 45, is not divisible by viii. When 172345 is divided past 8, the remainder is 5, since when 45 is divided past 8, the remainder is 5.
Divisibility by 9
A whole number is divisible by nine if the sum of all its digits is divisible by ix.
Examples:
The number 1737 is divisible by nine, since the sum of its digits is eighteen, which is divisible past 9.
The number 8882451 is divisible by nine, since the sum of its digits is 36, which is divisible by nine.
The number 762345 is divisible by nine, since the sum of its digits is 27, which is divisible by nine.
If a number is not divisible by nine, the residual when it is divided by 9 is the same as the remainder when the sum of its digits is divided past 9.
Examples:
The number 3248 is not divisible by nine, since the sum of its digits is 17, which is not divisible past 9. When 3248 is divided by 9, the remainder is 8, since when 17, the sum of its digits, is divided by ix, the remainder is eight.
The number 172345 is non divisible by 9, since the sum of its digits is 22, which is non divisible by 9. When 172345 is divided by 9, the rest is iv, since when 22, the sum of its digits, is divided by 9, the remainder is four.
Divisibility by 10
A whole number is divisible by x if the digit in its units position is 0.
Examples:
The number 1229570 is divisible by x since the last digit is 0.
The number 676767000 is divisible by 10 since the last digit is 0.
The number 129700190 is divisible past 10 since the last digit is 0.
If a number is not divisible by ten, the remainder when it is divided by 10 is the same equally the units digit.
Examples:
The number 145632 is non divisible by 10, since the last digit is ii. When 145632 is divided by 10, the rest is 2, since the units digit is 2.
The number 7332899 is not divisible by 10, since the concluding digit is 9. When 7332899 is divided past 10, the rest is four, since the units digit is ix.
Divisibility by 11
Starting with the units digit, add every other digit and think this number. Course a new number by adding the digits that remain. If the divergence betwixt these two numbers is divisible past 11, then the original number is divisible by 11.
Examples:
Is the number 824472 divisible by 11? Starting with the units digit, add every other number:ii + iv + 2 = 8. Then add the remaining numbers: seven + four + viii = nineteen. Since the difference between these 2 sums is 11, which is divisible by 11, 824472 is divisible by 11.
Is the number 49137 divisible by 11? Starting with the units digit, add together every other number:vii + 1 + 4 = 12. Then add the remaining numbers: 3 + nine = 12. Since the difference between these two sums is 0, which is divisible by 11, 49137 is divisible by 11.
Is the number 16370706 divisible past eleven? Starting with the units digit, add every other number:6 + seven + vii + 6 = 26. Then add together the remaining numbers: 0 + 0 + 3 + one=4. Since the difference between these two sums is 22, which is divisible by 11, 16370706 is divisible by 11.
Divisibility by 12
A number is divisible by 12 if it is divisible by 4 and divisible by 3. We can use each of the divisibility tests to cheque if a number is divisible by 12: its last two digits are divisible by 4 and the sum of its digits is divisible by 3.
Examples:
The number 724560 is divisible by 12, since the number formed by its last ii digits, 60, is divisible by 4, and the sum of its digits is xxx, which is divisible past 3.
The number 36297414 is not divisible by 12, since the number formed by its concluding two digits, 14, is non divisible past 4.
The number 367744 is not divisible by 12, since it is non divisible by 3. The sum of its digits is 29, which is non divisible by iii, and so the number 367942 is not divisible by 3.
Divisibility by 15
A number is divisible by 15 if information technology is divisible by 3 and divisible past 5. We can use each of the divisibility tests to check if a number is divisible past 15: its units digit is 0 or 5, and the sum of its digits is divisible by 3.
Example:
The number 7145580 is divisible by 15, since its units digit is even, and the sum of its digits is 30, which is divisible past three.
Divisibility by xvi
A whole number is divisible by 16 if the number formed by the last four digits is divisible by 16.
Examples:
The number 898630032 is divisible by 16 since the number formed by its last 4 digits, 32, is divisible by xvi.
The number 1772300000 is divisible by 16 since the number formed by its terminal four digits, 0, is divisible by xvi.
The number 339122481296 is divisible by 16 since the number formed by its concluding four digits, 1296, is divisible by sixteen.
If a number is not divisible by 16, the remainder when the number is divided past 16 is the aforementioned as the remainder when the last four digits are divided past 16.
Example:
The number 172411045 is not divisible by 16, since the number formed by its last 4 digits, 1045, is not divisible by sixteen. When 172411045 is divided by 16, the remainder is 5, since when 1045 is divided by xvi, the balance is five.
Divisibility by eighteen
A number is divisible by 18 if it is divisible by 2 and divisible past 9. We can use each of the divisibility tests to check if a number is divisible by xviii: its units digit is fifty-fifty and the sum of its digits is divisible past 9.
Examples:
The number 7145586 is divisible by 18, since its units digit is even, and the sum of its digits is 36, which is divisible by 9.
The number 2976633 is non divisible by 18, since its units digit is non fifty-fifty.
The number 367942 is not divisible by eighteen, since information technology is non divisible by nine. The sum of its digits is 31, which is not divisible by 9, so the number 367942 is non divisible by ix.
Divisibility by twenty
A number is divisible by 20 if its units digit is 0, and its tens digit is even. In other words, the concluding 2 digits form 1 of the numbers 0, twenty, 40, 60, or 80.
Examples:
The number 3351002760 is divisible by 20, since the number formed by its last ii digits is 60.
The number 802199730000 is divisible by 20, since the number formed by its terminal two digits is 0.
Divisibility past 22
A number is divisible by 22 if it is divisible past the numbers 2 and eleven. We can employ each of the divisibility tests to cheque if a number is divisible by 22: its units digit is even, and the divergence betwixt the sums of every other digit is divisible by 11.
Instance:
Is the number 117524 divisible past 22? The units digit is even, so information technology is divisible by two. The two sums of every other digit are 4 + 5 + 1 = 10 and 2 + 7 + 1 = 10, which take a difference of 0. Since 0 is divisible by 11, 117524 is divisible past 11. Thus, 117524 is divisible by 22, since it is divisible by both 2 and 11.
Divisibility by 25
A number is divisible by 25 if the number formed by the last two digits is any of 0, 25, 50, or 75 (the number formed by its last two digits is divisible by 25).
Examples:
The number 73224050 is divisible by 25, since its last 2 digits grade the number 50.
The number 1008922200 is divisible by 25, since its concluding two digits form the number 0.
Is 30/3 A Whole Number,
Source: https://mathleague.com/index.php?option=com_content&view=article&id=67&Itemid=67
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