Review of natural numbers

### 1.1. Review of natural numbers

**Lesson 1: **Write according to the pattern

Read number |
Write numbers |
Number includes |

Twenty-four thousand three hundred spirit eight |
24 308 |
2 dozen look, 4 thousand, 3 hundred, 8 units |

One hundred and sixty thousand two hundred and seventy-four |
||

1 237 005 | ||

8 million, 4 thousand, 9 tens |

__Solution guide:__

- To read or write natural numbers we read or write from the top row to the lower row, or from left to right.

Read number | Write numbers | Number includes |

Twenty-four thousand three hundred spirit eight |
24 308 |
2 dozen look, 4 thousand, 3 hundred, 8 units |

One hundred and sixty thousand two hundred and seventy-four |
160 274 |
one hundred thousand, sixty thousand, two hundred, 7 tens, 5 units |

One million two hundred thirty-seven thousand zero hundred and five |
1 237 005 |
1 million, 2 hundred thousand, 3 tens of thousands, 7 thousand, 5 units |

Eight million zero hundred and four thousand zero hundred and ninety |
8 004 090 | 8 million, 4 thousand, 9 tens |

**Lesson 2: **Write each of the following numbers as a sum (in the form)

1763; 5794; 20 292; 190 909

*Template: * 1763 = 1000 + 700 + 60 + 3

__Solution guide:__

- Determine which row the digits are in, and then write the number as the sum.

5794 = 5000 + 700 + 90 + 4

20 292 = 20 000 + 200 + 90 + 2

190 909 = 100 000 + 90 000 + 900 + 9

**Lesson 3:**

a) Read the following numbers and state which row and class the 5 digits 5 in each number belong to:

67 358 ; 851 904; 3 205 700; 195 080 126.

b) State the value of the digit 3 in each of the following numbers:

103; 1379; 8932; 13 064; 3 265 910.

__Solution guide:__

- To read natural numbers we read from the top row to the bottom row, or from left to right.
- The unit class consists of units, tens, and hundreds.
- The thousand class includes thousands, tens of thousands, and hundreds of thousands.
- The million class includes millions, tens of millions, hundreds of millions.

a)

- 67 358 read as: Sixty-seven thousand three hundred and fifty-eight.

Out of 67 358 digits 5 belong to tens, the unit class.

- 851 904 reads: Eight hundred and fifty-one thousand nine hundred and four.

In the number 851 904, the digit 5 belongs to the tens of thousands, class of thousands.

- 3 205 700 reads as Three million two hundred and five thousand seven hundred.

In the number 3 205 700, the digit 5 belongs to the thousands, class of thousands.

- 195 080 126 reads as: One hundred and ninety-five million zero hundred and eighty thousand one hundred and twenty-six.

In the number 195 080 126, the digit 5 belongs to millions, class million.

b) The digit 3 out of 103 is in the unit row, so the value is 3.

The digit 3 out of 1379 is in the hundreds, so the value is 300.

The digit 3 of 8932 is in the tens, so the value is 30.

The digit 3 of 13 064 is in the thousands, so the value is 3000.

The digit 3 out of 3 265 910 is in the millions, so the value is 3 000 000.

**Lesson 4:**

a) In the sequence of natural numbers, by how many units are two consecutive numbers more (or less) apart?

b) What is the smallest natural number?

c) Is there a largest natural number? Why ?

__Solution guide:__

- Based on the theory of the sequence of natural numbers.

a) In the sequence of natural numbers, two consecutive numbers are 1 more (or less) than each other.

b) The smallest natural number is 0.

c) There is no greatest natural number, because adding 1 to any number gives the next natural number.

**Lesson 5: **Write the correct number to get

a) Three consecutive natural numbers:

sixty seven ; …; 69. 798; 799;… …; 1000; 1001.

b) Three consecutive even numbers:

8; ten; … 98; …;102. … ;1000; 1002

c) Three consecutive odd numbers:

51; 53; … 199 ;…; 203. …; 999; 1001

__Solution guide:__

- Two consecutive natural numbers are 1 more or less different from each other.
- Two consecutive even numbers (or two odd numbers) are 2 more or less than each other.

a) 67; 68; 69 798; 799; 800 999; 1000; 1001

b) 8; ten; 12 98; 100; 102 998; 1000; 1002

c) 51; 53; 55 199; 201; 203 997; 999; 1001

### 1.2. Review of natural numbers (continued)

**Lesson 1: **Put >, <, = in the dot

989 … 1321 34 579 … 34 601

27 105 … 7985 150 482 … 150 459

8300 : 10 … 830 72 600 … 726 x 100

__Solution guide:__

Of two natural numbers:

- The number with more digits is the larger number. The number with fewer digits is smaller.
- If two numbers have equal digits, compare each pair of digits in the same row from left to right.

989 < 1321 34 579 < 34 601

27 105 > 7985 150 482 > 150 459

8300 : 10 = 830 72 600 = 726 x 100

**Lesson 2: **Write the following numbers in order from smallest to largest

a) 7426; 999; 7642; 7624.

b) 3158; 3518; 1853; 3190.

__Solution guide:__

- We compare the given numbers then sort them in order from smallest to largest.

a) We have 999 < 7426 < 7624 < 7642.

So the numbers written in order from smallest to largest are: 999; 7426; 7624; 7642.

b) We have: 1853 < 3158 < 3190 < 3518.

So the numbers written in order from smallest to largest are: 1853; 3158; 3190; 3518.

**Lesson 3: **Write the following numbers in order from largest to smallest

a) 1567; 1590; 897; 10261

b) 2476; 4270; 2490; 2518.

__Solution guide:__

- We compare the given numbers and then arrange them in order from largest to smallest.

a) We have: 10261 > 1590 > 1567 > 897.

So the numbers written in order from largest to smallest are: 10261; 1590; 1567; 897.

b) 4270 > 2518 > 2490 > 2476.

So the numbers written in order from largest to smallest are: 4270; 2518; 2490; 2476.

**Lesson 4:**

a) Write the smallest number: there is one digit; have two digits; have three digits.

b) Write the largest number: one digit; have two digits; have three digits.

c) Write the smallest odd number: there is one digit; have two digits; have three digits.

d) Write the largest even number: one digit; have two digits; have three digits.

__Solution guide:__

- Based on the theory of the sequence of natural numbers to write the numbers satisfying the problem requirements.

a) Smallest number: has one digit; have two digits; there are three digits 0 respectively; ten; 100.

b) Largest number : has one digit; have two digits; has three digits respectively 9; 99; 999.

c) Smallest odd number: has one digit; have two digits; has three digits 1 respectively; 11; 101.

d) Largest even number: has one digit; have two digits; has three digits of 8 respectively; 98; 998.

**Lesson 5: **Find x, knowing 57 < x < 62 and

a) x is an even number b) x is an odd number c) x is a round number

__Solution guide:__

- List numbers greater than 57, less than 62 and satisfying the condition of the problem.

a) Even numbers greater than 57 and less than 62 are 58; 60.

So x is: 58; 60

b) The odd numbers greater than 57 and less than 62 are 59; sixty one.

So x is 59; sixty one.

c) Round number greater than 57 and less than 62 is 60. So x is 60.

### 1.3. Review of natural numbers (continued)

**Lesson 1: **In the numbers 605; 7362; 2640; 4136; 1207; 20601

a) Which number is divisible by 2? Which number is divisible by 5?

b) Which number is divisible by 3? Which number is divisible by 9?

c) Which number is divisible by both 2 and 5?

d) Which number is divisible by 5 but not divisible by 3?

e) Which number is not divisible by both 2 and 9 ?

__Solution guide:__

Apply divisibility by 2, 3, 5, 9:

- Numbers ending in 0; 2; 4; 6; 8 is divisible by 2.
- Numbers ending in 0; 5 is divisible by 5.
- Numbers ending in 0 are divisible by both 2 and 5.
- Numbers whose sum of digits is divisible by 3 is divisible by 3.
- Numbers whose sum of digits is divisible by 9 is divisible by 9.

a) The numbers divisible by 2 are: 7362; 2640; 4136.

The numbers divisible by 5 are : 605 ; 2640.

b) The numbers divisible by 3 are: 7362; 2640; 20601.

The numbers divisible by 9 are: 7362; 20601.

c) The numbers that are divisible by both 2 and 5 are : 2640.

d) Numbers that are divisible by 5 but not by 3 are: 605

e) The number that is not divisible by both 2 and 9 is: 605; 1207.

**Lesson 2: **Write the appropriate number in the dot to get

a) …52 is divisible by 3;

b) 1…8 is divisible by 9.

c) 92… is divisible by both 2 and 5.

d) 25… is divisible by both 5 and 3.

__Solution guide:__

Apply divisibility by 2, 3, 5, 9:

- Numbers ending in 0; 2; 4; 6; 8 is divisible by 2.
- Numbers ending in 0; 5 is divisible by 5.
- Numbers ending in 0 are divisible by both 2 and 5.
- Numbers whose sum of digits is divisible by 3 is divisible by 3.
- Numbers whose sum of digits is divisible by 9 is divisible by 9.

a) For the number …52 to be divisible by 3, then ….+ 5 + 2 = …. + 7 is divisible by 3.

So you can write in the dot one of the following numbers: 2, 5, 8.

b) Similarly, for the number 1…8 to be divisible by 9, then 1 + ….+ 8 = 9 +…. is divisible by 9.

So you can write 0 or 9 in the dot.

c) For 92… to be divisible by both 2 and 5, then … must be 0.

So we write 0 in the dot.

d) 25… is divisible by 5 so …. can be 0 or 5.

– If … is 0 we have the number 250.

The number 250 has the sum of its digits 2 + 5 + 0 = 7. Since 7 is not divisible by 3, the number 250 is not divisible by 3 (Type).

– If … is 5 we have the number 255.

The number 255 has the sum of its digits 2 + 5 + 5 = 12 . Since 12 is divisible by 3, the number 255 is divisible by 3 (Choose).

So we write the digit 5 in the dot.

**Lesson 3: **Find x if 23 < x < 31 and x is an odd number divisible by 5.

__Solution guide:__

- Apply divisibility by 5: Numbers ending in 0; 5 is divisible by 5.

x is divisible by 5, so x ends with 0 or 5; x is odd, so x ends with 5.

Since 23 < x < 31, x is 25.

**Lesson 4: **With three zeros; 5; 2 write three-digit numbers (each with all three digits) that are both divisible by 5 and divisible by 2.

__Solution guide:__

- Numbers ending in 0 are divisible by both 2 and 5.

A number that is both divisible by 5 and divisible by 2 must have a digit ending in 0.

Hence with three zeros; 5; 2 we can write three-digit numbers (each number has all three digits) both divisible by 5 and divisible by 2 as: 250; 520.

**Lesson 5: **Mom bought some boxes of oranges and put them on plates. If you arrange 3 fruits on each plate, you will run out of oranges, if you arrange 5 fruits on each plate, you will run out of oranges. Knowing that the number of oranges is less than 20, how many oranges did the mother buy?

__Solution guide:__

If you arrange 3 oranges on each plate, you will run out of oranges, if you arrange 5 oranges on each plate, you will also run out of oranges, so the number of oranges must be a number that is both divisible by 3 and divisible by 5.

- Numbers ending in 0; 5 is divisible by 5.
- Numbers whose sum of digits is divisible by 3 is divisible by 3.

*Solution :*

If you arrange 3 oranges on each plate, you will run out of oranges, if you arrange 5 oranges on each plate, you will also run out of oranges, so the number of oranges must be both divisible by 3 and divisible by 5.

Again, there are less than 20 oranges, so the number must be less than 20.

So the number to find is 15, or mom buys 15 oranges.

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