Divide a five-digit number by a single-digit number

### 1.1. Knowledge to remember

**37648 : 4 = ?**

\(\begin{array}{l}

\begin{array}{*{20}{c}}

{37648}\\

{16}

\end{array}\left| {\begin{array}{*{20}{c}}

4\\

\hline

{9412}

\end{array}} \right.\\

\,\,\,\,\,\,\,04\\

\,\,\,\,\,\,\,\,\,\,08\\

\,\,\,\,\,\,\,\,\,\,\,\,\,0

\end{array}\)

37648 : 4 = …

- 37 divided by 4 get 9, write 9.

9 times 4 equals 36 ; 37 minus 36 equals 1.

- Down 6, get 16 ; 16 divided by 4 get 4, write 4.

4 times 4 equals 16 ; 16 minus 16 equals 0.

- Lower 4 ; 4 divided by 4 get 1, write 1.

1 times 4 equals 4 ; 4 minus 4 equals 0.

- Lower 8 ; 8 divided by 4 get 2, write 2.

2 times 4 equals 8 ; 8 minus 8 equals 0.

**12485 : 3 = ?**

\(\begin{array}{l}

\begin{array}{*{20}{c}}

{12485}\\

{04}

\end{array}\left| {\begin{array}{*{20}{c}}

3\\

\hline

{4161}

\end{array}} \right.\\

\,\,\,\,\,\,\,18\\

\,\,\,\,\,\,\,\,\,\,05\\

\,\,\,\,\,\,\,\,\,\,\,\,\,2

\end{array}\)

12485 : 3 = … (remainder …)

- 12 divided by 3 get 4, write 4.

4 times 3 equals 12 ; 12 minus 12 equals 0.

- Lower 4 ; 4 divided by 3 get 1, write 1.

1 times 3 equals 3 ; 4 minus 3 equals 1.

- Lose 8, get 18 ; 18 divided by 3 get 6, write 6.

6 times 3 equals 18 ; 18 minus 18 equals 0.

- Lower 5 ; 5 divided by 3 get 1, write 1.

1 times 3 equals 3 ; 5 minus 3 equals 2.

### 1.2. Textbook exercise solution page 163

**Lesson 1:** Calculate

\(\begin{array}{*{20}{c}}

{84848}\\

{}

\end{array}\left| {\begin{array}{*{20}{c}}

{\,\,\,4}\\

\hline

{}

\end{array}} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ ,\,\,\begin{array}{*{20}{c}}

{24693}\\

{}

\end{array}\left| {\begin{array}{*{20}{c}}

{\,\,\,3}\\

\hline

{}

\end{array}} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ ,\,\,\,\begin{array}{*{20}{c}}

{23436}\\

{}

\end{array}\left| {\begin{array}{*{20}{c}}

{\,\,\,3}\\

\hline

{}

\end{array}} \right.\)

**Solution guide:**

- Perform division from left to right.

\(\begin{array}{l}

\begin{array}{*{20}{c}}

{\,\,\,\,\,\,\,\,84848}\\

{04}

\end{array}\left| {\begin{array}{*{20}{c}}

4\\

\hline

{21212}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,\,08\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,04\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,08\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0

\end{array}\) \(\begin{array}{l}

\begin{array}{*{20}{c}}

{\,\,\,\,\,\,\,\,24693}\\

{\,\,\,\,\,\,06}

\end{array}\left| {\begin{array}{*{20}{c}}

3\\

\hline

{8231}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,09\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,03\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0

\end{array}\) \(\begin{array}{l}

\begin{array}{*{20}{c}}

{\,\,\,\,\,\,\,\,23436}\\

{\,\,\,\,\,\,24}

\end{array}\left| {\begin{array}{*{20}{c}}

3\\

\hline

{7812}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,03\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,06\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0

\end{array}\)

**Lesson 2:** A store has 36 550kg of cement, sold \(\frac{1}{5}\) that cement. Ask the store how many kilograms of cement are left?

__Solution guide:__

Yes: 36 550kg

Sold: \(\frac{1}{5}\) number of cement

Rest: ? kg.

– The volume of cement sold by the store is equal to 36 550kg divided by 5.

– The store has the remaining kilograms of cement equal to 36 550kg minus the volume of cement sold.

*Solution*

The store that sold kilograms of cement is:

36 550 : 5 = 7310 (kg)

The store that has the remaining kilograms of cement is:

36 550 – 7310 = 29240 (kg)

Answer: 29240kg.

**Lesson 3:** Calculate the value of the expression

a) 69218 – 26736 : 3

30507 + 27876 : 3

b) (35281 + 51645) : 2

(45405 – 8221) :4

__Solution guide:__

- Expressions containing addition, subtraction, multiplication and division operations are calculated in the order of multiplication and division first; plus, minus later.
- Expressions with parentheses are evaluated in parentheses first, outside parentheses.

69218 – 26736 : 3 = 69218 – 8912 = 60306

30507 + 27876 : 3 = 30507 + 9292 = 39799

(35281 + 51645) : 2 = 86926 : 2 = 43463

(45405 – 8221) : 4 = 37184 : 4 = 9296

**Lesson 4:**

Given 8 triangles, each one looks like this:

Arrange it in the form below:

__Solution guide:__

- Divide the shape to form into the given small triangles.

### 1.3. Textbook exercise solution page 164

**Lesson 1:** Calculate

\(\begin{array}{*{20}{c}}

{14729}\\

{}

\end{array}\left| {\begin{array}{*{20}{c}}

{\,\,\,2}\\

\hline

{}

\end{array}} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ ,\,\,\begin{array}{*{20}{c}}

{16538}\\

{}

\end{array}\left| {\begin{array}{*{20}{c}}

{\,\,\,3}\\

\hline

{}

\end{array}} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ ,\,\,\,\begin{array}{*{20}{c}}

{25295}\\

{}

\end{array}\left| {\begin{array}{*{20}{c}}

{\,\,\,4}\\

\hline

{}

\end{array}} \right.\)

__Solution guide:__

- Divide the numbers in order from left to right.

\(\begin{array}{l}

\begin{array}{*{20}{c}}

{\,\,\,\,\,\,\,\,14729}\\

{\,\,\,\,\,\,07}

\end{array}\left| {\begin{array}{*{20}{c}}

2\\

\hline

{7364}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,twelfth\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,09\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,first

\end{array}\) \(\begin{array}{l}

\begin{array}{*{20}{c}}

{\,\,\,\,\,\,\,\,16538}\\

{\,\,\,\,\,\,15}

\end{array}\left| {\begin{array}{*{20}{c}}

3\\

\hline

{5512}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,03\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,08\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2

\end{array}\) \(\begin{array}{l}

\begin{array}{*{20}{c}}

{\,\,\,\,\,\,\,\,25295}\\

{\,\,\,\,\,\,twelfth}

\end{array}\left| {\begin{array}{*{20}{c}}

4\\

\hline

{6323}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,09\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,15\\

\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3

\end{array}\)

**Lesson 2:** There are 10 250 m of fabric, sew each garment 3m. How many clothes can be sewn at most and how many meters of fabric are left?

__Solution guide:__

*Summary*

3m fabric : One set

10 250m fabric : ? sets and superfluous? m of fabric.

– Perform the division of the given number of meters of fabric by 3m.

– The number of clothes that can be sewn is equal to the quotient of division; balance is the number of meters of excess fabric.

*Solution:*

We have: 10 250 : 3 = 3416 (remainder 2 )

So 10 250m2 of fabric can sew at most 3416 sets of clothes and there is 2m of fabric left over.

Answer: 3416 clothes and 2m extra.

**Lesson 3: **Number ?

The dividend |
Divisor |
Dear |
Surplus |

15725 |
3 |
||

33272 |
4 |
||

42737 |
6 |

__Solution guide:__

- Take the value of the divisor divided by the divisor and then fill in the value of the quotient and remainder in the blanks.

The dividend |
Divisor |
Dear |
Surplus |

15725 |
3 |
5241 |
2 |

33272 |
4 |
8318 |
0 |

42737 |
6 |
7122 |
5 |

.

=====

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