Divide by three-digit number (continued)

### 1.1. Knowledge to remember

a) ** 41535 : 195 = ?**

*Sort in order from left to right:*

- 415 divided by 195 gives 2, write 2 ;

2 times 5 equals 10 ; 15 minus 10 equals 5, write 5 remember 1 ;

2 times 9 equals 18, plus 1 equals 19 ; 21 minus 19 equals 2, write 2 remember 2 ;

2 times 1 equals 2, add 2 equals 4 ; 4 minus 4 equals 0, write 0.

- Down 3, get 253 ; 253 divided by 195 gets 1, write 1 ;

1 times 5 equals 5 ; 13 minus 5 equals 8, write 8 remember 1 ;

1 times 9 equals 9, plus 1 equals 10 ; 15 minus 10 equals 5, write 5 remember 1 ;

1 times 1 equals 1, adding 1 equals 2 ; 2 minus 2 equals 0, write 0.

- Down 5, get 585 ; 585 divided by 195 gives 3, write 3 ;

3 times 5 equals 15 ; 15 minus 15 equals 0, write 0 remember 1 ;

3 times 9 equals 27, plus 1 equals 28 ; 28 minus 28 equals 0, write 0 remember 2 ;

3 times 1 equals 1, adding 2 equals 5 ; 5 minus 5 equals 0, write 0.

\(\begin{array}{l}

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

{41535}\\

{0253\,\,\,}

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

{195}\\

\hline

{213}

\end{array}} \right.\\

\,\,\,0585\\

\,\,\,\,\,\,000

\end{array}\)

41535 : 195 = 213.

b) **80120 : 245 = ?**

*Sort in order from left to right:*

- 801 divides 245 to get 3, write 3 ;

3 times 5 equals 15 ; 21 minus 15 equals 6, write 5 remember 2 ;

3 times 4 equals 12, add 2 equals 14 ; 20 minus 14 equals 6, write 6 remember 2 ;

3 times 2 equals 6, add 2 equals 8 ; 8 minus 8 equals 0, write 0.

- Down 2, get 662 ; 662 divided by 245 gives 2, write 2 ;

2 times 5 equals 10 ; 12 minus 10 equals 2, write 2 remember 1 ;

2 times 4 equals 8, plus 1 equals 9 ; 16 minus 9 equals 7, write 7 remember 1 ;

2 times 2 equals 4, add 1 equals 5 ; 6 minus 5 equals 1, write 1.

- Lower 0, get 1720 ; 1720 divided by 245 gives 7, write 7 ;

7 times 5 equals 35 ; 40 minus 35 equals 5, write 5 remember 4 ;

7 times 4 equals 28, adding 4 equals 32 ; 32 minus 32 equals 0, write 0 remember 3 ;

7 times 2 equals 14, add 3 equals 17 ; 17 minus 17 equals 0, write 0.

\(\begin{array}{l}

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

{80120}\\

{0662\,\,\,}

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

{245}\\

\hline

{327}

\end{array}} \right.\\

\,\,\,1720\\

\,\,\,\,\,\,005

\end{array}\)

80120 : 245 = 327 (remainder 5).

### 1.2. Textbook exercise solution page 88

**Lesson 1: **Calculate then calculate

a) 62321 : 307 b) 81350 : 187

**Solution guide:**

- Set the calculation by the vertical column, then divide in order from left to right.

a) b)

\(\begin{array}{l}

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

{62321}\\

{00921}

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

{307}\\

\hline

{203}

\end{array}} \right.\\

\,\,\,\,\,\,000

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

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

{81350}\\

{0655\,\,\,}

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

{187}\\

\hline

{435}

\end{array}} \right.\\

\,\,\,\,0940\\

\,\,\,\,\,\,\,\,\,\,\,\,5

\end{array}\)

**Lesson 2: **Find x

a) x × 405 = 86265 b) 89658 : x = 293

__Solution guide:__

Apply the rules:

- To find the unknown factor, divide the product by the known factor.
- To find the divisor we divide the divisor by the quotient.

a) x × 405 = 86265

x = 86265:405

x = 213

b) 89658 : x = 293

x = 89658 : 293

x = 306

**Lesson 3: **A factory produces 49410 products in a year. On average, how many products does that factory produce per day, knowing a working year of 305 days?

__Solution guide:__

- To find the average number of products per day of production, we take the total number of products produced divided by the number of working days.

*Summary*

305 days: 49410 products

1 day: ….products?

*Solution*

The average number of products produced per day is:

49410 : 305 = 162 (product)

Answer: 162 products.

### 1.3. Solve the exercises Textbook Practice page 89

**Lesson 1: **Calculate then calculate

a) 54322 : 346 b) 106141 : 413

25275 : 108 123220 : 404

86679 : 214 172869 : 258

__Solution guide:__

- Set the calculation by the vertical column, then divide in order from left to right.

a)

\(\begin{array}{l}

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

{54322}\\

{1972\,\,\,}

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

{346}\\

\hline

{157}

\end{array}} \right.\\

\,\,\,\,2422\\

\,\,\,\,\,\,\,000

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

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

{25275}\\

{0367\,\,\,}

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

{108}\\

\hline

{234}

\end{array}} \right.\\

\,\,\,\,0435\\

\,\,\,\,\,\,\,003

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

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

{86679}\\

{01079\,}

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

{214}\\

\hline

{405}

\end{array}} \right.\\

\,\,\,\,\,\,\,009

\end{array}\)

b)

\(\begin{array}{l}

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

{106141}\\

{\,\,\,2354\,}

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

{413}\\

\hline

{257}

\end{array}} \right.\\

\,\,\,\,\,\,\,2891\\

\,\,\,\,\,\,\,\,\,000

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

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

{123220}\\

{\,\,\,\,02020\,}

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

{404}\\

\hline

{305}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,\,\,000

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

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

{172869}\\

{\,\,\,1806\,}

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

{258}\\

\hline

{670}

\end{array}} \right.\\

\,\,\,\,\,\,\,\,0009

\end{array}\)

**Lesson 2:** People evenly divided 18kg of salt into 240 packages. How many grams of salt in each pack?

__Solution guide:__

- Exchange: 18kg = 18000g.
- To calculate the number of grams of salt in each package we take the total grams of salt divided by the number of salt packages to be divided, or perform the division: 18000 : 240.

*Solution*

Exchange: 18kg = 18000g

The number of grams of salt in each packet is:

18000 : 240 = 75(g)

Answer: 75g salt.

**Lesson 3: **A rectangular football field has an area of 7140m^{2}, length 105m.

a) Find the width of the football field;

b) Calculate the perimeter of the football field.

__Solution guide:__

- Width = area : length.
- Perimeter = (length + width) × 2

*Solution*

a) The width of the football field is:

7140 : 105 = 68(m)

b) The perimeter of the football field is:

(105 + 68) × 2 = 346(m)

Answer: a) 68m ;

b) 346m

.

=====

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