Divide by three digit number

### 1.1. Knowledge to remember

a) **1944 : 162**

*Sort in order from left to right:*

- 194 divided by 162 gets 1, write 1 ;

1 times 2 equals 2 ; 4 minus 2 equals 2, write 2 ;

1 times 6 equals 6 ; 9 minus 6 equals 3, write 3 ;

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

- Down 4, got 324 ; 324 divided by 162 gets 2, write 2 ;

2 times 2 equals 4 ; 4 minus 4 equals 2, write 0 ;

2 times 6 equals 12 ; 12 minus 12 equals 0, write 0 remember 1 ;

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

\(\begin{array}{l}

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

{1944}\\

{0324}

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

{162}\\

\hline

{twelfth}

\end{array}} \right.\\

\,\,\,000

\end{array}\)

1944 : 162 = 12.

b) **8469 : 241**

*Sort in order from left to right: *

- 846 divided by 241 gets 3, write 3 ;

3 times 1 equals 3 ; 6 minus 3 equals 3, write 3 ;

3 times 4 equals 12 ; 14 minus 12 equals 2, write 2 remember 1 ;

3 times 2 equals 6, add 1 equals 7 ; 8 minus 7 equals 1, write 1.

- Lower 9, get 1239 ; 1239 divide 241 to get 5, write 5 ;

5 times 1 equals 5 ; 9 minus 5 equals 4, write 0 ;

5 times 4 equals 20 ; 23 minus 20 equals 3, write 3 remember 2 ;

5 times 2 equals 10, adding 2 equals 12 ; 12 minus 12 equals 0, write 0.

\(\begin{array}{l}

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

{8469}\\

{1239}

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

{241}\\

\hline

{35}

\end{array}} \right.\\

\,\,\,034

\end{array}\)

8469 : 241 = 35 (remainder 34).

### 1.2. Textbook exercise solution page 86

**Lesson 1: **Calculate then calculate

a) 2120 : 424 b) 6420 : 321

1935 : 354 4957 : 165

**Solution guide:**

- Set calculated by vertical column, divided in order from left to right.

a)

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

{2120}\\

{\,\,\,000}

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

{424}\\

\hline

5

\end{array}} \right.\) \(\begin{array}{*{20}{c}}

{1935}\\

{\,\,\,165}

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

{354}\\

\hline

5

\end{array}} \right.\)

b)

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

{6420}\\

{\,\,\,000}

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

{321}\\

\hline

{20}

\end{array}} \right.\) \(\begin{array}{*{20}{c}}

{4957}\\

{\,\,\,007}

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

{165}\\

\hline

{30}

\end{array}} \right.\)

**Lesson 2: **Calculate the value of the expression

a) 1995 × 253 + 8910 : 495 b) 8700 : 25 : 4

__Solution guide:__

- Expressions with addition, subtraction, multiplication, and division operations perform multiplication and division first, and then perform addition and subtraction.
- Expressions with only division are performed from left to right, or apply the formula: a : b : c = a : (b × c).

a) 1995 × 253 + 8910 : 495

= 504735 + 18

= 504753

b) 8700 : 25 : 4

= 8700 : (25 × 4)

= 8700 : 100

= 87

**Lesson 3: **There are two stores, each store receives 7128m of fabric. On average, the first shop sells 264m of fabric every day, the second shop sells 297m of fabric. Which store sold out the fabric sooner and how many days earlier?

__Solution guide:__

- Calculating the number of days each shop sells out of that fabric, we take the number of fabrics received by the shop and divide it by the number of fabrics sold in 1 day.
- Compare the results to find out which shop sells out sooner (stores that sell out in a few days will sell out sooner).

*Solution*

The first store sold out the fabric in the number of days :

7128 : 264 = 27 (days)

The second shop sold out the fabric in the number of days :

7128 : 297 = 24 (days)

We have: 27 > 24.

So the 2nd store sold out earlier and earlier the number of days is :

27 – 24 = 3 (days)

Answer: 3 days.

### 1.3. Solve the exercises Textbook Practice page 87

**Lesson 1: **Calculate then calculate

a) 708 : 354 b) 704 : 234

7552 : 236 8770 : 365

9060 : 453 6260 : 156

__Solution guide:__

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

a)

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

{708}\\

{000}

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

{354}\\

\hline

2

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

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

{7552}\\

{\,\,472}

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

{236}\\

\hline

{32}

\end{array}} \right.\\

\,\,\,000

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

{9060}\\

{0000}

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

{453}\\

\hline

{20}

\end{array}} \right.\)

b)

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

{704}\\

{002}

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

{234}\\

\hline

2

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

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

{8770}\\

{1470}

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

{365}\\

\hline

{24}

\end{array}} \right.\\

\,\,\,010

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

{6260}\\

{0020}

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

{156}\\

\hline

{40}

\end{array}} \right.\)

**Lesson 2: **People put candy packets into 24 boxes, each box contains 120 packs. If each box contains 160 packs of tongs, how many boxes will be needed to stack all the candies?

__Solution guide:__

- To calculate the total number of candy packages, multiply the number of candies in a box by the number of boxes.
- Find the number of boxes needed if each box contains 160 candy packages, divide the total number of candy packs by 160.

*Solution*

The total number of candy packs is :

120 x 24 = 2880 (pack)

If each box contains 160 packets, the number of candy boxes needed is:

2880 : 160 = 18 (box)

Answer: 18 boxes.

**Lesson 3: **Calculate in two ways

a) 2205 : (35 × 7) b) 3332 : (4 × 49)

__Solution guide:__

- Method 1: Expressions with brackets are counted in parentheses first, outside the following brackets.
- Method 2: Applying the division of a number by a product: “When dividing a number by a product of two factors, we can divide that number by one factor, and then divide the result by the other factor”.

a) Method 1: Option 2:

2205 : (35 x 7) 2205 : (35 x 7)

= 2205 : 245 = 2205 : 35 : 7

= 9 = 63 : 7

= 9

b) Method 1: Method 2:

3332 : (4 x 49) 3332 : (4 x 49)

= 3332 : 196 = 3332 : 4 : 49

= 17 = 833 : 49

= 17

.

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