Associative property of addition

### 1.1. Knowledge to remember

Compare the values of the two expressions (a + b) + c and a + (b + c) in the following table:

a |
b |
c |
(a + b )+ c |
a + (b + c) |

5 |
4 |
6 |
(5 + 4) = 6 = 9 + 6 = 15 |
5 + (4 + 6) = 5 + 10 = 15 |

35 |
15 |
20 |
(35 + 15) + 20 = 50 + 20 = 70 |
35 + (15 + 20) = 35 + 35 = 70 |

28 |
49 |
51 |
(28 + 49) + 51 = 77 + 51 = 128 |
28 + (49 +51) = 28 + 100 = 128 |

We see that the values of (a +b) + c and of a + (b + c) are always equal, we write:

(a + b) + c = a + (b + c)

**When we add a sum of two numbers to a third number, we can add the first number to the sum of the second and third numbers.**

*Attention :* We can calculate the value of the expression a + b + c as follows:

a + b + c = (a + b) + c = a + (b + c)

### 1.2. Textbook exercise solution page 45

**Lesson 1:** Calculate by the most convenient way

a) 3254 + 146 + 1698 b) 921 + 898 + 2079

4367 + 199+501 1255 + 436 + 145

4400 + 2148 + 252 467 + 999 + 9533

__Solution guide:__

- Apply the commutative and associative properties of addition to group numbers whose sum is a hundred, round thousand, …

a) 3254 + 146 + 1698 = 3400 + 1698 = 5098

4367 + 199 + 501 = 4367 + (199 + 501) = 4367 + 700 = 5067

4400 + 2148 + 252 = 4400 + (2148 + 252) = 4400 + 2400 = 6800

b) 921 + 898 + 2079 = (921 + 2079) + 898 = 3000 + 898 = 3898

1255 + 436 + 145 = (1255 + 145) + 436 = 1400 + 436 = 1836

467 + 999 + 9533 = (467 + 9533) + 999 = 10 000 + 999 = 10 999

**Lesson 2: **A savings fund receives 75 500 000 VND on the first day, 86 950 000 VND on the second day, 14 500 000 VND on the third day. How much money did the savings fund receive in all three days?

__Solution guide:__

- Amount received on all three days = amount received on the first day + amount received on the second day + amount received on the third day.

*Solution*

All three days the savings fund received the amount of:

75 500 000 + 86 950 000 + 14 500 000 = 176 950 000 (VND)

Answer: 176 950 000 VND.

**Lesson 3:** Write the appropriate number or letter in the dot

a) a + 0 = … + a = …

b) 5 + a = … + 5

c) (a + 28) + 2 = a + (28 + …) = a + …

__Solution guide:__

- Apply the commutative property of addition: a + b = b + a.
- Apply the associative property of addition: (a + b) + c = a + (b + c)

a) a + 0 = 0 + a = a

b) 5 + a = a + 5

c) (a + 28) + 2 = a + (28 + 2) = a + 30

### 1.3. Textbook exercise solution page 46

**Lesson 1:** Set the calculation and then calculate the total

a) 2814 + 1429 + 3046

3925 + 618 + 535

b) 26387 + 14075 + 9210

54293 + 61934 + 7652

**Solution guide:**

- Set the calculation so that the digits are in the same row and column together, then add in order from right to left ie from units to tens and then to hundreds, thousands, …

a)

\(\begin{array}{l}

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

{2814}\\

{1429}\\

{3046}

\end{array}} \\

\,\,\,\,\,7289

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

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

{3925}\\

{\,\,618}\\

{\,\,535}

\end{array}} \\

\,\,\,\,\,5078

\end{array}\)

b)

\(\begin{array}{l}

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

{26387}\\

{14075}\\

{\,\,\,\,9210}

\end{array}} \\

\,\,\,\,\,49672

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

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

{54293}\\

{61934}\\

{\,\,\,\,7652}

\end{array}} \\

\,\,\,\,\,123879

\end{array}\)

**Lesson 2:** Calculate by the most convenient way

a) 96 + 78 + 4 b) 789 + 285 + 15

67 + 21 + 79 448 + 594 + 52

408 + 85 + 92 677 + 969 + 123

__Solution guide:__

- Apply the commutative and associative properties of addition to group together numbers whose sum is a hundred.

a) 96 + 78 + 4 = (96 + 4) + 78 = 100 + 78 = 178

67 + 21 + 79 = 67 + (21 + 79) = 67 + 100 = 167

408 + 85 + 92 = (408 + 92) + 85 = 500 + 85 = 585

b) 789 + 285 + 15 = 789 + (285 + 15) = 789 + 300 = 1089

448 + 594 + 52 = (448 + 52) + 594 = 500 + 594 = 1094

677 + 969 + 123 = (677 + 123) + 969 = 800 + 969 = 1769

**Lesson 3:** Find x

a) x – 306 = 504; b) x + 254 = 680

__Solution guide:__

Apply the rules:

- To find the number to be subtracted, we take the difference plus the minus number.
- To find the unknown term, subtract the known term from the sum.

a) x – 306 = 504 b) x + 254 = 680

x = 504 + 306 x = 680 – 254

x = 810 x = 426

**Lesson 4:** A commune has 5256 people. After a year, the population increased by 79 people. After another year, the population increased by 71 people. Ask:

a) How many people will the population of that commune increase after two years?

b) How many people will there be in the commune after two years?

__Solution guide:__

- Number of people added after two years = number of people added in the first year + number of people added in the second year.
- Population after two years = initial population + additional population after two years.

*Solution*

a) After two years the additional population of the commune is:

79+71 = 150 (person)

b) After two years, the population of that commune will be:

5256+150 = 5406 (person)

Answer: a) 150 people;

b) 5406 people.

**Lesson 5:** A rectangle has length a and width b.

Let P be the perimeter of the rectangle. The formula for calculating the perimeter of a rectangle is:

P = (a + b) x 2

(a, b are in the same unit).

Apply the above formula to calculate the perimeter of the rectangle, knowing :

a) a = 16cm, b = 12cm;

b) a = 45m, b = 15m

__Solution guide:__

- Replace the letters with numbers in the expression P = (a + b) x 2 and then calculate the value of that expression.

a) Perimeter of the rectangle is:

P = (16+12)×2 = 56cm.

b) Perimeter of the rectangle is:

P = (45+15)×2 = 120m.

.

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