Multiply a number by a sum
1.1. Knowledge to remember
Find and calculate the value of two expressions:
4 × (3 + 5) and 4 × 3 + 4 × 5
We have :
4 × (3 + 5) = 4 × 8 = 32
4 × 3 + 4 × 5 = 12 + 20 = 32
So: 4 × (3 + 5) = 4 × 3 + 4 × 5
When we multiply a number by a sum, we can multiply that number by each term of the sum, and then add the results together.
a × (b + c) = a × b + a × c
1.2. Solving Textbook Exercises
Lesson 1: Calculate the value of the expression and then write it in the blank (according to the pattern)
a 
b 
c 
a × (b + c) 
a × b + a × c 
4 
5 
2 
4 × (5 + 2) = 28 
4 × 5 + 4 × 2 = 28 
3 
4 
5 


6 
2 
3 

Solution guide:
 Replace letters with numbers and then evaluate those expressions.
a 
b 
c 
a × (b + c) 
a × b + a × c 
4 
5 
2 
4 × (5 + 2) = 28 
4 × 5 + 4 × 2 = 28 
3 
4 
5 
3 × (4 + 5) = 27 
3 × 4 + 3 × 5 = 27 
6 
2 
3 
6 × (2 + 3) = 30 
6 × 2 + 6 × 3 = 30 
Lesson 2:
a) Calculated in two ways:
36 × (7 + 3); 207 × (2 + 6)
b) Calculated in two ways (according to the form):
Sample: 38 × 6 + 38 × 4 = ?
Method 1: 38 × 6 + 38 × 4 = 228 + 152 = 380
Method 2: 38 × 6 + 38 × 4 = 38 × (6 + 4)
= 38 × 10 = 380
5 × 38 + 5 × 62; 135 × 8 + 135 × 2
Solution guide:
 When we multiply a number by a sum, we can multiply that number by each term of the sum, and then add the results together.
a × (b + c) = a × b + a × c
a) 36 × (7 + 3) = ?
Method 1: 36 × (7 + 3) = 36 × 10 = 360
Method 2: 36 × (7 + 3) = 36 × 7 + 36 × 3 = 360
+) 207 × (2 + 6) = ?
Method 1: 207 × (2 + 6) = 207 × 8 = 1656
Method 2: 207 × (2 + 6) = 207 × 2 + 207 × 6 = 1656
b) 5 × 38 + 5 × 62 =?
Option 1: 5 × 38 + 5 × 62 = 190 + 310 = 500
Option 2: 5 × 38 + 5 × 62 = 5 × (38 + 62) = 5 × 100 = 500
+) 135 × 8 + 135 × 2 = ?
Method 1: 135 × 8 + 135 × 2 = 1080 + 270 = 1350
Method 2: 135 × 8 + 135 × 2 = 135 × (8 + 2) = 135 × 10 = 1350
Lesson 3: Calculate and compare the value of the expression
(3 + 5) × 4 and 3 × 4 + 4 × 5
From the comparison, show how to multiply a sum by a number.
Solution guide:
 Expressions with parentheses are evaluated in parentheses first, outside parentheses.
 For expressions with multiplication and addition, we calculate the multiplication first and the addition later.
We have: (3 + 5) × 4 = 8 × 4 = 32
3 × 4 + 4 × 5 = 12 + 20 = 32
Are the two expressions equal or (3 + 5) × 4 = 3 × 4 + 4 × 5.
When multiplying a sum by a number we can multiply each term of the sum by that number and then add the result together.
Lesson 4: Apply properties of a number to a sum to calculate (in the form)
Template: 36 x 11 = 36 x (10 + 1)
= 36 x 10 + 36 x 1
= 360 + 36 = 396
a) 26 x 11 b) 213 x 11
35 x 101 123 x 101
Solution guide:
 Split 11 = 10 + 1, then apply multiplying a number by a sum to calculate the expression value.
a) 26 x 11 = 26 x (10 + 1)
= 26 x 10 + 26 x 1
= 260 + 26 = 286
35 x 101 = 35 x (100 + 1)
= 35 x 100 + 35 x 1
= 3500 + 35 = 3535
b) 213 x 11 = 213 x (10 + 1)
= 213 x 10 + 213 x 1
= 2130 + 213 = 2343
123 x 101 = 123 x (100 + 1)
= 123 x 100 + 123 x 1
= 12300 + 123 = 12423
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