Review on finding two numbers when knowing the sum and difference of those two numbers
Lesson 1 page 175: Write the correct number in the blank
Sum of two numbers 
318 $318$ 
[1945 $[1945$ 
3271 $3271$ 
Difference of two numbers 
42 $42$ 
eighty seven $eighty\; seven$ 
493 $493$ 
Big number 



Small number 


Solution guide:
Applying formula :
Large number = (Sum + Difference) : 2 ; Small number
$=$(Total
$$Brand) : 2.
Solution :
 Second column:
Big number is : (318 + 42) : 2 = 180
Small number is: 318−180 = 138
Big number is : (1945 + 87): 2 = 1016
Small number is : 1945−1016 = 929
Big number is : (3271 + 493) : 2 = 1882
Small number is : 3271−1882 = 1389
We have the following table of results:
Sum of two numbers 
318 $318$ 
[1945 $[1945$ 
3271 $3271$ 
Difference of two numbers 
42 $42$ 
eighty seven $eighty\; seven$ 
493 $493$ 
Big number 
180 $180$ 
1016 $1016$ 
1882 $1882$ 
Small number 
138 $138$ 
929 $929$ 
1389 $1389$ 
Lesson 2 page 175: Two teams planted 1375 trees. The first team planted 285 more trees than the second team. How many trees can each team plant?
Solution guide:
 Applying formula :
Big number
$=$(Total
$+$Brand) : 2 ; Small number
$=$(Total
$$Brand) : 2.
Solution
We have a diagram:
The number of trees planted by the first team is:
(1375 + 285) : 2 = 830 (tree)
The number of trees planted by the second team is:
1375−830 = 545 (tree)
Answer: Team 1: 830 trees;
Team 2: 545 plants.
Lesson 3 page 175: A rectangular field has a perimeter of 530m
$530m$, width less than length 47m
$47m$. Calculate the area of the field.
Solution guide:
 Calculate half circumference
$=$Perimeter : 2 . Then we have the sum (which is half the circumference) and the difference of the length and the width.
 Find the length and width according to the problem of finding two numbers when the sum and difference of the two numbers are known:
Big number
$=$(Total
$+$Brand) : 2 ; Small number = (Total
$$Brand) : 2.
Solution
Half of the perimeter of the field is:
530 : 2 = 265(m)
We have a diagram:
The width of the field is:
(265−47) : 2 = 109 (m)
The length of the field is:
265−109 = 156 (m)
The area of the field is:
156 × 109 = 17004 (m^{2})
Answer: 17004m^{2}.
Lesson 4 page 175: The average of two numbers is 135. Knowing one of the numbers is 246. Find the other.
Solution guide:
 Sum of two numbers = average × 2.
 Remaining = sum – known term.
Solution
The sum of the two numbers to find is:
135 × 2 = 270
The number to find is :
270−246 = 24
Answer: 24.
Lesson 5, page 175: Find two numbers whose sum is equal to the largest threedigit number and whose difference is equal to the largest twodigit number.
Solution guide:
 Find the largest threedigit number and the largest twodigit number. Then we have the sum and difference of those two numbers.
 Find those two numbers by the formula:
Big number
$=$(Total
$+$Brand) : 2 ; Small number = (Total
$$Brand) : 2.
Solution :
The largest threedigit number is 999. So the sum of the two numbers is 999.
The smallest twodigit number is 9 .
$9$. So the difference of two numbers is 99.
We have a diagram:
Small number is : (999−99) : 2 = 450
Big number is: 450 + 99 = 549
Answer: Large number: 549 ;
Number of babies: 45
$0$.
.
=====
Leave a Reply