A High School Drama Club presented two performances on William Shakespeare's "Romeo & Juliet" in their mini-theater. On the opening night 1,327 saw their performance. On the following night only 984 attended the show. What was the total attendance at the show?
A number produced when adding numbers is called a sum. If we add 5 and 2, the sum is 7. But let's study the solution to our problem.
Addends
1,327 = 1000 + 300 + 20 + 7
+ 984 = 900 + 80 + 4
= 1000 + 1200 + 100 + 11
= 1000 + 1000 + 200 + 100 + 10 + 1
= 2000 + 300 + 10 + 1
= 2311 (sum)
Therefore, the total attendance at the show was 2311 persons.
The shorter way to add,
1,327
+ 984
2,311
Start adding the digits from the ones column 7 + 4 = 10 + 1. In the sum, write 1 below the ones column and carry 1 ten to the tens column.
Add the tens column: 1 + 2 + 8 = 10 + 1. Write 1 in the tens column and carry 1 hundred to the hundreds column.
Add the hundreds: 1 + 3 + 9 = 10 + 3. Write 3 in the hundreds column and carry 1 thousand to the thousands place.
Add the thousands: 1 + 1 = 2. Write 2 in the thousands place. And so we arrive at the same sum which is 2,311.
Properties of Addition
Commutative Property
Is 4 + 6 = 6 + 4?
If the order or position of the addends is changed does the sum also changes? If no, then you are correct. In general, if a and b are whole numbers then a + b = b + a. And this is the commutative property of addition.
Associative Property
Try adding (1 + 7) + 2. Is it the sum the same with 1 + (7 + 2)?
As you noticed grouping the addends using parenthesis () does not affect the sum.If a, b, and c are three numbers, then (a + b) + c = a + (b + c). This is called the associative property of addition.
Identity Property
Zero is the identity element of addition. If we add 15 and 0 it is 15. Therefore, the sum of zero and a whole number is the whole number itself. In general, a + 0 = 0 + a = a, where any whole number a.
Remember to add two numbers at a time. For example we add the numbers below,
20 + 13 + 45 = 20 + (13 + 45) = 20 + 58 = 78
Let us check our answer: 78 - 58 = 20 or 78 - 20 = 58.
This tells us that to check if our sum is correct, subtract the sum with one of the addends and you will get the other addend.
Try the following:
I. Add and check.
a. 45
72
b. 58
36
c. 345
522
654
d. 25 520
72 587
17 692
II. Add and round off the sum to the nearest thousands.
e. 2 513 + 843 + 12 541+ 54
f. 41 225 + 10 + 5 167 + 890
2,311
Start adding the digits from the ones column 7 + 4 = 10 + 1. In the sum, write 1 below the ones column and carry 1 ten to the tens column.
Add the tens column: 1 + 2 + 8 = 10 + 1. Write 1 in the tens column and carry 1 hundred to the hundreds column.
Add the hundreds: 1 + 3 + 9 = 10 + 3. Write 3 in the hundreds column and carry 1 thousand to the thousands place.
Add the thousands: 1 + 1 = 2. Write 2 in the thousands place. And so we arrive at the same sum which is 2,311.
Properties of Addition
Commutative Property
Is 4 + 6 = 6 + 4?
If the order or position of the addends is changed does the sum also changes? If no, then you are correct. In general, if a and b are whole numbers then a + b = b + a. And this is the commutative property of addition.
Associative Property
Try adding (1 + 7) + 2. Is it the sum the same with 1 + (7 + 2)?
As you noticed grouping the addends using parenthesis () does not affect the sum.If a, b, and c are three numbers, then (a + b) + c = a + (b + c). This is called the associative property of addition.
Identity Property
Zero is the identity element of addition. If we add 15 and 0 it is 15. Therefore, the sum of zero and a whole number is the whole number itself. In general, a + 0 = 0 + a = a, where any whole number a.
Remember to add two numbers at a time. For example we add the numbers below,
20 + 13 + 45 = 20 + (13 + 45) = 20 + 58 = 78
Let us check our answer: 78 - 58 = 20 or 78 - 20 = 58.
This tells us that to check if our sum is correct, subtract the sum with one of the addends and you will get the other addend.
Try the following:
I. Add and check.
a. 45
72
b. 58
36
c. 345
522
654
d. 25 520
72 587
17 692
II. Add and round off the sum to the nearest thousands.
e. 2 513 + 843 + 12 541+ 54
f. 41 225 + 10 + 5 167 + 890
