Relation Between Multiplication and Division
What is a fact family?
A fact family can be defined as a group of math facts created using the same set of numbers.
The fact family has relationships between the three numbers involved.
12, 4 and 3 are the fact family. Where 4 and 3 are parts, while 12 is the whole.
Multiplication and Division Fact Family
Parts of division:
4.1.1 Multiplication facts in division
Robert mother arranged cups in shelves. She arranged 18 cups in 3 rows. How many cups did she arrange in each row?
This array can be shown as the relationship between multiplication and division.
Solution:
Multiplication:
3 rows of 6 cups.
3 x 6 = 18 cups.
Division:
18 cups in 3 equal rows.
18 ÷ 3 = 6.
Robert mother arranged 6 cups in each row.
A fact family shows how multiplication and division are related.
Fact family for 3, 6 and 18:
6 cups are arranged in each row.
Example2:
Richard arranged 12 apples in 3 rows on the table. How many apples did he arrange in each row?
Solution:
Multiplication:
3 rows of 4 apples.
3 x 4 = 12 apples.
Division:
12 apples in 3 equal rows.
12 ÷ 3 = 4.
4 apples in each row.
A fact family shows how multiplication and division are related.
Fact family for 3, 4 and 12:
4 apples are arranged in each row.
4.1.2 Divisor, quotient, dividend
Dividend:
The dividend is the number of objects to be divided.
Divisor:
The divisor is the number by which another number is divided.
Quotient:
The quotient is the answer to a division problem.
Example2:
Ria collected the bird’s images and she arranged them on the chart. There are 32 bird’s images arranged in 4 rows. How many birds did she arrange in each row?
Find 32 ÷ 4?
Solution:
Division:
32 birds in 4 equal rows.
8 bird’s images arranged in each row.
Dividend = 32
Divisor = 4
Quotient = 8.
Example3:
Mercy packed some cookies for her friend. She arranged 25 cookies in 5 rows. How many cookies did she arrange in each row?
Find 25 ÷ 5?
Solution:
Division:
25 cookies in 5 equal rows.
5 cookies are arranged in each row.
Dividend = 25
Divisor = 5
Quotient = 5.
Exercise:
- Write the fact family for 3, 4 and 12.
- Write the fact family for 8, 10 and 80.
- Use the relationship between the multiplication and the division to complete each equation:
- 2 x _____ =12.
12 ÷ 2 = _______. - 3 x _____ =21
21÷ 3 = ______.
- 2 x _____ =12.
- Use the relationship between multiplication and division to complete each equation:
- 2 x 9 = 18.
18 ÷ 2 = _____. - 3 x 8 = 24.
24 ÷ 3 =______.
- 2 x 9 = 18.
- Identify the dividend, divisor, quotient and remainder.
6. Susan is selling raffle tickets for 3 dollars. She collects a total of 40 dollars. Find the total number of tickets she sell?
7. 56 people have been invited to a banquet. The caterer is arranging tables. Each table has 8 people. How many tables are needed?
8. 60 passengers are on the bus. If there are 6 rows of seats on the bus, how many seats are there in each row?
9. Do division and complete the answers in empty spaces.
10. A piece of rope is 81 m long. How many 9 m long pieces can I cut from it?
Concept map:
What have we learned:
- Understand fact family.
- Understand how to use multiplication facts in division.
- Understand how to do division.
- Understand divisor, quotient, dividend.
- Identify divisor, quotient, dividend in the division problem.
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