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Using Patterns and Mental Math to Divide

Sep 28, 2022
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Key Concepts

  • Use patterns and mental math to divide
  • Estimate quotients with 2-digit divisors

Introduction

  • Division of whole numbers using division patterns 
  • Understand to use multiples of 10 
  • Understand to use multiplication patterns to find the quotient 
  • Use basic division facts to solve mental math divisions 
  • Estimate using compatible numbers 
  • Check the reasonableness 
  • Understand how to use compatible numbers and patterns to divide whole numbers

Use patterns and mental math to divide 

How to divide whole numbers using division patterns? 

Consider the below real-life scenario to understand pattern divisions: 

A bakery sells chocolates to local grocery stores in boxes; each box has 20 chocolates. How many boxes are used if 80 chocolates are sold? 800 chocolates are sold? 8000 chocolates are sold? 

Number of chocolates sold Number of chocolates per box Number of boxes 
80 20  
800 20  
8,000 20  

How do you use multiplication to divide 8,000 by 20? 

Solving patterns in two methods: 

parallel

Method 1: Multiples of 10 

Use basic facts and patterns with zeros to divide the large numbers.  

Here, the basic fact is

8÷2 = 4

80÷20 = 8 tens÷2 tens = 4

parallel

(using patterns with zeros) 

8,00÷20 = 80 tens÷2 tens = 40

8,000÷20 = 8,00 tens÷2 tens = 400

So, the number of chocolate boxes are: 

Number of chocolates sold Number of chocolates per box Number of boxes 
80 20 
800 20 40 
8,000 20 400 

Method 2: Use multiplication 

20×4=8020×4=80

20×40 = 800

20×400 = 8000

So,

8000÷20 = 400 boxes. 

Example 1: 

Find the quotient of 3,600 using basic division facts and patterns. 

Solution: 

Here we have to solve the question by finding the basic facts of multiplication. 

Step 1: Writing each expression as a multiplication fact. 

Step 2: Mark all the numbers in the basic fact to see the number of zeros to write in the quotient. 

Step 3: If there is a zero, the quotient has one zero less than the dividend. 

Basic division fact: 

36÷6 = 6

3,60÷6 = 60

3,600÷6 = ?

Using multiplication (multiples of 10): 

6×6 = 36

6×60 = 360

6×600 = 3,600

So,

3,600÷6 = 600

∴ The quotient of 3,600 is 600. 

Example 2: 

Using basic division facts, divide

480÷6480÷6

mentally. 

Solution: 

Given 

480÷6

Basic fact = 48÷6 = 8

⇒ 480÷6 = 80

∴ The quotient is 80. 

Estimate quotients with 2-digit divisors 

How to estimate quotients using compatible numbers? 

The following steps explain how do we estimate the quotients with compatible numbers: 

Consider the example 298÷25, use compatible numbers to find the estimated quotient. 

Solution:  

Given  

298÷25

Step 1: First, find the compatible numbers for 298 and 25. 

25 is close to its tens place. So, 25 rounds to 30. 

298 is close to its hundreds place. So, 298 rounds to 300. 

∴ 30 and 300 are compatible numbers. 

Step 2: Divide the compatible numbers. 

Using division patterns, 

300÷30 is the same as 30 tens ÷ 3 tens. 

⇒ 30÷3 = 10

∴ 300÷30 = 10

Step 3: Check for reasonableness. 

10 × 30 = 300 

So, a good estimate of 298÷25 is 10. 

Example 1:  

Estimate 228÷19, using compatible numbers. 

Solution: 

Given

228÷19

19 is close to its tens place. So, 19 rounds to 20. 

228 is close to its hundreds place. So, 228 rounds to 200. 

∴ 20 and 200 are compatible numbers. 

Using division patterns, 

200÷20 is the same as 20 tens ÷ 2 tens. 

⇒ 20÷2=1020÷2=10

∴ 200÷20 = 10

Check for reasonableness. 

10 × 20 = 200 

So, a good estimate of 228÷19 is 10. 

Exercise

Use mental math to find the quotient for the following questions (1 – 5):

  • 240 + 40 = 24tens + 4tens = ____.
  • 180+ 30
  • 6400 = 8
  • 2,800 = 71
  • 45,000 + 90

Estimate using compatible numbers for the following questions (6 – 8):

  • 276 = 42.
  • 5564+ 91.
  • 485 = 92.

A company purchased 225 bottles of milk. Each department needs 12 bottles. Find the
compatible numbers to estimate the number of departments that can get the bottles they
need.

Nancy wants to divide 300 lemons equally among 30 baskets. How many lemons does Nancy
need to fill each basket?

What have we learned

  • Understand division of whole numbers using division patterns
  • Understand to use multiples of 10
  • Understand to use multiplication patterns to find the quotient
  • Use basic division fact to solve mental math divisions
  • Estimate using compatible numbers
  • Check the reasonableness
  • Understand how to use compatible numbers and patterns to divide whole numbers

Concept Map

Concept Map
Concept Map estimate

 

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