More Multiplication and Division | Year 3 Mathematics IGCSE (Cambridge) - Class 3 PDF Download

Introduction:

In this chapter, we will expand our knowledge of multiplication and division. We will explore how to multiply and divide larger numbers, understand the relationship between multiplication and division, and learn new strategies to solve multiplication and division problems. By the end of this chapter, you will be more confident in multiplying and dividing numbers with ease!

1. Multiplying Larger Numbers

• Multiplying 2-Digit Numbers:

  We can multiply two-digit numbers by breaking the numbers into parts. For example, to multiply 23 by 4, we break it into:

  23 × 4 = (20 × 4) + (3 × 4) = 80 + 12 = 92

  This method makes it easier to multiply larger numbers by using smaller, simpler steps.

• Using the Distributive Property:

  The distributive property helps us break a problem into smaller parts. For example, if we need to multiply 34 by 5, we can split 34 into 30 and 4:

  34 × 5 = (30 × 5) + (4 × 5) = 150 + 20 = 170

  By distributing the multiplication over the addition, we make the problem simpler to solve.

2. Division with Larger Numbers

• Dividing by Single-Digit Numbers:

  To divide a larger number by a single-digit number, we can use long division. For example, to divide 56 by 4, we can write:

  56 ÷ 4 = 14

  We divide 56 into groups of 4 and find that 14 groups can be made. Long division helps us divide larger numbers into smaller parts.

• Using Long Division:

  Long division is a method we use when dividing larger numbers. The steps for dividing 123 by 3 are:

  • First, divide the first digit (1) by 3. 3 goes into 1 zero times, so we look at the next digit (12).
  • Now, divide 12 by 3. 3 goes into 12 four times (3 × 4 = 12).
  • Bring down the next digit (3) and divide 3 by 3, which gives 1. The result is 41.
  • 123 ÷ 3 = 41

3. Multiplication and Division Facts

• The Relationship Between Multiplication and Division:

  Multiplication and division are related. Division is the opposite of multiplication. For example:

  6 × 4 = 24, and 24 ÷ 4 = 6

  We can use our knowledge of multiplication to help with division. If we know that 6 × 4 = 24, we can use this to solve 24 ÷ 4 = 6.

• Using Times Tables to Divide:

  We can use the times tables to help with division. If we need to divide 36 by 6, we can think of the multiplication fact:

  6 × ? = 36

  The answer is 6, so 36 ÷ 6 = 6.

4. Division with Remainders

• What is a Remainder?

  When dividing a number and it doesn't divide exactly, the leftover part is called a remainder. For example:

  7 ÷ 3 = 2 remainder 1

  This means 7 can be divided into two groups of 3, with 1 left over.

• How to Write a Division with a Remainder:

  When you divide and there is a remainder, you can write it like this:

  15 ÷ 4 = 3 remainder 3

  This means that 15 divided by 4 gives 3 whole groups, with a remainder of 3.

• Remainders as Fractions:

  We can also write remainders as fractions. For example, 10 ÷ 3 is 3 remainder 1, which can also be written as:

  3 1/3

5. Word Problems with Multiplication and Division

• Word Problem 1:

  If there are 5 baskets with 6 apples in each, how many apples are there in total?

  5 × 6 = 30 apples

• Word Problem 2:

  If 36 students are divided into 4 equal groups, how many students are in each group?

  36 ÷ 4 = 9 students per group

• Word Problem 3:

  Sarah has 43 marbles. She gives 6 marbles to each friend. How many friends can she give marbles to, and how many marbles are left?

  43 ÷ 6 = 7 friends, remainder 1 marble

6. Practice Questions:

• Multiply 46 by 3.
• Divide 72 by 8.
• What is the quotient of 55 ÷ 4? Write the answer with a remainder.
• Calculate 36 ÷ 6 and explain the steps you took to get the answer.
• If you have 100 apples and you divide them equally into 4 baskets, how many apples are in each basket.