Multiplying decimals by integers | Year 6 Mathematics PDF Download

Methods for Mathematical Operations

In the realm of mathematical operations like addition, subtraction, multiplication, and division, it's crucial to employ various methods to ensure accuracy and efficiency.
Here are some key points to consider:

• A Formal Written Method:
  • Utilizing a more formal written method, often known as standard written algorithms, can provide a structured approach to solving mathematical problems.
• An Efficient Mental Method:
  • Employing mental methods can offer quick and effective ways to solve calculations without the need for extensive written work.
  • Mental methods may involve using strategies or 'jottings' to aid in remembering intermediate steps towards finding the final answer.
  • Regular practice with formal written methods is essential for building confidence, but mental methods are valuable in situations where they prove to be more efficient.

Understanding Multiplication Using Examples

When we consider the calculation 8.7 multiplied by 6 resulting in 52.2, it opens up a realm of related calculations that can be easily understood and computed.

Example 1:

5.48 lies between 5 and 6.
5.48 rounded to the nearest integer is 5 and 5.5 if rounded to one decimal place.
Therefore we could estimate that the answer would be between 45 (5 x 9) and 54 (6 x 9).

So…

• 5.48 x 900 = 4932 (49.32 x 100)
• 0.548 x 9 = 4.932 (49.32 ÷ 10)
• 5.48 x 18 = 98.64 (49.32 x 2)
• 5.48 x 19 = 104.12 (5.48 x 10) + (5.48 x 9) = 54.8 + 49.32

Example 2:
Sol: 8.7 lies between 8 and 9.
8.7 rounded to the nearest integer is 9.
Therefore we could estimate that the answer would be between 48 (8 x 6) and 54 (9 x 6)
A is an example of a mental method and B an example of a formal written method.
0.7 x 6 is just six lots of seven tenths or 42 tenths or 4.2.