3. Multiplication and division

Lesson

We have already practiced breaking apart numbers to help us solve multiplication problems . Let's try this problem to review.

Let's use an area model to find 77 \times 3.

a

Fill in the areas of each rectangle.

Worked Solution

b

What is the total area of all four rectangles?

Worked Solution

c

Find 77 \times 3.

Worked Solution

Idea summary

We have different ways we can solve multiplication problems, such as the area method and arrays. But as our numbers get larger, the algorithm method can be more useful.

This video introduces the distributive property.

We want to use the distributive property to rewrite 2\times 19 as easier multiplications.

a

This diagram shows how 2 groups of 19 objects can be split up.

Use the diagram to complete the blank to make the statement true.2\times19=2\times(10+⬚)

Worked Solution

b

Complete the blanks to show how 2 groups of (10+9) can be split up into smaller multiplications.

2\times(10+9)=2\times10 + 2 \times ⬚

Worked Solution

Idea summary

The distributive property of multiplication states that multiplying a sum is the same as multiplying each part and then adding. \begin{aligned} 5 \times 13 &= 5 \times (3+10) \\ &= 5 \times 3+5 \times 10 \end{aligned}

This video shows us how to use the distributive property to solve problems.

We want to find 2 \times 45.

Use the area model to complete the following:

\displaystyle 2\times 45 | \displaystyle = | \displaystyle 2\times \left(40+5\right) |

\displaystyle = | \displaystyle 2\times ⬚ + 2\times5 | |

\displaystyle = | \displaystyle ⬚ + ⬚ | |

\displaystyle = | \displaystyle ⬚ |

Worked Solution

Idea summary

If we have a number sentence such as 5\times 12 it can be rewritten as 5\times 10 + 5\times 2.

This video has another example of using it to solve problems.

We want to find 6 \times 795.

Use the area model to complete the following:

\displaystyle 6\times 795 | \displaystyle = | \displaystyle 6\times \left(700+900+5\right) |

\displaystyle = | \displaystyle 6\times ⬚ + 6\times ⬚ + 6\times ⬚ | |

\displaystyle = | \displaystyle ⬚ + ⬚ + ⬚ | |

\displaystyle = | \displaystyle ⬚ |

Worked Solution

Idea summary

We can represent the distributive property as splitting a rectangle into three parts, finding the area of each part and then adding them together.

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems