PRACTICE: Multiplication and Division

Lesson

Practice

Let's go over some of the  multiplication  and  division  strategies and problems we've looked at. These include:

• using arrays and area models

• partitioning numbers by place value

• using a vertical algorithm

We also looked at using a vertical algorithm to solve  multiplication  or  division  , for larger numbers. This strategy is useful if we need to trade, or regroup.

Examples

Example 1

Multiply 250 by 80.

Worked Solution
Create a strategy

Use the standard algorithm for multiplication to find the product.

Apply the idea

Set up the vertical algorithm: \begin{array}{c} &&2&5&0 \\ &\times &&8&0 \\ \hline &&&& \\ \hline \end{array}

First we will multiply 250 by 0.

Remember that all number that multiply to 0 is equal to 0. So we put 0 in the units, tens, and hundreds place.

\begin{array}{c} &&2&5&0 \\ &\times &&8&0 \\ \hline &&0&0&0 \\ \hline \end{array}

Now we will multiply 250 by the 8 in the tens place. We will write our answer underneath our previous answer.

Since we are multiplying by a number in the tens place we will place a 0 in the units place.

\begin{array}{c} &2&5&0 \\ \times& &8&0 \\ \hline &0&0&0 \\ &&& 0 \\ \hline \end{array}

8\times 0=0 so we put a 0 in the tens place:

\begin{array}{c} &2&5&0 \\ \times& &8&0 \\ \hline &0&0&0 \\ &&0& 0 \\ \hline \end{array}

8\times 5=40 so we put the 0 in the hundreds place and carry the 4 to the hundreds place.

\begin{array}{c} &{}^42&5&0 \\ \times& &8&0 \\ \hline &0&0&0 \\ &0&0& 0 \\ \hline \end{array}

8 \times 2=16 then add the carried 4 to get 20. Put the 0 in the thousands place and the 2 in the ten thousands place.

\begin{array}{c} &&& &{}^42&5&0 \\ &\times &&& &8&0 \\ \hline &&& &0&0&0 \\ &&2&0&0&0& 0 \\ \hline \end{array}

\begin{array}{c} &&& &{}^42&5&0 \\ &\times &&& &8&0 \\ \hline &&& &0&0&0 \\ &+&2&0&0&0& 0 \\ \hline &&2&0&0&0& 0 \\ \hline \end{array}

Example 2

Find the value of 856 \div 8.

Worked Solution
Create a strategy

Use the division algorithm.

Apply the idea

Set up the algorithm.

8 goes into 8 once, so we put a 1 in the hundreds column.

8 goes into 5 zero times with 5 remaining, so we put a 0 in the tens column and carry the 5 to the units column.

8 goes into 56 seven times, so we put a 7 in the units column.

856 \div 8 = 107

Example 3

Find the value of 3244 \div 4.

Worked Solution
Create a strategy

Use the division algorithm.

Apply the idea

Set up the algorithm.

4 goes into 3 zero times with 3 remaining, so we put a 0 in the thousands column and carry the 3 to the hundreds column.

4 goes into 32 eight times, so we put 8 in the hundreds column.

4 goes into 4 one time, so we put a 1 in the tens column.

4 goes into 4 one time, so we put a 1 in the units column.

3244 \div 4 = 811

Idea summary

Arrays and the area models are great to solve multiplication or division problems when there will be no remainder. If we are not sure, we can use the vertical algorithm strategy.

Outcomes

VCMNA209

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations