Multiplication using distributive law

In a nutshell

The distributive law is a method of multiplying which distributes, or 'spreads out' a multiplier between individual parts of an equation. This can often be used to simplify a question to make it easier to answer. 

The distributive law

You may be given a problem containing brackets and a multiplier. The distributive law can be used as an easier method to solve these questions.

Example 1

Solve the equation below using the distributive law.

$$5(4+12)=$$

Using the distributive law you multiply each term inside the brackets by the multiplier. 

​$$\begin{aligned}(5\times4)&+(5\times12) &= \\20 &+ 60 &= \\ &\underline{80}\end{aligned}$$

You may prefer to do this rather than $$5\times16 = 80$$ as this may be more difficult to calculate.

Note: A number outside of brackets means multiply the contents of the brackets by the number outside. This is an example of 'hidden Maths', where there is an 'invisible' times sign between the number outside the brackets and the opening bracket.

Applying the distributive law

When a multiplication problem is difficult, you can break up each component into simpler parts. Multiply these parts by the multiplier and then add the answers together.  

Example 2

Use the distributive law to solve the equation below.

$$7\times 34 =$$

​$$34$$ can be split into many parts as shown in the diagram. ​

  For this example, $$34$$​ can be broken up into $$30$$ and $$4$$.​

$$\begin{aligned}7&\times(30+4)&=\\(7\times30)&+(7\times4) &= \\210 &+ 28 &= \\ &\underline{238}\end{aligned}$$

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