One of the fun things that we can use number for is to solve riddles or problems.

Here is an example:

+ 7 = 10 what number goes in the box to make this sum correct? |

The answer is 3.

This kind of problem solving is called **Algebra**. It means finding out more
information from the information we already have.

**The best way to solve these puzzles is to always have a good system rather than just guessing.
**
For example in the problem above they have added 7 to the box to make 10. If we subtract 7 from the box and subtract 7 from the ten we have

+ 7 - 7 = 10 - 7 |

+ 0 = 3 |

Now adding nothing to any number does not change it. So the value of the box = 3

Try once again with this problem

+ 12 = 18 |

So what have they done to the box (they have added 12)

What do we do?

We do the opposite we subtract twelve from both sides of the = sign.

+ 12 - 12 = 18 -12 |

+ 0 = 6 so the number must be 6 |

This method seems complicated for easy problems but remember it works for simple and hard problems.

**Here are the steps to follow:**

1. look at the operation they are using ( + - X or ÷ )

2. You then do the ** opposite** (or **inverse operation**) to both sides of the equals sign. When the unknown is on its own, then its value will be on the other side of the equals sign.

**Watch this more complicated example**

? + 3 = 7

Here we have got rid of the empty box and replaced it with a letter. The letter
?

Remember that in algebra when we are multiplying things together we do not show the X sign

So two times P would be written 2P.

**Now try this one:**

? + 6 = 15

1. They have added six to the ? so we must - 6 on both sides of the equals sign

2. ? + 6 - 6 = 15 - 6

3. ? + 0 = 9

4. So ? = 9

5. We should ALWAYS check our answer 9 + 6 = 15. Now we know that it is right.

In the SATS the problems appear harder but have confidence in your working.

**
Try this common SAT type problem using this method you have just revised:**

X 14 = 112. |

What have they done to the box? They have X it by 14!

You should now do the **inverse** (opposite) of X and ÷ both side of the equals sign by 14:

X 14 ÷ 14 = 112 ÷ 14 |

X 1 = 8 |

Check your answer 8 X 14 = 112. So 8 is right.

That wasn't too bad was it? This method needs lots of practice but it is great fun and you can always check out your answers and KNOW that they are right.

We will be setting many of these problems later in the week, so watch out for them.

**
Review**

1. Always do the opposite (inverse) operation to that done to the box, on both sides of the equals sign

2. Check your answer in the original question to make sure it is right.

3. When you use letters instead of empty boxes do not show the X sign E.g. 4n means four times n.

(If n was 3 here, the answer would be 12)

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