**JSS 1 Mathematics First Term Week 5**

**Topic: USE OF SYMBOLS 1: LETTERS FOR NUMBERS**

Open sentences

14 + □ = 17. What number in the box will make this true? You may have seen problems like this before. 14 + □ = 17 will be true if 3 goes in the box: 14 + 3 = 17 is true,

We say 14 + □ = 17 is an **open sentence**. Any value can go in the box, but usually, only one value can make an open sentence true.

Exercises

1. 3 + 2 = □

2. 8 – 7 = □

3. 7 + 7 = □

**Letters for numbers**

In mathematics we use letters of the alphabets to stand for numbers instead of boxes. We write 14 + x instead of 14 + □. Any letter can be used. For example, 14 + *a* would be just as good as 14 + x. Capital letters are not used; only small letters are used.

When using a letter instead of a number, the letter can stand for any number in general. Thus the value of 14 + x depends on the value of x.

For example,

If x stands for 2, 14 + x has the value 16;

If x stands for 12, 14 + x has the value 26;

If x stands for 5, 14 + x has the value 19.

When letters and numbers are used together in this way, the mathematics is called **generalized arithmetic **or **algebra** The word algebra comes to us from an important book written around AD830 by Mohammed Musa al Khowarizmi, a noted mathematician from Baghdad. The title of the book was Al-jabr wa’l Muqabalah.

The statement 14 + x = 17 is called an **algebraic sentence**. It means 14 plus a number x makes 17, or 14 plus x equals 17.

In the next exercise, each letter stands for a number. The number that the letter stands for sh0uld make the sentence true. For example, 14 + x = 17will be true if x stands for 3.

We write this:

If 14 + x = 17

Then x = 3

**Exercise**

Each sentence is true. Find the number that each letter stands for.

1. x = 2 + 7

2. x = 3 – 10

3. y = 9 + 5

4. z = 18 + 11

5. z = 15 – 8

What is the value of z + 6? The value of x + 6 depends on what x stands for.

If x = 3, then x + 6 = **3 **+ 6 = 9

If x = 8, then x + **8 **+ 6 = 14

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