# FORM ONE MATHEMATICS STUDY NOTES TOPIC 1-3.

**TOPIC 1: NUMBERS**

we
know that when we count we start 1,2 .... . But there are other numbers
like 0, negative numbers and decimals. All these types of numbers are
categorized in different groups like counting numbers, integers,real
numbers, whole numbers and rational and irrational numbers according to
their properties. all this have been covered in this chapter

Integers

Identify integers

Consider a number line below

The
numbers from 0 to the right are called positive numbers and the numbers
from 0 to the left with minus (-) sign are called negative numbers.
Therefore all numbers with positive (+) or negative (-) sign are called
integers and they are denoted by Î–. Numbers with positive sign are
written without showing the positive sign. For example +1, +2, +3, …
they are written simply as 1, 2, 3, … . But negative numbers must carry
negative sign (-). Therefore integers are all positive and negative
numbers including zero (0). Zero is neither positive nor negative
number. It is neutral.

The
numbers from zero to the right increases their values as the increase.
While the numbers from zero to the left decrease their values as they
increase. Consider a number line below.

If
you take the numbers 2 and 3, 3 is to the right of 2, so 3 is greater
than 2. We use the symbol ‘>’ to show that the number is greater than
i. e. 3 >2(three is greater than two). And since 2 is to the left of
3, we say that 2 is smaller than 3 i.e. 2<3. The symbol ‘<’ is
use to show that the number is less than.

Consider
numbers to the left of 0. For example if you take -5 and -3. -5 is to
the left of -3, therefore -5 is smaller than -3. -3 is to the right of
-5, therefore -3 is greater than -5.

Generally, the number which is to the right of the other number is greater than the number which is to the left of it.

If
two numbers are not equal to each to each other, we use the symbol ‘≠’
to show that the two numbers are not equal. The not equal to ‘≠’ is the
opposite of is equal to ‘=’.

Example 21

Represent the following integers Î– on a number line

- 0 is greater than Î– and Î– is greater than -4
- -2 is less than Î– and Î– is less than or equal to 1.

Solution

a.
0 is greater than Î– means the integers to the left of zero and Î– is
greater than -4 means integers to the left of -4. These numbers are -1,
-2 and -3. Consider number line below

b.
-2 is less than Î– means integers to the right of -2 and Î– is less than
or equal to 1 means integers to the left of 1 including 1. These
integers are -1, 0 and 1. Consider the number line below

Example 22

Put the signs ‘is greater than’ (>), ‘is less than’ (<), ‘is equal to’ (=) to make a true statement.

Addition of Integers

Add integers

Example 23

2 + 3

Show a picture of 2 and 3 on a number line.

When
drawing integers on a number line, the arrows for the positive numbers
goes to the right while the arrows for the negative numbers goes to the
left. Consider an illustration bellow.

The
distance from 0 to 3 is the same as the distance from 0 to -3, only the
directions of their arrows differ. The arrow for positive 3 goes to the
right while the arrow for the negative 3 goes to the left.

Example 24

-3 + 6

Solution

Subtraction of Integers

Subtract integers

Since
subtraction is the opposite of addition, if for example you are given
5-4 is the same as 5 + (-4). So if we have to subtract 4 from 5 we can
use a number line in the same way as we did in addition. Therefore 5-4
on a number line will be:

Take five steps from 0 to the right and then four steps to the left from 5. The result is 1.

Multiplication of Integers

Multiply integers

Example 25

2×6 is the same as add 2 six times i.e. 2×6 = 2 + 2 + 2 + 2 + 2 +2 = 12. On a number line will be:

Multiplication
of a negative integer by a negative integer cannot be shown on a number
line but the product of these two negative integers is a positive
integer.

From
the above examples we note that multiplication of two positive integers
is a positive integer. And multiplication of a positive integer by a
negative integer is a negative integer. In summary:

- (+)×,(+) = (+)
- (-)×,(-) = (+)
- (+)×,(-) = (-)
- (-)×,(+) = (-)

Division of Integers

Divide integers

Example 26

6÷3 is the same as saying that, which number when you multiply it by 3 you will get 6, that number is 2, so, 6÷3 = 2.

Dividing
two integers which are both positive the quotient (answer) is a
positive integer. If they are both negative also the quotient is
positive. If one of the integer is positive and the other is negative
then the quotient is negative. In summary:

- (+)÷(+) = (+)
- (-)÷(-) = (+)
- (+)÷(-) = (-)
- (-)÷(+) = (-)

Mixed Operations on Integers

Perform mixed operations on integers

You
may be given more than one operation on the same problem. Do
multiplication and division first and then the rest of the signs. If
there are brackets, we first open the brackets and then we do division
followed by multiplication, addition and lastly subtraction. In short we
call it BODMAS. The same as the one we did on operations on whole
numbers.

Example 27

9÷3 + 3×2 -1 =

Solution

9÷3 + 3×2 -1

=3 + 6 -1 (first divide and multiply)

=8 (add and then subtract)

Example 28

(12÷4 -2) + 4 – 7=

Solution

(12÷4 -2) + 4 – 7

=1 + 4 – 7 (do operations inside the brackets and divide first)

=5 – 7 (add)

=2

**TOPIC 2: FRACTIONS**

A fraction is a number which is expressed in the form of

**a/b**where**a -**is the top number called numerator and**b**- is the bottom number called denominator.
Addition of Fractions

Add fractions

Operations on fractions involves

**addition, subtraction, multiplication**and**division**- Addition and subtraction of fractions is done by putting both fractions under the same denominator and then add or subtract
- Multiplication of fractions is done by multiplying the numerator of the first fraction with the numerator of the second fraction, and the denominator of the first fraction with the denominator the second fraction.
- For mixed fractions, convert them first into improper fractions and then multiply
- Division of fractions is done by taking the first fraction and then multiply with the reciprocal of the second fraction
- For mixed fractions, convert them first into improper fractions and then divide

Example 11

Find

**Solution**

Subtraction of Fractions

Subtract fractions

Example 12

Evaluate

**Solution**

Multiplication of Fractions

Multiply fractions

Example 13

Division of Fractions

Divide fractions

Example 14

Mixed Operations on Fractions

Perform mixed operations on fractions

Example 15

Example 16

Word Problems Involving Fractions

Solve word problems involving fractions

Example 17

- Musa is years old. His father is 3¾times as old as he is. How old is his father?
- 1¾of a material are needed to make suit. How many suits can be made from

**TOPIC 3: DECIMAL AND PERCENTAGE**

The Concept of Decimals

Explain the concept of decimals

A
decimal- is defined as a number which consist of two parts separated by
a point.The parts are whole number part and fractional part

Example 1

Example 2

Conversion of Fractions to Terminating Decimals and Vice Versa

Convert fractions to terminating decimals and vice versa

The first place after the decimal point is called tenths.The second place after the decimal point is called hundredths e.t.c

**Consider the decimal number 8.152**

**NOTE**

- To convert a fraction into decimal, divide the numerator by denominator
- To convert a decimal into fraction, write the digits after the decimal point as tenths, or hundredths or thousandths depending on the number of decimal places.

Example 3

Convert the following fractions into decimals

**Solution**

Divide the numerator by denominator

thanks for your notes they are great but bad thing the notes for mathematics form one 4-6 are missing

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