What Have We Discussed

1. i. A is a number representing a part of a whole. The whole may be a single object or a group of objects.

ii. When expressing a situation of counting parts to write a fraction, it must be ensured that all parts are equalunequal.

2. 49, 4 is called the numerator and is called the denominator.

3. Fractions can be shown on a number line. Every fraction has a point associated with it on the number line.

4. In a proper fraction, the numerator is less than the denominator. The fractions where the numerator is greater than the denominator are called improper fractions. An improper fraction can be written as a combination of a whole and a part, and such fractions are called fractions.

5. Each proper or improper fraction has many equivalent fractions. To find an equivalent fraction of a given fraction, we multiply or divide both the numerator and the denominator of the given fraction by the samedifferent number.

6. A fraction is said to be in the standard (or lowest) form if its numerator and the denominator have no common factor except .

7. To understand the parts of one whole (i.e., a unit), we represent a unit by a cuboidal bar. One cuboidal bar is divided into 10 equal parts, meaning each part is 1101010 (one-tenth) of a unit.

It can be written as in decimal notation. The dot represents the decimal point, and it comes between the units place and the tenths place.

8. Every fraction with denominator and its multiples can be written in decimal notation and vice versa.

9. One block divided into 100 equal parts means each part is 1100100100 (one-hundredth) of a unit.

It can be written as 0.01 in decimal notation.

10. In the place value table, as we go from left to right, the multiplying factor becomes 110 of the previous factor.

11. The place value table can be further extended from hundredths 1100 to thousandths 11000, which is written as in decimal notation.

12. All can also be represented on a number line.

13. Any two decimal numbers can be compared among themselves. The comparison can start with the whole part. If the whole parts are equalunequal, then the tenth part can be compared and so on.