Properties of rational numbers

Let’s solve the 1)… . John has read 2) … … … … books as Bill. John has read 7 books. How many books has Bill read?

This problem is easily translated into the 3)… 2n = 7, where n represents the number of books that Bill has read. If we are allowed to use only 4) …, the equation 2n=7 has no 5)… . This is an indication that the 6)… of integers does not meet all our needs.

If we try to solve the equation 2n = 7 we will find that n = 7/2 as to 7) … a multiplier you should divide the 8)… 7 by the multiplier 2. It is the name for a rational number. As we know a rational number is a 9) … of two integers p/q where q is not 10) … to 0. The denominator denotes the number of equal parts into which the 11) … is divided. The 12) … denotes how many of these parts are taken.

Fractions representing 13) … less than 1, like 2/3 for example are called 14) … fractions. Fractions which name a number equal or greater than 1, like 3/3 or 3/2, are called 15) … fractions. There are numbers like 1 ½ (one and one second) which name a whole number and a 16) … number. Such numerals are called 17) … fractions. Fractions which represent the same fractional numbers like 1/2, 2/4, 4/8 and so on are called 18) … fractions.

We can change such fractions to their 19) … or lower terms. If the numerator and denominator of the fraction are relatively prime we call it the 20)… fraction. The process of bringing a fractional number to lower terms is called 21) ... a fraction. Multiplying both integers named in the numerator and denominator of the fraction by the same whole number simply produces another name for the fractional number.

To reduce a fraction to lower terms you must determine the 22) … … … . The greatest common factor is the largest possible 23) … by which the numerator as well as denominator is divisible.

You can also perform all 24) … operations with rationals. Before performing addition or 25) … with fractional numerals you must bring them to a 26) … … . When multiplying with fractions you should find the 27) … of the numerators and the product of denominators. Dividing simple fractions one by another you must multiply the numerator of the dividend by the denominator of the 28) … and also multiply the denominator of the 29) … by the numerator of the divisor. For example 3/8 : 5/9 = 3/8 ∙ 9/5

From the above we can draw the 30) … that mathematical concepts and principles are just as valid in the case of rational numbers as in the case of integers.

Task 8

Prepare the reports on the following topics:

1. The types of fractions.

2. Performing arithmetic operations with rationals.

3. Main properties of rationals.

Task 9

Tell the class about properties of rational numbers using the questions on the module text as a plan.

Task 10

Read the text and render it in English.

Reciprocal Fractions

To find the reciprocal of a fraction, flip it over, so that the numerator becomes the denominator and the denominator becomes the numerator. That is: the reciprocal of 4/5 is 5/4.

Note that the product of a fraction and its reciprocal is always: 4/5 5/4 = 20/20 = 1

In the case of a whole number, think of it as having a denominator of 1: the reciprocal of 5 is 1/5. 5/1 1/5 = 5/5 = 1

Every number has a reciprocal except for 0. There is nothing you can multiply by 0 to create a product of 1, so it has no reciprocal. Reciprocals are used when dividing fractions.

Task 11

Read the text and translate it into Ukrainian.