Description Reflect and Review Teasers Answers Recall basics of fractions. Review

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$1. Revision Recall basics of fractions. are equivalent fractions of. Since Write five equivalent fractions of. 2.$ $and q 0. The group of numbers includes natural numbers, whole numbers, integers, fractions and decimals.$ (ii) Numerator is positive, denominator is negative.

(ii) Numerator is positive, denominator is negative.

1 1. Revision Recall basics of fractions. are equivalent fractions of. Since Write five equivalent fractions of. 2. Rational Numbers A number is defined as a number which can be represented in the form of, where p and q are integers and q 0. The group of numbers includes natural numbers, whole numbers, integers, fractions and decimals. A number can be in one of the following forms: (i) Numerator is positive, denominator is also positive. (ii) Numerator is positive, denominator is negative. (iii) Numerator is negative, is a positive number, since both numerator and denominator are negative. Divide the following group of numbers as positive and negative numbers:,,, Answers Positive numbers:, Negative numbers:, 1

2 denominator is positive. (iv) Numerator is negative, denominator is also negative. Cases (i) and (iv) give a positive number, whereas cases (ii) and (iii) give a negative number. 3. Equivalent Rational Numbers If we multiply the numerator and denominator of a number by another non-zero integer, we get a number equivalent to it. fractions to. Since are equivalent. and Write three equivalent fractions of. 4. Representing Rational Numbers on a Number Line Rational numbers can be represented on number line, same as integers and fractions. See below the table Represent on number line. is represented on the number line as follows:

3 5. Rational Numbers in the Standard Form A number is said to be in the standard form, if its denominator is a positive integer and the numerator and denominator do not have a common factor other than 1. Standard form of is. Since HCF of 96 and 144 is 48, so it gets reduced to denominator is positive.. Also, the Find the standard form of the following 6. Comparison of Rational Numbers While comparing two numbers, (i) If both are positive, they are compared as fractions. (ii) If one is positive and the other is negative, the positive number is always greater than the negative number. (iii) If both are negative, firstly they are compared as fractions, without considering the sign, and then as negative integers. To compare : On comparing we get. So,. Arrange in ascending order. 3

4 7. Rational Numbers between Two Rational Numbers There are uncountable numbers between any two numbers. are five number between and. So, and Find four number between and.. 8. Addition of Rational Numbers Addition of number is possible only when the denominators are same. The additive inverse of is. To add: Find the sum of the following: ( ) ( ) ( ) ( ) Answers 9. Subtraction of Rational Numbers Subtracting a number from another is same as adding the additive inverse of the second to the first. To subtract: ( ): ( ) Solve the following: ( ) ( ) ( ) 4

5 10. Multiplication of Rational Numbers The product of two numbers is obtained by multiplying the respective numerators and denominators with each other. The multiplicative inverse or reciprocal of a number is where a andb are non-zero integers. To multiply: ( ) ( ): ( ) ( ) Multiply: ( ) ( ) ( ) ( ) Division of Rational Numbers Dividing a number by another number is same as multiplying by the reciprocal of the divisor. To divide: ( ) ( ): ( ) ( ) ( ) ( ) Find the value of: ( ) ( ) ( ) 56 5

6 12. Rational Numbers as Decimal Numbers On representing a number as a decimal, if the number of digits after the decimal point is finite, then such decimals are called terminating decimal; if the number of digits after the decimal point are repeating endlessly, then such decimals are called nonterminating decimals. In non-terminating decimal numbers, the repeated part after the decimal point is expressed using a bar over it. = 7.75 and this can be explained as shown below: Convert the following into decimals numbers. Answers Word Problems Applications in various real life situations. If to make a bottle of milk shake, of fruit pulp is required, then using 8 of fruit pulp we can make 10 bottles of juice. Since, number of bottle of juice = 10. From a cloth of length, Ankita cuts shirt and to stitch a to stitch a top. Find the remaining piece. In a packet of 75 beads, are blue in colour. Sheetal used of the blue beads to make a bracelet. What fraction of the beads from the packet was used to make the bracelet? Also, find the total number of unused beads beads were unused. 6

Rational number operations can often be simplified by converting mixed numbers to improper fractions Add EXAMPLE:

$Rational number operations can often be simplified by converting mixed numbers to improper fractions Add EXAMPLE:$ Rational number operations can often be simplified by converting mixed numbers to improper fractions Add ( 2) EXAMPLE: 2 Multiply 1 Negative fractions can be written with the negative number in the numerator