Page 1 Points to Remember : 1. Fraction. The number of the forms a b where p and q are integers and q 0, is called a fraction. Here p is called the num- erator and ‘q’ is called the denominator. Fraction can also be represent on a number line. e.g. 2 3 5 7 11 19 , , are called fractions. 2 3 means two parts from 3 and is read as two-third. 5 7 means, five parts from 7 and is read five-seventh. 11 19 means 11 parts from 19 and is read as eleven-nineteenth. 2. (A) Equivalent fractions. Two or more fractions representing the same part of a whole are called equivalent fractions. (B) Rule to form equivalent fractions. To get a fractions equivalent to a given fractions, we multiply or divide the numerator and denominator of the given fraction by the same non-zero number. (C) To test of two equivalent fractions. Let a b and c d are two equivalent fractions, these a b c d ad = bc. In other words, we can say that if ad = bc then, fractions a b and c d are equal. 3. Like and unlike fractions : (A) Like fractions. Fractions having same denominators are called like fractions e.g. 1 7 3 7 5 7 4 7 , , , . (B) Unlike fractions. Fractions with different denominators are called unlike fractions e.g. 2 3 5 7 4 9 , , . (C) To convert unlike fractions to like fractions. We can convert unlike fractions into like fractions by equalising their denominator with the help of using their L.C.M. 4. Fractions in simplest form or in lowest terms. A fraction is said to be in the simplest form if the HCF of its numerator and denominator is 1. 5. Proper, improper and mixed fractions : (A) Proper fractions. A fraction whose numerator is less than its denominator is called a proper fraction e.g. 1 2 5 7 4 9 , , etc. (B) Improper fractions : A fraction whose numerator is greater than its denominator, is called improper fraction e.g. 5 4 7 3 9 2 , , etc. (C) Mixed fractions. A combination of a whole number and a proper fraction is Page 2 Points to Remember : 1. Fraction. The number of the forms a b where p and q are integers and q 0, is called a fraction. Here p is called the num- erator and ‘q’ is called the denominator. Fraction can also be represent on a number line. e.g. 2 3 5 7 11 19 , , are called fractions. 2 3 means two parts from 3 and is read as two-third. 5 7 means, five parts from 7 and is read five-seventh. 11 19 means 11 parts from 19 and is read as eleven-nineteenth. 2. (A) Equivalent fractions. Two or more fractions representing the same part of a whole are called equivalent fractions. (B) Rule to form equivalent fractions. To get a fractions equivalent to a given fractions, we multiply or divide the numerator and denominator of the given fraction by the same non-zero number. (C) To test of two equivalent fractions. Let a b and c d are two equivalent fractions, these a b c d ad = bc. In other words, we can say that if ad = bc then, fractions a b and c d are equal. 3. Like and unlike fractions : (A) Like fractions. Fractions having same denominators are called like fractions e.g. 1 7 3 7 5 7 4 7 , , , . (B) Unlike fractions. Fractions with different denominators are called unlike fractions e.g. 2 3 5 7 4 9 , , . (C) To convert unlike fractions to like fractions. We can convert unlike fractions into like fractions by equalising their denominator with the help of using their L.C.M. 4. Fractions in simplest form or in lowest terms. A fraction is said to be in the simplest form if the HCF of its numerator and denominator is 1. 5. Proper, improper and mixed fractions : (A) Proper fractions. A fraction whose numerator is less than its denominator is called a proper fraction e.g. 1 2 5 7 4 9 , , etc. (B) Improper fractions : A fraction whose numerator is greater than its denominator, is called improper fraction e.g. 5 4 7 3 9 2 , , etc. (C) Mixed fractions. A combination of a whole number and a proper fraction is called a mixed fraction e.g. 1 5 7 2 3 4 5 1 8 , , etc. (D) To convert a mixed fraction into an improper fraction. We know that a mixed fraction = A whole number + a fraction e.g. 1 5 7 1 5 7 1 7 5 7 7 5 7 12 7 . Method. Multiply the whole number with the denominator of the fraction and add the numerator of the fraction, then the new numerator is the numerator of the improper fraction with same denominator. (E) To convert an improper fraction with a mixed fraction. On dividing the numerator by denominator, we get quotient i.e. whole number. Then, whole number plus Remainder Denominator is the required mixed fraction e.g. 15 4 3 3 4 3 3 4 . 6. Comparison of fractions : (A) Comparing fractions with same denominator. Rule. Among two fractions with the same denominator, the greater numerator is greater fraction. (B) Comparing fractions with same numerator. Rule. Among two fraction with same numerator the one with smaller denominator is the greater fraction. (C) General method for comparison : (i) By means of cross multiplication. (ii) By converting the given fractions into like fractions. 7. Addition of fractions : (A) Addition of like fractions Sum of their numerators Denominator (B) Addition of unlike fractions. Change the given fractions into equivalent like fractions and then add them as given in (A). 8. Subtraction of fractions. We use similar methods as in addition for subtraction of fractions. Exercise 5A Q.1. Write the fraction representing the shaded portion : (i) (ii) (iii) (iv) (v) (vi) Sol. (i) 4 3 (ii) 4 1 (iii) 3 2 (iv) 10 3 (v) 9 4 (vi) 8 3 Q.2. Shade 9 4 of the given figure. Page 3 Points to Remember : 1. Fraction. The number of the forms a b where p and q are integers and q 0, is called a fraction. Here p is called the num- erator and ‘q’ is called the denominator. Fraction can also be represent on a number line. e.g. 2 3 5 7 11 19 , , are called fractions. 2 3 means two parts from 3 and is read as two-third. 5 7 means, five parts from 7 and is read five-seventh. 11 19 means 11 parts from 19 and is read as eleven-nineteenth. 2. (A) Equivalent fractions. Two or more fractions representing the same part of a whole are called equivalent fractions. (B) Rule to form equivalent fractions. To get a fractions equivalent to a given fractions, we multiply or divide the numerator and denominator of the given fraction by the same non-zero number. (C) To test of two equivalent fractions. Let a b and c d are two equivalent fractions, these a b c d ad = bc. In other words, we can say that if ad = bc then, fractions a b and c d are equal. 3. Like and unlike fractions : (A) Like fractions. Fractions having same denominators are called like fractions e.g. 1 7 3 7 5 7 4 7 , , , . (B) Unlike fractions. Fractions with different denominators are called unlike fractions e.g. 2 3 5 7 4 9 , , . (C) To convert unlike fractions to like fractions. We can convert unlike fractions into like fractions by equalising their denominator with the help of using their L.C.M. 4. Fractions in simplest form or in lowest terms. A fraction is said to be in the simplest form if the HCF of its numerator and denominator is 1. 5. Proper, improper and mixed fractions : (A) Proper fractions. A fraction whose numerator is less than its denominator is called a proper fraction e.g. 1 2 5 7 4 9 , , etc. (B) Improper fractions : A fraction whose numerator is greater than its denominator, is called improper fraction e.g. 5 4 7 3 9 2 , , etc. (C) Mixed fractions. A combination of a whole number and a proper fraction is called a mixed fraction e.g. 1 5 7 2 3 4 5 1 8 , , etc. (D) To convert a mixed fraction into an improper fraction. We know that a mixed fraction = A whole number + a fraction e.g. 1 5 7 1 5 7 1 7 5 7 7 5 7 12 7 . Method. Multiply the whole number with the denominator of the fraction and add the numerator of the fraction, then the new numerator is the numerator of the improper fraction with same denominator. (E) To convert an improper fraction with a mixed fraction. On dividing the numerator by denominator, we get quotient i.e. whole number. Then, whole number plus Remainder Denominator is the required mixed fraction e.g. 15 4 3 3 4 3 3 4 . 6. Comparison of fractions : (A) Comparing fractions with same denominator. Rule. Among two fractions with the same denominator, the greater numerator is greater fraction. (B) Comparing fractions with same numerator. Rule. Among two fraction with same numerator the one with smaller denominator is the greater fraction. (C) General method for comparison : (i) By means of cross multiplication. (ii) By converting the given fractions into like fractions. 7. Addition of fractions : (A) Addition of like fractions Sum of their numerators Denominator (B) Addition of unlike fractions. Change the given fractions into equivalent like fractions and then add them as given in (A). 8. Subtraction of fractions. We use similar methods as in addition for subtraction of fractions. Exercise 5A Q.1. Write the fraction representing the shaded portion : (i) (ii) (iii) (iv) (v) (vi) Sol. (i) 4 3 (ii) 4 1 (iii) 3 2 (iv) 10 3 (v) 9 4 (vi) 8 3 Q.2. Shade 9 4 of the given figure. Sol. In the figure, 9 4 is shaded 3. In the given figure, if we say that the shaded region is 4 1 , then identify the error in it. Sol. In the figure, whole rectangle is not divided into four equal parts. Q. 4. Write a fraction for each of the following : (i) three-fourths (ii) four-sevenths (iii) two-fifths (iv) three-tenths (v) one-eighth (vi) five-sixths (vii) eight-ninths (viii) seven-twelfths Sol. (i) Three-fourths 3 4 . (ii) Four-sevenths 4 7 . (iii) Two-fifths 2 5 . (iv) Three-tenths 3 10 . (v) One-eighth 1 8 . (vi) Five-sixths 5 6 . (vii) Eight-ninths 8 9 . (viii) Seven-twelfths 7 12 . Ans. Q. 5. Write down the numerator and denomi- nator in each of the following fractions : (i) 4 9 (ii) 11 6 (iii) 15 8 (iv) 12 17 (v) 1 5 Sol. (i) In 4 9 , numerator is 4 and denominator is 9. (ii) In 11 6 , numerator is 6 and denominator is 11. (iii) In 15 8 , numerator is 8 and denominator is 15. (iv) In 12 17 , numerator is 12 and denominator is 17. (v) 1 5 , numerator is 5 and denominator is 1. Q. 6. Write down the fraction in which (i) numerator = 3, denominator = 8 (ii) numerator = 5, denominator = 12 (iii) numerator = 7, denominator = 16 (iv) numerator = 8, denominator = 15 Sol. (i) Numerator = 3, Denominator = 8, then fraction 3 8 . (ii) Numerator = 5, Denominator = 12, then fraction = 12 5 . (iii) Numerator = 7, Denominator = 16, then fraction 7 16 . (iv) Numerator = 8, Denominator = 15, then fraction 8 15 . Ans. Q.7. Write down the fractional number for each of the following : Page 4 Points to Remember : 1. Fraction. The number of the forms a b where p and q are integers and q 0, is called a fraction. Here p is called the num- erator and ‘q’ is called the denominator. Fraction can also be represent on a number line. e.g. 2 3 5 7 11 19 , , are called fractions. 2 3 means two parts from 3 and is read as two-third. 5 7 means, five parts from 7 and is read five-seventh. 11 19 means 11 parts from 19 and is read as eleven-nineteenth. 2. (A) Equivalent fractions. Two or more fractions representing the same part of a whole are called equivalent fractions. (B) Rule to form equivalent fractions. To get a fractions equivalent to a given fractions, we multiply or divide the numerator and denominator of the given fraction by the same non-zero number. (C) To test of two equivalent fractions. Let a b and c d are two equivalent fractions, these a b c d ad = bc. In other words, we can say that if ad = bc then, fractions a b and c d are equal. 3. Like and unlike fractions : (A) Like fractions. Fractions having same denominators are called like fractions e.g. 1 7 3 7 5 7 4 7 , , , . (B) Unlike fractions. Fractions with different denominators are called unlike fractions e.g. 2 3 5 7 4 9 , , . (C) To convert unlike fractions to like fractions. We can convert unlike fractions into like fractions by equalising their denominator with the help of using their L.C.M. 4. Fractions in simplest form or in lowest terms. A fraction is said to be in the simplest form if the HCF of its numerator and denominator is 1. 5. Proper, improper and mixed fractions : (A) Proper fractions. A fraction whose numerator is less than its denominator is called a proper fraction e.g. 1 2 5 7 4 9 , , etc. (B) Improper fractions : A fraction whose numerator is greater than its denominator, is called improper fraction e.g. 5 4 7 3 9 2 , , etc. (C) Mixed fractions. A combination of a whole number and a proper fraction is called a mixed fraction e.g. 1 5 7 2 3 4 5 1 8 , , etc. (D) To convert a mixed fraction into an improper fraction. We know that a mixed fraction = A whole number + a fraction e.g. 1 5 7 1 5 7 1 7 5 7 7 5 7 12 7 . Method. Multiply the whole number with the denominator of the fraction and add the numerator of the fraction, then the new numerator is the numerator of the improper fraction with same denominator. (E) To convert an improper fraction with a mixed fraction. On dividing the numerator by denominator, we get quotient i.e. whole number. Then, whole number plus Remainder Denominator is the required mixed fraction e.g. 15 4 3 3 4 3 3 4 . 6. Comparison of fractions : (A) Comparing fractions with same denominator. Rule. Among two fractions with the same denominator, the greater numerator is greater fraction. (B) Comparing fractions with same numerator. Rule. Among two fraction with same numerator the one with smaller denominator is the greater fraction. (C) General method for comparison : (i) By means of cross multiplication. (ii) By converting the given fractions into like fractions. 7. Addition of fractions : (A) Addition of like fractions Sum of their numerators Denominator (B) Addition of unlike fractions. Change the given fractions into equivalent like fractions and then add them as given in (A). 8. Subtraction of fractions. We use similar methods as in addition for subtraction of fractions. Exercise 5A Q.1. Write the fraction representing the shaded portion : (i) (ii) (iii) (iv) (v) (vi) Sol. (i) 4 3 (ii) 4 1 (iii) 3 2 (iv) 10 3 (v) 9 4 (vi) 8 3 Q.2. Shade 9 4 of the given figure. Sol. In the figure, 9 4 is shaded 3. In the given figure, if we say that the shaded region is 4 1 , then identify the error in it. Sol. In the figure, whole rectangle is not divided into four equal parts. Q. 4. Write a fraction for each of the following : (i) three-fourths (ii) four-sevenths (iii) two-fifths (iv) three-tenths (v) one-eighth (vi) five-sixths (vii) eight-ninths (viii) seven-twelfths Sol. (i) Three-fourths 3 4 . (ii) Four-sevenths 4 7 . (iii) Two-fifths 2 5 . (iv) Three-tenths 3 10 . (v) One-eighth 1 8 . (vi) Five-sixths 5 6 . (vii) Eight-ninths 8 9 . (viii) Seven-twelfths 7 12 . Ans. Q. 5. Write down the numerator and denomi- nator in each of the following fractions : (i) 4 9 (ii) 11 6 (iii) 15 8 (iv) 12 17 (v) 1 5 Sol. (i) In 4 9 , numerator is 4 and denominator is 9. (ii) In 11 6 , numerator is 6 and denominator is 11. (iii) In 15 8 , numerator is 8 and denominator is 15. (iv) In 12 17 , numerator is 12 and denominator is 17. (v) 1 5 , numerator is 5 and denominator is 1. Q. 6. Write down the fraction in which (i) numerator = 3, denominator = 8 (ii) numerator = 5, denominator = 12 (iii) numerator = 7, denominator = 16 (iv) numerator = 8, denominator = 15 Sol. (i) Numerator = 3, Denominator = 8, then fraction 3 8 . (ii) Numerator = 5, Denominator = 12, then fraction = 12 5 . (iii) Numerator = 7, Denominator = 16, then fraction 7 16 . (iv) Numerator = 8, Denominator = 15, then fraction 8 15 . Ans. Q.7. Write down the fractional number for each of the following : (i) 3 2 (ii) 9 4 (iii) 5 2 (iv) 10 7 (v) 3 1 (vi) 4 3 (vii) 8 3 (viii) 14 9 (ix) 11 5 (x) 15 6 Sol. (i) 3 2 = two-thirds (ii) 9 4 = four-ninths (iii) 5 2 = two-fifths (iv) 10 7 = seven-tenths (v) 3 1 = one-thirds (vi) 4 3 = three-fourth (vii) 8 3 = three-eighths (viii) 14 9 = nine-fourteenths (ix) 11 5 = five-elevanths (x) 15 6 = six-fifteenths Q.8. What fraction of an hour is 24 minutes ? Sol. 24 minutes is the fraction of 1 hour i.e., 60 minutes = 60 24 Q.9. How many natural numbers are there from 2 to 10 ? What fraction of them are prime numbers ? Sol. Natural number between 2 to 10 are 2, 3, 4, 5, 6, 7, 8, 9, 10 = 9 Out of these prime number are 2, 3, 5, 7 = 4 Fraction = 9 4 Q. 10. Determine 2 3 of a collection of (i) 3 2 of 15 pens (ii) 3 2 of 27 balls (iii) 3 2 of 36 balloons Sol. (i) 2 3 of 15 pens 2 3 15= 2 × 5 = 10 pens. (ii) 2 3 of 27 balls 2 3 27 2 9 18 balls . (iii) 2 3 of 36 balloons 2 3 36 = 2 × 12 = 24 balloons. Ans. Q. 11. Determine 3 4 of a collection of (i) 16 cups (ii) 28 rackets (iii) 32 books Sol. (i) 3 4 of 16 cups 3 4 16 = 3 × 4 = 12 cups. (ii) 3 4 of 28 rackets 3 4 28 = 3 × 7 = 21 rackets. (iii) 3 4 of 32 books 3 4 32 = 3 × 8 = 24 books. Ans. Page 5 Points to Remember : 1. Fraction. The number of the forms a b where p and q are integers and q 0, is called a fraction. Here p is called the num- erator and ‘q’ is called the denominator. Fraction can also be represent on a number line. e.g. 2 3 5 7 11 19 , , are called fractions. 2 3 means two parts from 3 and is read as two-third. 5 7 means, five parts from 7 and is read five-seventh. 11 19 means 11 parts from 19 and is read as eleven-nineteenth. 2. (A) Equivalent fractions. Two or more fractions representing the same part of a whole are called equivalent fractions. (B) Rule to form equivalent fractions. To get a fractions equivalent to a given fractions, we multiply or divide the numerator and denominator of the given fraction by the same non-zero number. (C) To test of two equivalent fractions. Let a b and c d are two equivalent fractions, these a b c d ad = bc. In other words, we can say that if ad = bc then, fractions a b and c d are equal. 3. Like and unlike fractions : (A) Like fractions. Fractions having same denominators are called like fractions e.g. 1 7 3 7 5 7 4 7 , , , . (B) Unlike fractions. Fractions with different denominators are called unlike fractions e.g. 2 3 5 7 4 9 , , . (C) To convert unlike fractions to like fractions. We can convert unlike fractions into like fractions by equalising their denominator with the help of using their L.C.M. 4. Fractions in simplest form or in lowest terms. A fraction is said to be in the simplest form if the HCF of its numerator and denominator is 1. 5. Proper, improper and mixed fractions : (A) Proper fractions. A fraction whose numerator is less than its denominator is called a proper fraction e.g. 1 2 5 7 4 9 , , etc. (B) Improper fractions : A fraction whose numerator is greater than its denominator, is called improper fraction e.g. 5 4 7 3 9 2 , , etc. (C) Mixed fractions. A combination of a whole number and a proper fraction is called a mixed fraction e.g. 1 5 7 2 3 4 5 1 8 , , etc. (D) To convert a mixed fraction into an improper fraction. We know that a mixed fraction = A whole number + a fraction e.g. 1 5 7 1 5 7 1 7 5 7 7 5 7 12 7 . Method. Multiply the whole number with the denominator of the fraction and add the numerator of the fraction, then the new numerator is the numerator of the improper fraction with same denominator. (E) To convert an improper fraction with a mixed fraction. On dividing the numerator by denominator, we get quotient i.e. whole number. Then, whole number plus Remainder Denominator is the required mixed fraction e.g. 15 4 3 3 4 3 3 4 . 6. Comparison of fractions : (A) Comparing fractions with same denominator. Rule. Among two fractions with the same denominator, the greater numerator is greater fraction. (B) Comparing fractions with same numerator. Rule. Among two fraction with same numerator the one with smaller denominator is the greater fraction. (C) General method for comparison : (i) By means of cross multiplication. (ii) By converting the given fractions into like fractions. 7. Addition of fractions : (A) Addition of like fractions Sum of their numerators Denominator (B) Addition of unlike fractions. Change the given fractions into equivalent like fractions and then add them as given in (A). 8. Subtraction of fractions. We use similar methods as in addition for subtraction of fractions. Exercise 5A Q.1. Write the fraction representing the shaded portion : (i) (ii) (iii) (iv) (v) (vi) Sol. (i) 4 3 (ii) 4 1 (iii) 3 2 (iv) 10 3 (v) 9 4 (vi) 8 3 Q.2. Shade 9 4 of the given figure. Sol. In the figure, 9 4 is shaded 3. In the given figure, if we say that the shaded region is 4 1 , then identify the error in it. Sol. In the figure, whole rectangle is not divided into four equal parts. Q. 4. Write a fraction for each of the following : (i) three-fourths (ii) four-sevenths (iii) two-fifths (iv) three-tenths (v) one-eighth (vi) five-sixths (vii) eight-ninths (viii) seven-twelfths Sol. (i) Three-fourths 3 4 . (ii) Four-sevenths 4 7 . (iii) Two-fifths 2 5 . (iv) Three-tenths 3 10 . (v) One-eighth 1 8 . (vi) Five-sixths 5 6 . (vii) Eight-ninths 8 9 . (viii) Seven-twelfths 7 12 . Ans. Q. 5. Write down the numerator and denomi- nator in each of the following fractions : (i) 4 9 (ii) 11 6 (iii) 15 8 (iv) 12 17 (v) 1 5 Sol. (i) In 4 9 , numerator is 4 and denominator is 9. (ii) In 11 6 , numerator is 6 and denominator is 11. (iii) In 15 8 , numerator is 8 and denominator is 15. (iv) In 12 17 , numerator is 12 and denominator is 17. (v) 1 5 , numerator is 5 and denominator is 1. Q. 6. Write down the fraction in which (i) numerator = 3, denominator = 8 (ii) numerator = 5, denominator = 12 (iii) numerator = 7, denominator = 16 (iv) numerator = 8, denominator = 15 Sol. (i) Numerator = 3, Denominator = 8, then fraction 3 8 . (ii) Numerator = 5, Denominator = 12, then fraction = 12 5 . (iii) Numerator = 7, Denominator = 16, then fraction 7 16 . (iv) Numerator = 8, Denominator = 15, then fraction 8 15 . Ans. Q.7. Write down the fractional number for each of the following : (i) 3 2 (ii) 9 4 (iii) 5 2 (iv) 10 7 (v) 3 1 (vi) 4 3 (vii) 8 3 (viii) 14 9 (ix) 11 5 (x) 15 6 Sol. (i) 3 2 = two-thirds (ii) 9 4 = four-ninths (iii) 5 2 = two-fifths (iv) 10 7 = seven-tenths (v) 3 1 = one-thirds (vi) 4 3 = three-fourth (vii) 8 3 = three-eighths (viii) 14 9 = nine-fourteenths (ix) 11 5 = five-elevanths (x) 15 6 = six-fifteenths Q.8. What fraction of an hour is 24 minutes ? Sol. 24 minutes is the fraction of 1 hour i.e., 60 minutes = 60 24 Q.9. How many natural numbers are there from 2 to 10 ? What fraction of them are prime numbers ? Sol. Natural number between 2 to 10 are 2, 3, 4, 5, 6, 7, 8, 9, 10 = 9 Out of these prime number are 2, 3, 5, 7 = 4 Fraction = 9 4 Q. 10. Determine 2 3 of a collection of (i) 3 2 of 15 pens (ii) 3 2 of 27 balls (iii) 3 2 of 36 balloons Sol. (i) 2 3 of 15 pens 2 3 15= 2 × 5 = 10 pens. (ii) 2 3 of 27 balls 2 3 27 2 9 18 balls . (iii) 2 3 of 36 balloons 2 3 36 = 2 × 12 = 24 balloons. Ans. Q. 11. Determine 3 4 of a collection of (i) 16 cups (ii) 28 rackets (iii) 32 books Sol. (i) 3 4 of 16 cups 3 4 16 = 3 × 4 = 12 cups. (ii) 3 4 of 28 rackets 3 4 28 = 3 × 7 = 21 rackets. (iii) 3 4 of 32 books 3 4 32 = 3 × 8 = 24 books. Ans. Q.12. Neelam has 25 pencils. She gives 5 4 of them to Meena. How many pencils does Meena get ? How many pencils are left with Neelam ? Sol. Total number of pencils Neelam has = 25 No. of pencils given to Meena = 5 4 of 25 = 5 4 × 25 = 20 No. of pencils left with Neelam = 25 – 20 = 5 Q. 13. Represent each of the following fractions on a number line : (i) 3 8 (ii) 5 9 (iii) 4 7 (iv) 2 5 (v) 4 1 Sol. (i) 3 8 Take a line segment OA = one unit of length Divide it into 8 equal parts and take 3 parts at P, then P represents 3 8 . (ii) 5 9 (a) Take a line segment OA = one unit of length. (b) Divide it into nine equal parts and take 5 parts at P, then P represents 5 9 . (iii) 4 7 (a) Take a line segment OA = one unit of length. (b) Divide it into 7 equal parts and take 4 parts at P then P represents 4 7 . (iv) 2 5 (a) Take a line segment OA = 1 unit of length. (b) Divide it with 5 equal parts and take 2 parts and P then P represents 2 5 . (v) 4 1 (a) Take a line segment OA = 1 unit of length. (b) Divide it with 4 equal parts and take 1 parts and P then P represents 4 1 . 0 1 2 3 4 1 4 P Exercise 5B Q. 1. Which of the following are proper fractions ? 2 1 , 5 3 , 10 6 , 4 7 , 2, 8 15 , 16 16 , 11 10 , 10 23 Sol. We know that, a fraction is proper if its denominator is greater than its numerator. Therefore, 2 1 , 5 3 and 10 11 are proper fractions. Ans. Q. 2. Which of the following are improperRead More

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

191 videos|221 docs|43 tests