a) b) -4 + ( -5) c) d) 2 - ( -2) f)

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1 CLASS VII New Integers A 1. The integer consist of, and numbers 2. The numbers less than zero are called integer. 3. All the numbers which are less than zero have sign. 4. Zero is greater than integer. 5. The natural numbers are integers. 6. On the number line of integers, the value increases as we move from left side to the side. 7. is the largest negative integer. 8. is the smallest positive integer. 9. is neither positive nor negative. B 1. Represent the following on the number line a) b) -4 + ( -5) c) d) 2 - ( -2) f) Predecessor: one less than a given integer. To find the predecessor --- subtract 1 from the given number or add -1 to the number. Predecessor of a is a Write the predecessor of the following integers 10, - 10, 100, -100, 0, -1, 1, Successor one more than a given integer. To find the successor of a integer--- Add 1 to a given number. Successor of a is a Write the successor of the following integers 9, - 9, -11, 11, -99, -40, 101, 1000, Arrange in the ascending order: a) o, -3, 5, -1 b) 10, -10, 5, -5, 0, -1, 1 1

2 5. Arrange in the descending order: a) -20, -30, - 7, -16, - 9 b) 100, -100, 0, 97, - 99 When we add or subtract two integers---- 1) If two integers have same (like ) sign --- Write the common sign and Add the two numbers without looking at the sign. Example -3-9 = - ( 3 + 9) = ) If two integers have different( unlike) sign Write the sign of larger number ( absolute value) and subtract the smaller from the larger. Example: = - (10 7 ) (Here 10 is greater therefore write the sign of 10) = Simplify the following a) 17 8 b) c) d) e) When we solve problems having sign before the integer. First remove the bracket and then solve. Example: -3 (-10) -3 ( -10) --- We have - sign, so write the additive inverse of the number inside the bracket or write the opposite of the number inside the bracket. Inverse or opposite of -10 is (-10) = = 7 Example -3 + (-10) sign is there before the bracket, just copy the number inside the bracket and remove the + sign which is before the bracket (-10) = = Simplify a) -8 - ( -8 ) b) 100 (- 90 ) c) ( - 15) d) 17 + ( -20) 7. Subtract the first from the second a) 34, 25 b) - 30, -35 c) 50, -45 d) -90, Subtract -39 from Subtract 28 from -28 2

3 10. Insert <,> or = sign a) b) 0 (-2) c) d) e) (-7) f) 10 ( - 10) 2 x 10 g) ( - 30) 7 ( -2) h) (-5) 13. Fill in the blanks. a) = -10 b) 7 - = 10 c) 12 + = 10 d) = 10 e) -3 + = - 18 f) + (-9) = 27 g) 45 - ( ) = - 5 h) - 45 ( ) = Find the number which is a) 6 more than -5 b) 5 less than -6 c) the predecessor of -20 d) the successor of -100 e) 10 more than ( -3 7) Playing with numbers 1. 6 x 7 = and are factors of. is multiple of and. 2. Find all the factors of the following numbers. 24, 28, 27, 32, 36, 45, How many factors are there for 18? 4. Pick out all the common factors of 12 and Write first four multiples of each of the following given numbers. 3, 8 and Fill in the blanks a. is factor of every numbers. 3

4 b. The largest factor of the given number is c. The smallest multiple of the natural number is the number d. The smallest factor of 25 is. e. The smallest multiple of 6 is. f. All the numbers which are divisible by 2 are called. g. The composite numbers have more than factors. h. Numbers which have only two factors are called Prime Numbers: Numbers which have only two factors 1 and the number itself. Composite numbers: Numbers which have more than two factors. 1 is neither prime nor composite number as it has only one factor. 7. Write all the prime numbers between is not a prime number. Why? Even Numbers : Numbers which are divisible by 2. If the unit digit of a number is of 0, 2, 4, 6, 8 The number is even number. Odd Numbers: Numbers which are not divisible by 2. If the unit digit of a number is of 1, 3, 5, 7, 9 The number is odd number. 9. Classify into even and odd numbers. 998, 598, 735, 2111, 34857, What is the number which is even and also a prime. 11. What can you say about the units digit of odd numbers? 12. Find out the numbers divisible by2 362, 731, 895, 8246, 13. Find out the numbers which is divisible by , 345, 1230, Find out the numbers which is divisible by both 2 and , 1090, 2000,

5 15. Find the HCF of the following numbers. a) 36 and 42 b) 15 and 50 c) 24 and Find the LCM a) 12 and 16 b) 25 and 50 c) 18 and Fill in the blanks Numbers HCF LCM 1 6 and and and and and and and and 30 Fraction 1. Write the fractions representing the shaded portion: 2. Colour the part according to the given fraction: + 3. What part of your family is male? 5

6 Types of fractions Proper fractions: Fractions, where the numerator is less than the denominator. Improper fractions: If the numerator is greater than the denominator, the fractions are improper fraction. Mixed fractions: An improper fraction can be written as combination of a whole and a part, and such fraction then called mixed fraction. 1 ¾ 3/2 1/10 4/4 5/ Pick out all the proper fractions 6. Why is not a proper fraction? To convert improper fraction into mixed fraction. Divide the numerator by the denominator and express the answer as Improper fraction = Quotient 3 Example = 3 7. Change the following improper fractions into mixed numeral 7/5 To convert mixed fraction into improper fractions--- Example = = 8. Express in the improper fraction To Find Equivalent Fractions Either multiply or divide both numerator and denominator by the same number. It is easier by multiplying. 6

7 Example: Find three equivalent fractions of Sol Three equivalent fractions of are = = = = = 9. Find three equivalent fractions of 6/ Fill up the empty boxes. 2 = = To reduce into simplest form : Find the HCF of the numerator and denominator. Example Sol HCF of 30 and 45 is 15 ( 15 x 2 =30 and 15 x 3 = 45 = = 11. Reduce the following fractions to simplest ( lowest) form. 12. How many 1/8 th are there in a whole?!3. Put <, > or = signs. a) b) c) d) e)1 f) 14. Find the sum a) b) c) 4 d) d) e) f) g)1 h) i)3 15. Find the difference. a) b) c) d) e) 7

8 f) g) h) i) 2 j) Decimal 1. Determine the whole and decimal part. a) 3.2 b) Write in words. a) 1.2 b) 0.35 c) d) e) Write each of the following as decimals. a) Five tenth b) Three tens and three tenths c) Sixteen point three. d) Four hundreds four ones and four hundredths e) Nine thousand nine hundred point five To convert fraction into decimal--- Example 1) In denominator 2 is a factor of 10 = = = 0.5 or Divide the numerator by denominator Write each of the following as decimals: a) b) c) d) e) f) g) h) i) 3 To change decimal into fraction Separate the whole and decimal parts. Count the number of digits in the decimal part. Divide the number by 10,100 or 1000 accordingly with the number of digits in the decimal parts or the number of digits after the decimal point 8

9 Example 21.3 =, 0.17 = (note the answer must be in the simplest form) 5. Write the following decimals as fractions: a) 0.7 b) 0.23 c) 1.5 d) e) Which is greater? a) 0.4 or 0.5 b) 0.07 or 0.7 c) 7.7 or 7.07 d) 12.3 or 1.23 e) or Calculate a) b) c) d) e) f) g) h) Subtract ; a) Rs from Rs 30.6 b) 0.512m from 1m c) km from 150km. UNDERSTANGING ELEMENTARY SHAPES 1. Measure the sides of the figure given below using scale. A B D C 2. Draw line segment of the following measure: a) 4cm b) 3.5 cm c) 10cm d) 6.3 cm 3. Match the following: 1) Reflex angle a) less than ) Obtuse angle b) equals to

10 3) Acute angle c) more than 90 0 and less than ) Right angle d) equal to ) Straight angle e) greater than and less than ) Complete angle f) equal to Classify the following angles as zero, acute, obtuse, reflex, right and complete angle: 52 0, 103 0, 89 0, 90 0, 359 0, , 89 0, 360 0, 0 0, Classify the following angles. 10