NCERT Class 7 Mathematics

ALGEBRAIC EXPRESSIONS 239 EXAMPLE 6 From the sum of 2y^2 + 3yz, – y^2 – yz – z^2 and yz + 2z^2 , subtract the sum of 3y^2 – z^2 ...

240 MATHEMATICS (viii) 3p^2 q^2 – 4pq + 5, – 10 p^2 q^2 , 15 + 9pq + 7p^2 q^2 (ix) ab – 4a, 4b – ab, 4a – 4b (x) x^2 – y^2 – 1, ...

ALGEBRAIC EXPRESSIONS 241 (ii) In 4x – 3, we get 4 x – 3 = (4 × 2) – 3 = 8 – 3 = 5 (iii) I n 1 9 – 5x^2 , we get 19 – 5x^2 = 19 ...

242 MATHEMATICS (ii) 7a – 4b, we get 7 a – 4b = 7 × 3 – 4 × 2 = 21 – 8 = 13. (iii) a^2 + 2ab + b^2 , we get a^2 + 2ab + b^2 = 3^ ...

ALGEBRAIC EXPRESSIONS 243 12.8 USING ALGEBRAIC EXPRESSIONS – FORMULAS AND RULES We have seen earlier also that formulas and rule ...

244 MATHEMATICS If a natural number is denoted by n, 2n is an even number and (2n+ 1) an odd number. Let us check it for any nu ...

ALGEBRAIC EXPRESSIONS 245 Make similar pattern with basic figures as shown (The number of segments required to make the figure i ...

246 MATHEMATICS From one vertex of a pentagon? Check it, it is 2. From one vertex of a hexagon? It is 3. The number of diagonals ...

ALGEBRAIC EXPRESSIONS 247 Use the given algebraic expression to complete the table of number patterns. S. Expression Terms No. ...

248 MATHEMATICS In situations such as solving an equation and using a formula, we have to find the value of an expression. The ...

13.1 INTRODUCTION Do you know what the mass of earth is? It is 5,970,000,000,000,000,000,000,000 kg! Can you read this number? M ...

250 MATHEMATICS We have used numbers like 10, 100, 1000 etc., while writing numbers in an expanded form. For example, 47561 = 4 ...

EXPONENTS AND POWERS 251 a × a × b × b × b × b can be expressed as a^2 b^4 (read as a squared into braised to the power of 4). E ...

252 MATHEMATICS (ii) 432 = 2 × 216 = 2 × 2 × 108 = 2 × 2 × 2 × 54 = 2 × 2 × 2 × 2 × 27 = 2 × 2 × 2 × 2 × 3 × 9 = 2 × 2 × 2 × 2 × ...

EXPONENTS AND POWERS 253 Express each of the following numbers using exponential notation: (i) 5 1 2 (ii) 3 4 3 (iii) 7 2 9 (iv ...

254 MATHEMATICS Can you write the appropriate number in the box. (–11)^2 × (–11)^6 = (–11) b^2 × b^3 =b (Remember, base is same; ...

EXPONENTS AND POWERS 255 For non-zero integers b and c, b^10 ÷ b^5 =b c^100 ÷ c^90 =c In general, for any non-zero integer a, am ...

256 MATHEMATICS EXAMPLE 7 Can you tell which one is greater (5^2 ) × 3 or   2 3 5? SOLUTION (5^2 ) × 3 means 5^2 is multiplied ...

EXPONENTS AND POWERS 257 (ii) (2a)^4 =2a × 2a × 2a × 2a = (2 × 2 × 2 × 2) × (a×a×a×a) =2^4 × a^4 (iii) ( – 4m)^3 = (– 4 × m)^3 = ...

258 MATHEMATICS 35 ÷ 35 =35 – 5 = 3^0 So 30 =1 Can you tell what 7^0 is equal to? 73 ÷ 73 =7^3 –^3 = 7^0 And 3 3 7 7 = 7×7×7 1 7 ...