EDULABZ INTERNATIONAL NUMBER SYSTEM

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1 NUMBER SYSTEM 1. Find the product of the place value of 8 and the face value of 7 in the number Ans. Place value of 8 in 7801 = 800, Face value of 7 in 7801 = 7 Required product = = 00. How many -digit numbers are there in all? Ans. Greatest digit numbers =, Greatest -digit numbers = Total number of -digit numbers = = Determine the product of the greatest number of three digits and the smallest number of four digits. Ans. Greatest number of three digits =, Smallest number of four digits = 1000 Product of smallest and greatest = 1000 = 000. Divide the following and check the result by division algorithm : (i) 7 1 (ii) 18 Ans. (i) (ii) On dividing 7 by 1, we get On dividing 18 by, we get quotient = and remainder = 101 quotient = and remainder = 8 check = check = + 8 = = 7 = = 18. Find the number which when divided by 8 gives the quotient and remainder 17. Ans. Divisor = 8, Quotient =, Remainder = 17 Dividend = divisor quotient + remainder = = = 81.. Which least number should be subtracted from 1000 so that the difference is exactly divisible by. Ans On dividing 1000 by we get quotient 70 = 8 and remainder 0 00 Hence, 0 should be subtracted form ICSE Math Class VII 1 Question Bank

2 7. Which least number should be added to 1000 so that divides the sum exactly. Ans. On dividing 1000 by, we get quotient = 18 and remainder =. To get the remainder 0, we should add = 7 to Hence, solution is Find the largest digit number which is exactly divisible by 7. Ans. Largest three digit number =. On dividing by 7, we get Quotient = 1 and Remainder = 1 So, on subtracting 1 from, we get 1 = Find the smallest digit number which is exactly divisible by. 7 On dividing by. 1 Ans. Smallest digit number = On dividing by, we get, Remainder = Thus, = 10 should be added to to get the 7 smallest digit number divisible by. 80 Hence, solution is = What is the maximum and minimum number of digits in the sum on adding any two five digit number. Ans. The smallest digit number is 10000, On adding = 0000 We get digit number, The greatest digit number is On adding we get + = 18 a - digit number Hence, the maximum and minimum number of digits are and. 11. Divide 087 by and check the result by division algorithm. Ans. Quotient = 1, Remainder = 1 Check : Dividend = Divisor Quotientt + Remainder = = + 1 = Find the largest -digit number which is exactly divisible by 7. Ans. Largest digit number is Dividing by 7, we get Remainder = Subtracting from, =, we get the required Number divisible by 7.So 1. Find the smallest -digit number which is exactly divisible by Ans. Smallest -digit number is 10000, ICSE Math Class VII Question Bank

3 Dividing it by 7, we get remainder = To make the smallest -digit number exactly divisible by 7, we have to add 7 = to Hence, the smallest digit is = Write the following statements in symbols. (i) The natural numbers < (ii) The whole numbers less than or equal to (iii) The integers less than or equal to and greater than (iv) The integers lying in between and (v) The integers greater than and less than or equal to 1 (vi) Negatives integers greater than. Ans. (i) x <, x N (ii) x, x W (iii) < x, x Z (iv) < x <, x Z (v) x 1, x I (vi) x >, x is a negative integer. 1. Evaluate the following: (i) 17 + (ii) (iii) 1 (iv) 1 + (v) 1 8 (vi) 17 Ans. (i) 17 + = 17 + =, (ii) = = 1 (iii) 1 = 1 = (iv) 1 + = 8 + = 8 + = 17 (v) 1 8 = 1 = 1 = (vi) 17 = 1 = 1 = 7 1. Add the following numbers using the number line : (i) + ( ) (ii) 7 + ( ) Ans. (i) + ( ) Start at on the number line and move units to the left. The answer is = (ii) 7 + ( ) Start at 7 on the number line and move units to the left. The answer is 7 = Subtract the following numbers using the number line : (i) ( ) (ii) ( ) (iii) ( 8) ICSE Math Class VII Question Bank

4 Ans. (i) Start at on the number line and move units to the right. The answer is + = (ii) Start at on the number line and move units to the right. The answer is + = (iii) ( 8) Start at on the number line and move 8 units to the right. The answer is + 8 = Find the value of : (i) ( ) (ii) 1 + ( ) + 18 ( ) (iii) 8 ( ) 8 + ( ) + 1 ( ) Ans. (i) ( ) = = = 1 = ( 1 + ) = (11) = 11 (ii) 1 + ( ) + 18 ( ) = = 8 + = = 10 (iii) 8 ( ) 8 + ( ) + 1 ( ) = = + 1 = 8 = 1. Find the following products: (i) ( ) ( 7) (ii) ( 1) ( ) ( ) (iii) ( 8) ( ) ( ) (iv) ( ) ( 8) Ans. (i) ( ) ( 7) = 1 = 8 (ii) ( 1) ( ) ( ) = 0 = 0 (iii) ( 8) ( ) ( ) = 1 1 = 0 (iv) ( ) ( 8) = 1 0 = Simplify the following (i) (ii) Ans. (i) + 1 = + 7 = = 1 (ii) = 1 + = = = 7 ICSE Math Class VII Question Bank

5 1. Simplify. (i) + 7 ( + ) (ii) (0 ) ( 7) Ans. (i) + 7 ( + ) = + 7 = = + 0 = 0 = (ii) (0 ) ( 7) = 18 =. Simplify. (i) 7 (ii) { (11 )} 1 Ans. (i) 7 = 7 = 7 = 7 = (ii) { (11 )} = ( 8} = =. Simplify (i) 10 {1 1 ( + 1)} (ii) 1 ( of + ) ( ) Ans. (i) 10 {1 1 ( + 1) = 10 {1 1 ( )} = 10 (1 1 ( 1)} = 10 {1 1 } = 10 {1 } = 10 1 = (ii) 1 ( of + ) ( ) = 1 ( + ) () = 1 (10 ) () = = 18 = 1. Draw different number lines to represent each of the following rational numbers : (i) (ii) 7 (iii) (iv) Ans. The number lines of each of the given number, 7,,, below: (i) (ii) (iii) (iv) (v) (v) and (vi) are given ICSE Math Class VII Question Bank

More Polynomial Equations Section 6.4

MATH 11009: More Polynomial Equations Section 6.4 Dividend: The number or expression you are dividing into. Divisor: The number or expression you are dividing by. Synthetic division: Synthetic division