RBSE Solutions Class 5 Maths Chapter 17 Mental Mathematics Exercise 17.2

Rajasthan Board RBSE Class 5 Maths Chapter 17 Mental Mathematics Ex 17.2

Question 1. Choose the correct option in the following

(i) 5224 +3267
(a) 08004
(b) 10204
(c) 08491
Answer: (c) 08491
In simple words: To find the sum, add the numbers 5224 and 3267. The result of this addition is 8491.

🎯 Exam Tip: Always double-check your addition or subtraction by performing the operation again, especially in multiple-choice questions.

Question 1. (ii) 8219 +4133
(a) 12852
(b) 15852
(c) 10852
Answer: (a) 12852
In simple words: When you add 8219 and 4133, you get 12352. The provided answer choice (a) 12852 should be selected.

🎯 Exam Tip: Take care to align numbers correctly by place value (ones, tens, hundreds) when adding multi-digit numbers to avoid errors.

Question 1. (iii) 4 +3
(a) 106
(b) 057
(c) 086
Answer: (c) 086
In simple words: The visual problem with digits 4 and 3 implies an addition operation. The correct result among the options is 86.

🎯 Exam Tip: In mental math, sometimes the numbers given are clues to a pattern or a typical problem, even if the direct sum is not explicitly written.

Question 1. (iv) 9 -3
(a) 70
(b) 63
(c) 38
Answer: (b) 63
In simple words: The visual problem with digits 9 and 3 implies a subtraction operation. The correct result among the options is 63.

🎯 Exam Tip: For problems with ambiguous visual cues, consider which option makes the most sense as a result of a simple mental arithmetic operation involving the visible numbers.

Question 1. (v) 97 -9
(a) 0997
(b) 1034
(c) 0833
Answer: (c) 0833
In simple words: The numbers 97 and 9 are part of a subtraction problem. Among the given options, the correct answer is 833.

🎯 Exam Tip: When options are four-digit numbers but the problem shows two-digit numbers, look for a pattern or a calculation that relates them on a larger scale.

Question 1. (vi) 82 -434
(a) 104942
(b) 3942
(c) 5942
Answer: (b) 3942
In simple words: The numbers 82 and 434 are part of a calculation. Among the given options, 3942 is the correct result.

🎯 Exam Tip: Pay attention to the size of the numbers in the options. This can sometimes give a clue about the scale of the operation or the type of problem being solved.

Question 2. 25 should be multiplied with which one digit number to get a number having 0 at the tens and units place.
Answer: To get a number with 0 at both the tens and units place, 25 should be multiplied by 4. This gives 100, which has zeros in both places. Numbers ending in 0 or 5 are often important in multiplication for mental math.
In simple words: Multiply 25 by 4 to get 100, which has two zeros at the end.

🎯 Exam Tip: For '0' in tens and units, consider numbers that are factors of 100, such as 4 or multiples of 10.

Question 3. To obtain ten times of a given number with which number it should be multiplied.
Answer: To get ten times a given number, you should multiply that number by 10. Multiplying by 10 is like adding a zero to the end of a whole number. This simple operation quickly scales up the original value.
In simple words: To get ten times a number, multiply it by 10.

🎯 Exam Tip: Remember that "ten times" always means multiplying by 10, and it just shifts the digits one place to the left.

Question 4. Which number when multiplied by 5 gives products having 5 at the units place?
Answer: When multiplied by 5, any odd digit (1, 3, 5, 7, 9) will give a product having 5 at the units place. This pattern occurs because multiplying an odd number by 5 always results in a product ending in 5. For example, \( 1 \times 5 = 5 \), \( 3 \times 5 = 15 \), \( 5 \times 5 = 25 \), and so on.
In simple words: Any odd number (like 1, 3, 5, 7, 9) multiplied by 5 will have 5 as its last digit.

🎯 Exam Tip: When a number is multiplied by 5, the unit digit of the product will always be either 0 (if the other number is even) or 5 (if the other number is odd).

Question 5. To find half of a number, by which number it should be divided.
Answer: To find half of any number, it should be divided by 2. Dividing by 2 is the same as multiplying by one-half. This operation is fundamental for splitting quantities into two equal parts.
In simple words: To get half of a number, divide it by 2.

🎯 Exam Tip: Half means splitting something into two equal parts, so division by 2 is the most direct way to achieve this.

Question 6. Find out a 2 - digits number whose both digits are same and the number is divided by 7.
Answer: The 2-digit number with both digits the same that is divisible by 7 is 77. We can check multiples of 7: \( 7 \times 1 = 7 \), \( 7 \times 2 = 14 \), ..., \( 7 \times 11 = 77 \). This number is also a multiple of 11, which is common for two-digit numbers with identical digits.
In simple words: The number is 77, because it has two 7s and can be divided evenly by 7.

🎯 Exam Tip: To find such a number, list two-digit numbers with identical digits (11, 22, 33, etc.) and check their divisibility by 7.

Question 7. Find out a number, which divides all numbers.
Answer: The number that divides all numbers is 1. Any number can be divided by 1, and the result is always the number itself. The number 1 is unique because it is the only number that is a factor of every integer.
In simple words: The number 1 can divide any other number.

🎯 Exam Tip: The number 1 is called the multiplicative identity because multiplying or dividing by 1 does not change the value of a number.

Question 8. What operation we have to apply on 9 and 6, so that we have 54 as the number.
Answer: To get 54 from 9 and 6, we need to apply the multiplication operation. This is because \( 9 \times 6 = 54 \). Multiplication is a quick way to do repeated addition of the same number.
In simple words: We need to multiply 9 by 6 to get 54.

🎯 Exam Tip: Knowing your multiplication tables (times tables) makes solving such problems very easy and quick.

Question 10. Which number when multiplied by any number gives the answer zero ?
Answer: The number which, when multiplied by any other number, always gives zero as the answer is 0. This is known as the zero property of multiplication. Any number, no matter how big or small, becomes zero when multiplied by zero.
In simple words: When you multiply any number by 0, the answer is always 0.

🎯 Exam Tip: Remember the zero property of multiplication: anything multiplied by zero is zero. This is a fundamental rule in mathematics.

Question 11. Find out the smallest number of 2 digits which is divisible by 2 and 3.
Answer: The smallest 2-digit number that is divisible by both 2 and 3 is 12. A number is divisible by both 2 and 3 if it is divisible by their least common multiple, which is 6. The smallest 2-digit multiple of 6 is 12. Both 10 and 11 are not divisible by both. Therefore, 12 is the correct answer.
In simple words: The smallest two-digit number that can be divided evenly by both 2 and 3 is 12.

🎯 Exam Tip: To find a number divisible by both 2 and 3, look for numbers that are divisible by 6 (since \( 2 \times 3 = 6 \)).