Class 8 Maths, Chapter 13 (NCERT). 15 questions by concept, 6 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
Think of a date. Multiply the month by 5, add 2, multiply by 4, add 3, multiply by 5, then add the day. Which number must be subtracted from the final answer to find the date?
(d) 55
Adding 2 then multiplying by 4 and by 5 puts 40 into the answer; adding 3 then multiplying by 5 puts 15 in. So 55 must be subtracted.
Take the number 47. Reverse its digits, subtract the smaller number from the larger, then divide by 9. What is the quotient?
(d) 3
Reversing 47 gives 74, and . Then , which is the difference of the digits, .
Each box is the sum of the two boxes directly below it. The top box is 60 and the bottom row is 12, blank, 8. What number goes in the middle box of the bottom row?
(b) 20
Call the middle box . The middle row is and , and these add to the top box.
So , which gives and .
The 2-digit number with tens digit 3 and ones digit 1 is added to the number made by reversing its digits. What is the sum?
(a) 44
The number is 31 and reversing its digits gives 13. Adding, 31 + 13 = 44, which is 11 times the digit sum 4.
Think of a date. Multiply the month by 5, add 6, multiply by 4, add 9, multiply by 5, then add the day. The date is day 26 of month 1. What is the final answer?
(b) 291
Month 1 gives 5, then 11, then 44, then 53, then 265. Adding the day 26 gives 291.
Think of a number, double it, add four, divide by two, then subtract the number you thought of. Starting with 6, what is the final result?
(c) 2
Double 6 to get 12, add four to get 16, divide by two to get 8. Subtracting the 6 you started with leaves 2.
Think of a number, add 3, double it, add 4, divide by two, then subtract the number you thought of. Starting with 4 and then with 10, what are the two final results?
(c) 5 and 5
From 4 the steps give 7, 14, 18, 9 and then 5. From 10 they give 13, 26, 30, 15 and again 5. The start drops out, so both results are 5.
Each box is the sum of the two boxes directly below it. The top box is 10, the left box of the middle row is 4, and the first box of the bottom row is 1. What number goes in the last box of the bottom row?
(d) 3
Going down means subtracting. The right middle box is and the middle bottom box is .
The last box is .
Each box is the sum of the two boxes directly below it. The bottom row is 3, 4, 3. What number goes in the top box?
(a) 14
The middle row is and . The top box is .
Each box is the sum of the two boxes directly below it. The bottom row is the first three Virahāṅka-Fibonacci numbers, 1, 2, 3. What number goes in the top box?
(a) 8
The middle row is 1 + 2 = 3 and 2 + 3 = 5. The top box is 3 + 5 = 8.
Each box is the sum of the two boxes directly below it. The top box is 50, the right box of the second row is 22, and the bottom row has 4 in its first box and 6 in its third box. What number goes in the second box of the bottom row?
(b) 9
The left box of row 2 is . Call the second bottom box ; the two boxes under 28 are and .
So , which gives and . The complete bottom row is 4, 9, 6, 1. Moving upward, the rows are 13, 15, 7; then 28, 22; then 50.
Each box is the sum of the two boxes directly below it. The pyramid was filled with middle row , and top box . What is the correct expression for the top box?
(c)
The middle row is right. The top box is , not .
Each box is the sum of the two boxes directly below it. A pyramid has four rows and its bottom row is 8, 19, 21, 13. Without building the entire pyramid, what number is in the topmost row?
(a) 141
For four rows the top is the first number, plus three times the second, plus three times the third, plus the last: 8 + 57 + 63 + 13 = 141.
A grid is picked from a page of a calendar. Its top-left number is 6. What is the sum of the four numbers in the grid?
(a) 40
The grid is 6, 7, 13 and 14, since the numbers below 6 and 7 are a week later. Their sum is 6 + 7 + 13 + 14 = 40.
In a grid, shapes stand for numbers and the last column of each row is the sum of the shapes to its left. The first row is square, square, square and its sum is 27. The second row is circle, circle, square and its sum is 19. What number does the circle stand for?
(d) 5
Three squares make 27, so the square is 9. Then circle + circle + 9 = 19, so two circles make 10 and the circle is 5.
Wrong
(x + 3)² = x² + 9
Why it feels right. I square each term I can see.
Right
Squaring a sum means multiplying both complete brackets.
Worked example
