Class 6 Challenging Mathematics Worksheet

1.

Word Problem In the number 623541, determine the place values of the digits 6 and 5. Compute the difference between these place values and then multiply the result by 2. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Identify place values: 6 is in the hundred-thousands place (600000) and 5 is in the thousands place (5000).

Step 2: Compute the difference: 600000 - 5000 = 595000.

Step 3: Multiply by 2: 595000 × 2 = 1190000

Answer: 1190000

2.

Word Problem Using the digits 6, 0, 8, 4, and 1 exactly once, form the greatest possible number. Next, form the smallest possible number (ensuring the number does not begin with 0). Finally, subtract the smaller number from the greater one. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Arrange digits in descending order for the greatest number: 8, 6, 4, 1, 0 → 86410.

Step 2: Arrange digits in ascending order for the smallest number, ensuring the first digit isn’t 0: 1, 0, 4, 6, 8 → 10468.

Step 3: Subtract: 86410 - 10468 = 75942

Answer: 75942

3.

Word Problem From the digits 3, 4, 9, and 0, determine how many unique 4-digit numbers can be formed without repetition. Then identify how many of these numbers are even. Finally, add these two results together. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Total 4-digit numbers: First digit choices (cannot be 0) = 3 options; remaining digits = 3! = 6; Total = 3×6 = 18.

Step 2: To count even numbers, the units digit must be 0 or 4.

- If unit digit is 0: First digit from {3,4,9} = 3 options, remaining 2 digits = 2! = 2; Count = 3×2 = 6.

- If unit digit is 4: First digit from {3,9} (since 0 is allowed but not as first digit) = 2 options, remaining 2 digits = 2; Count = 2×2 = 4.

Total even numbers = 6 + 4 = 10.

Step 3: Sum = 18 + 10 = 28

Answer: 28

4.

Word Problem Two petrol tanks contain 6325 ℓ and 4890 ℓ respectively. First, compute the difference between these two volumes and round this difference to the nearest hundred. Then, calculate the percentage this rounded difference represents of the smaller tank’s volume. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Compute the exact difference: 6325 - 4890 = 1435.

Step 2: Round 1435 to the nearest hundred: 1435 ≈ 1400.

Step 3: Percentage = (1400 / 4890) × 100 ≈ 28.62%

Answer: 28.62%

5.

Word Problem Estimate the product 958 × 387 by rounding each factor to the nearest hundred. Then, subtract 100 from the estimated product. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Round the numbers: 958 → 1000 and 387 → 400.

Step 2: Multiply the rounded numbers: 1000 × 400 = 400000.

Step 3: Subtract 100: 400000 - 100 = 399900

Answer: 399900

6.

Word Problem Estimate the quotient 2838 ÷ 125 by rounding both the dividend and the divisor to the nearest hundred. Then, add 5 to the estimated quotient. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Round the numbers: 2838 → 2800 and 125 → 100.

Step 2: Divide the rounded numbers: 2800 ÷ 100 = 28.

Step 3: Add 5: 28 + 5 = 33

Answer: 33

7.

Word Problem A school management spends $26,756 on teachers' pay, $325,378 on building construction, $5,780 on games, and $8,235 on other work. Calculate the total expenditure and then find by how much this total exceeds $360,000. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Compute the total: 26756 + 325378 = 352134; 352134 + 5780 = 357914; 357914 + 8235 = 366149.

Step 2: Difference from 360000: 366149 - 360000 = 6149

Answer: 6149

8.

Word Problem Madhu had $9031 and after buying a TV she was left with $1356. Determine the price of the TV and then subtract 100 from this price. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Price of the TV = 9031 - 1356 = 7675.

Step 2: Subtract 100: 7675 - 100 = 7575

Answer: 7575

9.

Word Problem The population of a country was 906450600 in 1990 and increased by 9889700 in 1991. Compute the population in 1991 and then determine 1% of that population. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: New population = 906450600 + 9889700 = 916340300.

Step 2: Calculate 1%: (1/100) × 916340300 = 9163403

Answer: 9163403

10.

Word Problem From a set of numbers, compute the sum for two groups: (a) 1086, 2117, 3543, and 1284; (b) 2637, 1283, 2549, and 98713. Then, subtract the sum of group (a) from group (b). Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Sum of group (a): 1086 + 2117 = 3203; 3203 + 3543 = 6746; 6746 + 1284 = 8030.

Step 2: Sum of group (b): 2637 + 1283 = 3920; 3920 + 2549 = 6469; 6469 + 98713 = 105182.

Step 3: Subtract: 105182 - 8030 = 97152

Answer: 97152

11.

Word Problem Determine whether 48 and 28 are perfect numbers. Assign a value of 1 if a number is perfect and 0 if it is not, then add these two values. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: 48 is not a perfect number, so assign 0.

Step 2: 28 is a perfect number (sum of proper divisors equals 28), so assign 1.

Step 3: Sum = 0 + 1 = 1

Answer: 1

12.

Word Problem Identify all prime numbers between 30 and 50. Then multiply these primes together and determine the last two digits of the product. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: The primes between 30 and 50 are 31, 37, 41, 43, and 47.

Step 2: Calculate the product step-wise modulo 100:

31 × 37 = 1147, last two digits = 47;

47 × 41 = 1927, last two digits = 27;

27 × 43 = 1161, last two digits = 61;

61 × 47 = 2867, last two digits = 67.

Answer: 67

13.

Word Problem Using Roman numerals, solve the equation: LXX + x = LXXVI. First convert the numerals to decimals, solve for x, and then subtract 5 from the value of x. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Convert: LXX = 70 and LXXVI = 76.

Step 2: Solve for x: 70 + x = 76, so x = 6.

Step 3: Subtract 5: 6 - 5 = 1

Answer: 1

14.

Word Problem Given the equation LIX = y + IX in Roman numerals, convert to decimals and solve for y. Then multiply the resulting value of y by 3. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Convert: LIX = 59 and IX = 9.

Step 2: Solve for y: 59 = y + 9, so y = 50.

Step 3: Multiply by 3: 50 × 3 = 150

Answer: 150

15.

Word Problem Determine the sum of the predecessor of 97801 and 90526. Then calculate how much this sum falls short of 200000. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Predecessor of 97801 is 97800.

Step 2: Sum = 97800 + 90526 = 188326.

Step 3: Difference from 200000: 200000 - 188326 = 11674

Answer: 11674

16.

Word Problem Find the product of the successor of 147 and 389. Then divide the product by 7 and round down to the nearest whole number. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Successor of 147 is 148.

Step 2: Compute the product: 148 × 389 = 57572.

Step 3: Divide by 7: 57572 ÷ 7 ≈ 8224.57, rounding down gives 8224

Answer: 8224

17.

Word Problem Using the distributive property, compute 632 × 1001. Then, calculate 99 × 82 and subtract this product from the first result. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Calculate 632 × 1001 = 632632.

Step 2: Calculate 99 × 82 = 8118.

Step 3: Subtract: 632632 - 8118 = 624514

Answer: 624514

18.

Word Problem Compute 1002 × 8716 using the distributive property. Then add 500 to the result. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Calculate 1002 × 8716 = (1000×8716) + (2×8716) = 8716000 + 17432 = 8733432.

Step 2: Add 500: 8733432 + 500 = 8733932

Answer: 8733932

19.

Word Problem Simplify the expression: 34 - [32 - {31 - (18 - 15 - 1)}]. Then add 10 to your simplified result. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Evaluate inner parentheses: (18 - 15 - 1) = 2.

Step 2: Evaluate the curly braces: {31 - 2} = 29.

Step 3: Evaluate the square brackets: [32 - 29] = 3.

Step 4: Compute: 34 - 3 = 31; then add 10: 31 + 10 = 41

Answer: 41

20.

Word Problem Simplify the expression: [4 × {6 + (9 - 4 + 2)} + 5] and then subtract 3 from the result. Show your working.

3 pts

Working:

Answer:

Worked Solution:

Step 1: Inside the parentheses: (9 - 4 + 2) = 7.

Step 2: Inside the curly braces: 6 + 7 = 13.

Step 3: Multiply: 4 × 13 = 52.

Step 4: Add 5: 52 + 5 = 57; then subtract 3: 57 - 3 = 54

Answer: 54

21.

Fill in the Blank The digit in the hundred-thousands place in 623541 is _____ .

3 pts

Answer: 6

22.

Fill in the Blank When forming the greatest number from the digits 6, 0, 8, 4, and 1, the digit placed in the ten-thousands position is _____ .

3 pts

Answer: 8

23.

Fill in the Blank In the set {3, 4, 9, 0}, when forming a 4-digit even number, the units digit must be _____ .

3 pts

Answer: 0

24.

Fill in the Blank Rounding 6325 to the nearest hundred gives _____ .

3 pts

Answer: 6300

25.

Fill in the Blank Rounding 4890 to the nearest hundred gives _____ .

3 pts

Answer: 4900

26.

Fill in the Blank When estimating the product 958 × 387 by rounding, 958 rounds to _____ .

3 pts

Answer: 1000

27.

Fill in the Blank When estimating the product 958 × 387 by rounding, 387 rounds to _____ .

3 pts

Answer: 400

28.

Fill in the Blank To estimate the quotient 2838 ÷ 125, if 2838 is rounded to the nearest hundred it becomes _____ .

3 pts

Answer: 2800

29.

Fill in the Blank To estimate the quotient 2838 ÷ 125, if 125 is rounded to the nearest hundred it becomes _____ .

3 pts

Answer: 100

30.

Fill in the Blank The additive identity for whole numbers is _____ .

3 pts

Answer: 0

31.

Fill in the Blank The sum of an odd number and an even number is always _____ .

3 pts

Answer: odd

32.

Fill in the Blank The total expense for building construction and teachers' pay, amounting to $325378 and $26756 respectively, is _____ .

3 pts

Answer: 352134

33.

Fill in the Blank After spending on various school items, if the total expenditure is $366149, then it exceeds $360000 by _____ .

3 pts

Answer: 6149

34.

Fill in the Blank If Madhu had $9031 and is left with $1356 after buying a TV, then the price of the TV is _____ .

3 pts

Answer: 7675

35.

Fill in the Blank The population increased from 906450600 by _____ to become 916340300.

3 pts

Answer: 9889700

36.

Fill in the Blank The sum of the numbers 1086, 2117, 3543, and 1284 is _____ .

3 pts

Answer: 8030

37.

Fill in the Blank The sum of the numbers 2637, 1283, 2549, and 98713 is _____ .

3 pts

Answer: 105182

38.

Fill in the Blank Among the prime numbers between 30 and 50, the smallest prime is _____ .

3 pts

Answer: 31

39.

Fill in the Blank In Roman numerals, LXX represents _____ in decimal form.

3 pts

Answer: 70

40.

Fill in the Blank Converting the Roman numeral LIX yields the decimal number _____ .

3 pts

Answer: 59