25 Math Problems for 4th Graders with Answers and Explanations
Welcome to a collection of 25 exciting math problems designed specifically for 4th graders. These problems cover a variety of math concepts, including addition, subtraction, multiplication, division, fractions, and more. Each question is labeled with its corresponding math subcategory and difficulty level, ranging from easy to medium. Detailed step-by-step explanations are provided to guide you through the problem-solving process. Let's embark on this math adventure and expand your knowledge and skills!
Problem 1: Addition of Two-digit Numbers (Arithmetic) - Easy
Calculate 42 + 19.
Solution:
Step 1: Add the ones place: 2 + 9 = 11. Write down the 1 and carry over the 10.
Step 2: Add the tens place and the carried over 10: 4 + 1 + 10 = 15.
Answer: 42 plus 19 equals 61.
Problem 2: Identifying Geometric Shapes (Geometry) - Easy
Which of the following shapes has four equal sides?
a) Square
b) Rectangle
c) Triangle
d) Circle
Solution:
a) Square
Answer: The shape that has four equal sides is a square.
Problem 3: Subtraction of Three-digit Numbers (Arithmetic) - Easy
Subtract 387 from 542.
Solution:
Step 1: Subtract the ones place: 2 - 7 = -5. Borrow 1 from the tens place.
Step 2: Subtract the tens place: (4 - 1) - 8 = -5. Borrow 1 from the hundreds place.
Step 3: Subtract the hundreds place: (5 - 1) - 3 = 1.
Answer: 542 minus 387 equals 155.
Problem 4: Counting Money (Arithmetic) - Easy
You have 3 quarters and 4 dimes. How much money do you have in total?
Solution:
Step 1: Multiply the number of quarters by 25 cents: 3 × 25 = 75 cents.
Step 2: Multiply the number of dimes by 10 cents: 4 × 10 = 40 cents.
Step 3: Add the two amounts together: 75 cents + 40 cents = 115 cents.
Answer: You have a total of 115 cents.
Problem 5: Simplifying Fractions (Arithmetic) - Easy
Simplify the fraction 6/12.
Solution:
Step 1: Find the greatest common divisor (GCD) of 6 and 12, which is 6.
Step 2: Divide both the numerator and the denominator by the GCD: (6 ÷ 6) / (12 ÷ 6) = 1/2.
Answer: The simplified fraction is 1/2.
Problem 6: Multiplication of Two-digit Numbers (Arithmetic) - Medium
Calculate 34 × 27.
Solution:
Step 1: Multiply the ones place: 4 × 7 = 28.
Step 2: Multiply the tens place: 3 × 7 = 21. Place a zero at the end.
Step 3: Add the partial products: 28 + 210 = 238.
Answer: 34 multiplied by 27 equals 238.
Problem 7: Identifying Equivalent Fractions (Arithmetic) - Medium
Which of the following fractions is equivalent to 3/4?
a) 6/12
b) 4/5
c) 9/10
d) 2/3
Solution:
d) 2/3
Answer: The fraction equivalent to 3/4 is 2/3.
Problem 8: Division with Remainders (Arithmetic) - Medium
Divide 207 by 8 and write the quotient with the remainder.
Solution:
Step 1: Divide 207 by 8: 8 goes into 20 two times (2 × 8 = 16).
Step 2: Calculate the remainder: 20 - 16 = 4.
Answer: The quotient of 207 divided by 8 is 25 with a remainder of 4.
Problem 9: Comparing Fractions (Arithmetic) - Medium
Which fraction is greater: 5/8 or 7/12?
Solution:
Step 1: Find a common denominator: The least common multiple of 8 and 12 is 24.
Step 2: Rewrite the fractions with a denominator of 24:
(5/8) = (15/24),
(7/12) = (14/24).
Step 3: Compare the numerators: 15 is greater than 14.
Answer: 5/8 is greater than 7/12.
Problem 10: Area of Rectangles (Geometry) - Medium
Find the area of a rectangle with a length of 15 cm and a width of 8 cm.
Solution:
Step 1: Use the formula for the area of a rectangle: Area = length × width.
Step 2: Substitute the given values: Area = 15 cm × 8 cm.
Step 3: Calculate: Area = 120 cm².
Answer: The area of the rectangle is 120 cm².
Problem 11: Multiplication of Fractions (Arithmetic) - Medium
Multiply 3/4 by 5/6.
Solution:
Step 1: Multiply the numerators: 3 × 5 = 15.
Step 2: Multiply the denominators: 4 × 6 = 24.
Answer: 3/4 multiplied by 5/6 equals 15/24.
Problem 12: Word Problems with Addition and Subtraction (Arithmetic) - Medium
The school library had 75 books, and 26 books were borrowed by students. How many books are left in the library?
Solution:
Step 1: Subtract the number of books borrowed from the total number of books: 75 - 26 = 49.
Answer: There are 49 books left in the library.
Problem 13: Estimation and Rounding (Arithmetic) - Medium
Estimate the sum of 294 and 187 to the nearest hundred.
Solution:
Step 1: Round each number to the nearest hundred: 300 and 200.
Step 2: Add the rounded numbers: 300 + 200 = 500.
Answer: The estimated sum of 294 and 187 to the nearest hundred is 500.
Problem 14: Fraction of a Set (Arithmetic) - Medium
Out of a bag containing 24 marbles, 3/4 are red. How many red marbles are there?
Solution:
Step 1: Calculate the number of red marbles: (3/4) × 24 = (3 × 24) / 4 = 72 / 4 = 18.
Answer: There are 18 red marbles.
Problem 15: Multiplication of Three-digit Numbers (Arithmetic) - Hard
Calculate 523 × 48.
Solution:
Step 1: Multiply the ones place: 3 × 8 = 24.
Step 2: Multiply the tens place: 2 × 8 = 16. Place a zero at the end.
Step 3: Multiply the hundreds place: 5 × 8 = 40. Place two zeros at the end.
Step 4: Add the partial products: 40,000 + 16,000 + 24 = 56,024.
Answer: 523 multiplied by 48 equals 56,024.
Problem 16: Division of Whole Numbers (Arithmetic) - Hard
Divide 1,728 by 12.
Solution:
Step 1: Divide the thousands place: 1,728 ÷ 12 = 144.
Answer: 1,728 divided by 12 equals 144.
Problem 17: Comparing Decimals (Arithmetic) - Hard
Which decimal is greater: 4.376 or 4.367?
Solution:
Step 1: Compare the whole numbers: 4 is equal in both decimals.
Step 2: Compare the tenths place: 3 is greater than 2.
Step 3: Compare the hundredths place: 7 is greater than 6.
Step 4: Compare the thousandths place: 6 is greater than 7.
Answer: 4.376 is greater than 4.367.
Problem 18: Fraction of a Whole (Arithmetic) - Hard
Find 2/5 of 75.
Solution:
Step 1: Multiply the fraction by the whole number: (2/5) × 75 = (2 × 75) / 5 = 150/5 = 30.
Answer: 2/5 of 75 is equal to 30.
Problem 19: Time Conversion (Measurement) - Hard
Convert 3 hours and 45 minutes to minutes.
Solution:
Step 1: Multiply the number of hours by 60: 3 hours × 60 = 180 minutes.
Step 2: Add the minutes: 180 minutes + 45 minutes = 225 minutes.
Answer: 3 hours and 45 minutes is equal to 225 minutes.
Problem 20: Perimeter of Rectangles (Geometry) - Hard
Find the perimeter of a rectangle with a length of 12 cm and a width of 7 cm.
Solution:
Step 1: Use the formula for the perimeter of a rectangle: Perimeter = 2 × (length + width).
Step 2: Substitute the given values: Perimeter = 2 × (12 cm + 7 cm).
Step 3: Calculate: Perimeter = 2 × 19 cm = 38 cm.
Answer: The perimeter of the rectangle is 38 cm.
Problem 21: Multiplication and Division with Powers of 10 (Arithmetic) - Hard
Simplify (6 × 10³) ÷ (3 × 10²).
Solution:
Step 1: Simplify the numerator: 6 × 10³ = 6,000.
Step 2: Simplify the denominator: 3 × 10² = 300.
Step 3: Divide the numerator by the denominator: 6,000 ÷ 300 = 20.
Answer: (6 × 10³) ÷ (3 × 10²) simplifies to 20.
Problem 22: Estimation and Rounding (Arithmetic) - Hard
Estimate the product of 427 and 62 to the nearest thousand.
Solution:
Step 1: Round each number to the nearest thousand: 1,000 and 0.
Step 2: Multiply the rounded numbers: 1,000 × 0 = 0.
Answer: The estimated product of 427 and 62 to the nearest thousand is 0.
Problem 23: Word Problems with Fractions (Arithmetic) - Hard
Out of 24 students, 5/6 went on a field trip. How many students went on the field trip?
Solution:
Step 1: Calculate the number of students who went on the field trip: (5/6) × 24 = (5 × 24) / 6 = 20.
Answer: 20 students went on the field trip.
Problem 24: Identifying Patterns (Arithmetic) - Hard
What is the next number in the pattern: 4, 9, 14, 19, ...?
Solution:
Step 1: Observe the pattern: Each number increases by 5.
Step 2: Determine the next number: 19 + 5 = 24.
Answer: The next number in the pattern is 24.
Problem 25: Word Problems with Multiple Operations (Arithmetic) - Hard
A store sold 78 packs of pencils, each containing 12 pencils. If each pencil costs 25 cents, how much money did the store make from selling the pencils?
Solution:
Step 1: Calculate the total number of pencils sold: 78 packs × 12 pencils/pack = 936 pencils.
Step 2: Multiply the number of pencils by the cost per pencil: 936 pencils × 25 cents/pencil = 23,400 cents.
Step 3: Convert cents to dollars: 23,400 cents ÷ 100 = $234.
Answer: The store made $234 from selling the pencils.
Congratulations on completing the 25 exciting math problems for 4th graders! Through these problems, you have explored various mathematical concepts and enhanced your problem-solving skills. Keep practicing and challenging yourself to excel in mathematics. Remember, math is all around us, and by developing a strong foundation, you can navigate the world of numbers with confidence. Great job!
Problem 1: Addition of Two-digit Numbers (Arithmetic) - Easy
Calculate 42 + 19.
Solution:
Step 1: Add the ones place: 2 + 9 = 11. Write down the 1 and carry over the 10.
Step 2: Add the tens place and the carried over 10: 4 + 1 + 10 = 15.
Answer: 42 plus 19 equals 61.
Problem 2: Identifying Geometric Shapes (Geometry) - Easy
Which of the following shapes has four equal sides?
a) Square
b) Rectangle
c) Triangle
d) Circle
Solution:
a) Square
Answer: The shape that has four equal sides is a square.
Problem 3: Subtraction of Three-digit Numbers (Arithmetic) - Easy
Subtract 387 from 542.
Solution:
Step 1: Subtract the ones place: 2 - 7 = -5. Borrow 1 from the tens place.
Step 2: Subtract the tens place: (4 - 1) - 8 = -5. Borrow 1 from the hundreds place.
Step 3: Subtract the hundreds place: (5 - 1) - 3 = 1.
Answer: 542 minus 387 equals 155.
Problem 4: Counting Money (Arithmetic) - Easy
You have 3 quarters and 4 dimes. How much money do you have in total?
Solution:
Step 1: Multiply the number of quarters by 25 cents: 3 × 25 = 75 cents.
Step 2: Multiply the number of dimes by 10 cents: 4 × 10 = 40 cents.
Step 3: Add the two amounts together: 75 cents + 40 cents = 115 cents.
Answer: You have a total of 115 cents.
Problem 5: Simplifying Fractions (Arithmetic) - Easy
Simplify the fraction 6/12.
Solution:
Step 1: Find the greatest common divisor (GCD) of 6 and 12, which is 6.
Step 2: Divide both the numerator and the denominator by the GCD: (6 ÷ 6) / (12 ÷ 6) = 1/2.
Answer: The simplified fraction is 1/2.
Problem 6: Multiplication of Two-digit Numbers (Arithmetic) - Medium
Calculate 34 × 27.
Solution:
Step 1: Multiply the ones place: 4 × 7 = 28.
Step 2: Multiply the tens place: 3 × 7 = 21. Place a zero at the end.
Step 3: Add the partial products: 28 + 210 = 238.
Answer: 34 multiplied by 27 equals 238.
Problem 7: Identifying Equivalent Fractions (Arithmetic) - Medium
Which of the following fractions is equivalent to 3/4?
a) 6/12
b) 4/5
c) 9/10
d) 2/3
Solution:
d) 2/3
Answer: The fraction equivalent to 3/4 is 2/3.
Problem 8: Division with Remainders (Arithmetic) - Medium
Divide 207 by 8 and write the quotient with the remainder.
Solution:
Step 1: Divide 207 by 8: 8 goes into 20 two times (2 × 8 = 16).
Step 2: Calculate the remainder: 20 - 16 = 4.
Answer: The quotient of 207 divided by 8 is 25 with a remainder of 4.
Problem 9: Comparing Fractions (Arithmetic) - Medium
Which fraction is greater: 5/8 or 7/12?
Solution:
Step 1: Find a common denominator: The least common multiple of 8 and 12 is 24.
Step 2: Rewrite the fractions with a denominator of 24:
(5/8) = (15/24),
(7/12) = (14/24).
Step 3: Compare the numerators: 15 is greater than 14.
Answer: 5/8 is greater than 7/12.
Problem 10: Area of Rectangles (Geometry) - Medium
Find the area of a rectangle with a length of 15 cm and a width of 8 cm.
Solution:
Step 1: Use the formula for the area of a rectangle: Area = length × width.
Step 2: Substitute the given values: Area = 15 cm × 8 cm.
Step 3: Calculate: Area = 120 cm².
Answer: The area of the rectangle is 120 cm².
Problem 11: Multiplication of Fractions (Arithmetic) - Medium
Multiply 3/4 by 5/6.
Solution:
Step 1: Multiply the numerators: 3 × 5 = 15.
Step 2: Multiply the denominators: 4 × 6 = 24.
Answer: 3/4 multiplied by 5/6 equals 15/24.
Problem 12: Word Problems with Addition and Subtraction (Arithmetic) - Medium
The school library had 75 books, and 26 books were borrowed by students. How many books are left in the library?
Solution:
Step 1: Subtract the number of books borrowed from the total number of books: 75 - 26 = 49.
Answer: There are 49 books left in the library.
Problem 13: Estimation and Rounding (Arithmetic) - Medium
Estimate the sum of 294 and 187 to the nearest hundred.
Solution:
Step 1: Round each number to the nearest hundred: 300 and 200.
Step 2: Add the rounded numbers: 300 + 200 = 500.
Answer: The estimated sum of 294 and 187 to the nearest hundred is 500.
Problem 14: Fraction of a Set (Arithmetic) - Medium
Out of a bag containing 24 marbles, 3/4 are red. How many red marbles are there?
Solution:
Step 1: Calculate the number of red marbles: (3/4) × 24 = (3 × 24) / 4 = 72 / 4 = 18.
Answer: There are 18 red marbles.
Problem 15: Multiplication of Three-digit Numbers (Arithmetic) - Hard
Calculate 523 × 48.
Solution:
Step 1: Multiply the ones place: 3 × 8 = 24.
Step 2: Multiply the tens place: 2 × 8 = 16. Place a zero at the end.
Step 3: Multiply the hundreds place: 5 × 8 = 40. Place two zeros at the end.
Step 4: Add the partial products: 40,000 + 16,000 + 24 = 56,024.
Answer: 523 multiplied by 48 equals 56,024.
Problem 16: Division of Whole Numbers (Arithmetic) - Hard
Divide 1,728 by 12.
Solution:
Step 1: Divide the thousands place: 1,728 ÷ 12 = 144.
Answer: 1,728 divided by 12 equals 144.
Problem 17: Comparing Decimals (Arithmetic) - Hard
Which decimal is greater: 4.376 or 4.367?
Solution:
Step 1: Compare the whole numbers: 4 is equal in both decimals.
Step 2: Compare the tenths place: 3 is greater than 2.
Step 3: Compare the hundredths place: 7 is greater than 6.
Step 4: Compare the thousandths place: 6 is greater than 7.
Answer: 4.376 is greater than 4.367.
Problem 18: Fraction of a Whole (Arithmetic) - Hard
Find 2/5 of 75.
Solution:
Step 1: Multiply the fraction by the whole number: (2/5) × 75 = (2 × 75) / 5 = 150/5 = 30.
Answer: 2/5 of 75 is equal to 30.
Problem 19: Time Conversion (Measurement) - Hard
Convert 3 hours and 45 minutes to minutes.
Solution:
Step 1: Multiply the number of hours by 60: 3 hours × 60 = 180 minutes.
Step 2: Add the minutes: 180 minutes + 45 minutes = 225 minutes.
Answer: 3 hours and 45 minutes is equal to 225 minutes.
Problem 20: Perimeter of Rectangles (Geometry) - Hard
Find the perimeter of a rectangle with a length of 12 cm and a width of 7 cm.
Solution:
Step 1: Use the formula for the perimeter of a rectangle: Perimeter = 2 × (length + width).
Step 2: Substitute the given values: Perimeter = 2 × (12 cm + 7 cm).
Step 3: Calculate: Perimeter = 2 × 19 cm = 38 cm.
Answer: The perimeter of the rectangle is 38 cm.
Problem 21: Multiplication and Division with Powers of 10 (Arithmetic) - Hard
Simplify (6 × 10³) ÷ (3 × 10²).
Solution:
Step 1: Simplify the numerator: 6 × 10³ = 6,000.
Step 2: Simplify the denominator: 3 × 10² = 300.
Step 3: Divide the numerator by the denominator: 6,000 ÷ 300 = 20.
Answer: (6 × 10³) ÷ (3 × 10²) simplifies to 20.
Problem 22: Estimation and Rounding (Arithmetic) - Hard
Estimate the product of 427 and 62 to the nearest thousand.
Solution:
Step 1: Round each number to the nearest thousand: 1,000 and 0.
Step 2: Multiply the rounded numbers: 1,000 × 0 = 0.
Answer: The estimated product of 427 and 62 to the nearest thousand is 0.
Problem 23: Word Problems with Fractions (Arithmetic) - Hard
Out of 24 students, 5/6 went on a field trip. How many students went on the field trip?
Solution:
Step 1: Calculate the number of students who went on the field trip: (5/6) × 24 = (5 × 24) / 6 = 20.
Answer: 20 students went on the field trip.
Problem 24: Identifying Patterns (Arithmetic) - Hard
What is the next number in the pattern: 4, 9, 14, 19, ...?
Solution:
Step 1: Observe the pattern: Each number increases by 5.
Step 2: Determine the next number: 19 + 5 = 24.
Answer: The next number in the pattern is 24.
Problem 25: Word Problems with Multiple Operations (Arithmetic) - Hard
A store sold 78 packs of pencils, each containing 12 pencils. If each pencil costs 25 cents, how much money did the store make from selling the pencils?
Solution:
Step 1: Calculate the total number of pencils sold: 78 packs × 12 pencils/pack = 936 pencils.
Step 2: Multiply the number of pencils by the cost per pencil: 936 pencils × 25 cents/pencil = 23,400 cents.
Step 3: Convert cents to dollars: 23,400 cents ÷ 100 = $234.
Answer: The store made $234 from selling the pencils.
Congratulations on completing the 25 exciting math problems for 4th graders! Through these problems, you have explored various mathematical concepts and enhanced your problem-solving skills. Keep practicing and challenging yourself to excel in mathematics. Remember, math is all around us, and by developing a strong foundation, you can navigate the world of numbers with confidence. Great job!