Education

4th Grade Math Problems: Topics, Solved Examples & Practice

I explain everything 4th graders learn in math, from multi-digit multiplication, long division, fractions, decimals, and geometry, step-by-step and mapped to the US Common Core State Standards.

Nikita Joshi

Nikita Joshi

— 12 min read
4th Grade Math Problems: Topics, Solved Examples & Practice

The way math is taught makes all the difference. When children can see a concept through visuals, explore it through guided simulations, and practice smart mental strategies instead of memorizing steps, they begin to understand, not just answer.

As someone who has spent time researching how kids learn math, my goal here is to share simple ways to solve math problems. The problems, solved examples, and curriculum structure you'll find here are based on content designed and taught by certified Cuemath tutors. They work with Grade 4 students every day and customize their teaching to each child's learning gaps and goals.

What Do 4th Graders Learn in Math?

According to the US Common Core State Standards for Mathematics, 4th grade math curriculum is divided into 5 core domains. 4th grade is the year of transition. Students move from foundational arithmetic toward multi-step reasoning, abstract fraction concepts, and geometry.

Domain

Key Skills

Topics Introduced in 4th Grade

Operations & Algebraic Thinking

Multi-step word problems, factors, multiples, prime vs. composite numbers, patterns

Prime/composite; factor pairs

Number & Operations in Base Ten

Place value to 1,000,000; compare/round large numbers; multi-digit multiplication; long division

Multi-digit multiplication; formal long division

Number & Operations (Fractions)

Equivalent fractions; comparing fractions; add/subtract fractions with like denominators; multiply fractions by whole numbers; decimals to hundredths

Fraction equivalence; fraction × whole number; decimals

Measurement & Data

Unit conversions (customary & metric); area and perimeter; angle measurement; line plots

Angle measurement with a protractor; unit conversion

Geometry

Lines, rays, line segments; parallel & perpendicular lines; angle types; triangle & quadrilateral classification; symmetry

Parallel/perpendicular; right/acute/obtuse triangles

🎯 Grade 4 Focus Areas: The CCSS defined 3 core areas for 4th grade — (1) developing understanding and fluency with multi-digit multiplication and division, (2) developing understanding of fraction equivalence, and (3) understanding geometric figures and their properties.

Multi-Digit Multiplication

Students multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

The most common strategies are the standard algorithm, the partial products method, and the area model.

Solved Problems on Multi-Digit Multiplication

Problem 1: Calculate: 347 × 6

1
Break 347 into place values: 300 + 40 + 7
2
Multiply each part by 6:
7 × 6 = 42
40 × 6 = 240
300 × 6 = 1,800
3
Add the partial products:
1,800
+  240
+   42
_______
2,082
✓ Answer: 347 × 6 = 2,082

Problem 2: Calculate: 53 × 47 using the area model.

1
Split both numbers as per place value: 53 = 50 + 3 and 47 = 40 + 7
2
Fill in the four cells of the area model:
50 × 40 = 2,000
50 × 7 = 350
3 × 40 = 120
3 × 7 = 21
    40       7

   ┌────────┬────────┐
50 │ 2,000  │ 350   │
   ├────────┼────────┤
3  │ 120    │ 21    │
   └────────┴────────┘
3
Add all four partial products:
2,000 + 350 + 120 + 21 = 2,491
✓ Answer: 53 × 47 = 2,491

Problem 3: A school cafeteria serves lunch to 248 students every day. How many students are served lunch over 5 school days?

1
Identify what we know: 248 students per day × 5 days
2
Set up the multiplication: 248 × 5
3
Use partial products:
200 × 5 = 1,000
40 × 5 = 200
8 × 5 = 40
4
Add: 1,000 + 200 + 40 = 1,240
✓ Answer: 1,240 students are served over 5 days.

Long Division

Students find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and the relationship between multiplication and division.

A good formula for the long division steps is DMSB: Divide → Multiply → Subtract → Bring down.

Solved Problems on Long Division

Problem 4: Calculate: 846 ÷ 3

1
Divide — How many times does 3 go into 8? 2 times. Write 2 above the 8.
2
Multiply — 2 × 3 = 6. Write 6 below 8.
3
Subtract — 8 − 6 = 2.
4
Bring down — Bring the 4 down to get 24.
5
Repeat — 3 goes into 24 exactly 8 times. 8 × 3 = 24. 24 − 24 = 0. Bring down 6. 3 goes into 6 exactly 2 times.
  282
  ─────
3 │ 8 4 6
  6
  ──
  2 4
  2 4
  ──
    6
    6
    ──
    0 ← no remainder
✓ Answer: 846 ÷ 3 = 282

Problem 5: Calculate: 1,357 ÷ 4 (find the quotient and remainder)

1
4 into 1? 0 times (1 is less than 4). Move to next digit. 4 into 13? 3 times. Write 3 above the 3.
2
3 × 4 = 12. Subtract: 13 − 12 = 1. Bring down 5 → 15.
3
4 into 15? 3 times. 3 × 4 = 12. 15 − 12 = 3. Bring down 7 → 37.
4
4 into 37? 9 times. 9 × 4 = 36. 37 − 36 = 1. No more digits to bring down.
339 ┌──── 4 │ 1357 12 ____ 15 12 ____ 37 36 ____ 1 ← remainder
✓ Answer: 1,357 ÷ 4 = 339 remainder 1 (or 339 R1)

Problem 6: A teacher has 97 pencils. She wants to give 8 pencils to each student. How many students can receive 8 pencils, and how many pencils will be left over?

1
Identify the operation: We're dividing 97 pencils into groups of 8.
2
Divide: 97 ÷ 8. 8 goes into 97 12 times (8 × 12 = 96). Remainder = 97 − 96 = 1.
3
Interpret the remainder: The remainder of 1 means 1 pencil is left over — it does NOT represent an extra student.
✓ Answer: 12 students can receive 8 pencils each; 1 pencil will be left over.

Fractions

In 4th grade curriculum, fractions are a major focus area. Students learn to explain fraction equivalence using visual fraction models and number lines, compare fractions with different numerators and denominators, and add and subtract fractions with like denominators. The US Common Core also introduces the concept of multiplying a fraction by a whole number

Solved Problems on Fractions

Problem 7: Show that 2/4 and 3/6 are equivalent fractions.

1
Method 1 — Cross-multiply to test: 2 × 6 = 12 and 4 × 3 = 12. Since both products are equal, the fractions are equivalent.
2
Method 2 — Simplify both: 2/4 ÷ (2/2) = 1/2. 3/6 ÷ (3/3) = 1/2. Both simplify to 1/2.
3
Method 3 — Scale up 2/4: Multiply numerator and denominator of 2/4 by 3/3: (2×3)/(4×3) = 6/12. Multiply 3/6 by 2/2: (3×2)/(6×2) = 6/12. Both equal 6/12. ✓
✓ Answer: Yes, 2/4 = 3/6. Both are equal to 1/2.

Problem 8: Add: 3/8 + 2/8

1
Check the denominators: Both fractions have the same denominator (8). When denominators match, add only the numerators.
2
Add numerators: 3 + 2 = 5. The denominator stays 8.
3
Check if result can be simplified: 5/8 — 5 and 8 share no common factor other than 1. Already in simplest form.
✓ Answer: 3/8 + 2/8 = 5/8

Problem 9: Compare 3/4 and 5/6. Which is larger?

1
Find a common denominator: The least common multiple of 4 and 6 is 12.
2
Convert both fractions:
3/4 = (3×3)/(4×3) = 9/12
5/6 = (5×2)/(6×2) = 10/12
3
Compare: 9/12 vs. 10/12. Since 10 > 9, we have 10/12 > 9/12.
✓ Answer: 5/6 > 3/4 (5/6 is larger)

Decimals

4th-grade students learn to read, write, and compare decimals to hundredths, and relate decimals to equivalent fractions (e.g., 0.7 = 7/10).

This is a bridge standard: it connects fraction fluency from earlier in 4th grade to the decimal operations introduced in 5th grade.

Solved Problems on Decimals

Problem 10: Write 0.47 as a fraction and explain what each digit means.

1
Read the decimal: 0.47 is read as "forty-seven hundredths." The last digit (7) is in the hundredths place.
2
Break down by place value: The 4 is in the tenths place (= 4/10 = 40/100). The 7 is in the hundredths place (= 7/100).
3
Write as a fraction: 0.47 = 47/100. This fraction is already in simplest form because 47 is a prime number.
✓ Answer: 0.47 = 47/100 ("forty-seven hundredths")

Problem 11: Order these decimals from least to greatest: 0.6, 0.06, 0.62, 0.59

1
Rewrite all with equal decimal places (hundredths):
0.6 = 0.60
0.06 = 0.06
0.62 = 0.62
0.59 = 0.59
2
Compare as whole numbers of hundredths: 6, 59, 60, 62
3
Order from smallest to largest: 6 → 59 → 60 → 62, which means 0.06 → 0.59 → 0.60 → 0.62
✓ Answer: 0.06, 0.59, 0.6, 0.62

Geometry & Angles

Grade 4 geometry focuses on classifying shapes by their properties and measuring angles. Students learn that an angle is a fraction of the full 360° rotation of a circle, and that right angles measure exactly 90°. They use protractors to measure to the nearest degree and classify triangles by angle type (acute, right, obtuse) and by side length (equilateral, isosceles, scalene).

Solved Problems on Geometry & Angles

Problem 12: An angle measures 135°. Is it acute, right, or obtuse? Explain your reasoning.

1
Recall the definitions: Acute = less than 90°. Right = exactly 90°. Obtuse = greater than 90° but less than 180°. Straight = exactly 180°.
2
Place 135° on the scale: 90° < 135° < 180°. The angle is greater than a right angle and less than a straight angle.
✓ Answer: 135° is an obtuse angle.

Problem 13: The three angles of a triangle measure 45°, 90°, and x°. Find x. What type of triangle is this?

1
Key fact: The angles of any triangle sum to 180°.
2
Set up the equation: 45° + 90° + x° = 180°
3
Solve for x: 135° + x° = 180°, so x° = 180° − 135° = 45°
4
Classify: The triangle has one 90° angle → it is a right triangle. Two equal angles (45° each) and two equal sides → it is also an isosceles right triangle.
✓ Answer: x = 45°. The triangle is an isosceles right triangle.

Measurement & Data

Students solve problems involving the measurement and conversion of measurements from a larger unit to a smaller unit. For example, converting feet to inches, pounds to ounces, or liters to milliliters. They also find the area and perimeter of rectangles and composite figures.

📏 Quick Conversions 1 foot = 12 inches | 1 yard = 3 feet | 1 mile = 5,280 feet | 1 pound = 16 ounces | 1 gallon = 4 quarts | 1 quart = 2 pints | 1 pint = 2 cups

Solved Problems on Measurement & Data

Problem 14: A hallway is 7 yards long. How many feet long is the hallway?

1
Recall the conversion: 1 yard = 3 feet
2
Multiply: 7 yards × 3 feet per yard = 21 feet
✓ Answer: The hallway is 21 feet long.

Problem 15: A rectangular garden is 12 meters long and 9 meters wide. What is the perimeter of the garden? What is the area?

1
Perimeter formula: P = 2 × (length + width) = 2 × (12 + 9) = 2 × 21 = 42 meters
2
Area formula: A = length × width = 12 × 9 = 108 square meters
✓ Perimeter = 42 m · Area = 108 m2

Multi-Step Word Problems

Students solve problems using all four operations, and must decide which operations to use and in what order.

Problem 16: A bookstore sold 124 fiction books and 89 non-fiction books on Monday. On Tuesday, it sold 3 times as many books as on Monday. How many books were sold in total over the two days?

1
Step 1 – Monday total: 124 + 89 = 213 books sold on Monday.
2
Step 2 – Tuesday total: 3 × 213 = 639 books sold on Tuesday.
3
Step 3 – Grand total: 213 + 639 = 852 books over two days.
✓ Answer: 852 books were sold over the two days.

Problem 17: Mia earns $8 per hour babysitting. She worked 6 hours last weekend and wants to save enough to buy a jacket that costs $75. How much more money does she need to save after last weekend?

1
Calculate earnings: $8 × 6 hours = $48
2
Find the gap: $75 − $48 = $27
✓ Answer: Mia needs $27 more to buy the jacket.
⚠️ Common Mistake: In multi-step problems, students often apply operations in the wrong order. Always re-read the problem after each step to confirm what you have found and what the question is actually asking for at the end.

Best Online Math Tutoring Platforms for 4th Graders in the USA

There is no shortage of websites where a 4th grader can find solved math problems (including this blog). But parents who've seen their child practice for weeks without making real progress usually identify the same root cause: the child is copying steps, not building understanding.

That is not something a worksheet or a video can fully provide. It requires a skilled human tutor.

In the past, I have reviewed the best math tutoring platforms in detail. You can have a look:

Best Online Math Tutoring Platforms in 2026, As Per Reviews
In this blog, I review the top 10 online math tutoring platforms based on parent & student reviews and explain why Cuemath is the best overall. You can find the right math tutoring service based on learning goals and the right fit.
CuemathNikita Joshi

My Verdict

The right math tutoring platforms depend on what your child actually needs.

  • If your child needs extra practice alongside school, Khan Academy and IXL are genuinely good free-to-low-cost tools.
  • They are decent, standards-aligned, and good enough for motivated students.
  • If your child is behind, struggling with specific concepts, or attending school without really understanding the math, Khan Academy or IXL will not work.
  • Your child needs a human tutor who can watch how your child thinks. For that, the combination of live 1:1 tutoring, a structured curriculum, and a pedagogy built around student reasoning is needed.
  • This makes Cuemath the best math tutoring platform among those reviewed here, particularly for Grade 4, where conceptual foundations (fractions, division, multi-step reasoning) become the basis for everything that follows in middle school.
"Our 4th grader actually looks forward to math now! The teacher makes lessons fun, interactive, and easy to follow, building a strong foundation and love for learning."
— Sushma, Parent of Grade 4 student, Trustpilot Review

Cuemath's 4th-grade math curriculum is designed as per the US Common Core State Standards covered in this article. Below are sample 4th-grade math worksheets. These are the actual materials students encounter in sessions, not worksheets generated to fill time.

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Frequently Asked Questions (FAQs)

What math topics do 4th graders learn according to Common Core?

According to the Common Core State Standards for 4th grade, students learn across five domains: Operations & Algebraic Thinking, Number & Operations in Base Ten, Number & Operations (Fractions), Measurement & Data, and Geometry. The three focus areas are multi-digit multiplication and division, fraction equivalence and operations, and geometric measurement and classification.

How is 4th grade math different from 3rd grade math?

Third grade focuses on multiplication and division facts within 100 and introducing fractions as parts of a whole. Fourth grade extends this significantly: students multiply multi-digit numbers (up to 4-digit × 1-digit), perform formal long division with remainders, develop fraction equivalence and comparison with unlike denominators, and learn decimal notation to hundredths. Geometric reasoning also becomes more formal, with angle measurement and shape classification by properties.

What are good 4th grade math problems for practice at home?

Good at-home practice should span all five CCSS domains. For multiplication, practice 3-digit × 1-digit and 2-digit × 2-digit problems. For division, work on long division with 3–4 digit dividends and single-digit divisors, including problems with remainders. For fractions, compare fractions with unlike denominators and practice adding and subtracting fractions with the same denominator. For decimals, practice reading, writing, and comparing tenths and hundredths. For word problems, use multi-step problems that require two or more operations.

How do you explain long division to a 4th grader?

Use the DMSB formula: Divide, Multiply, Subtract, Bring down. Understand each step of the problem properly: "How many times does [divisor] fit into [portion of dividend]?. Multiply that number by the divisor. Subtract. Bring down the next digit."

Division is just asking what number times [divisor] equals [dividend]. Remainders are explained as what's left over after sharing equally.

What are prime and composite numbers, and are they in 4th grade?

Yes, identifying prime and composite numbers is a part of 4th grade math curriculum. A prime number has exactly two factors: 1 and itself (e.g., 2, 3, 5, 7, 11, 13). A composite number has more than two factors (e.g., 6 has factors 1, 2, 3, 6). 1 is neither prime nor composite. Students also learn to find all factor pairs for numbers from 1 to 100.

About the Author
Nikita Joshi | Edtech Writer, Cuemath
5 years in edtech (content, curriculum & product research). I observe live Cuemath classes, talk to parents about the specific problems their kids get stuck on, and work closely with certified Cuemath tutors to make sure everything I write reflects how students actually think and learn, not just what the textbook says.
Math problems in this blog have been reviewed by Cuemath's team of expert tutors, trained in US Common Core State Standards and working daily with 4th–6th grade students.

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