Add, subtract, multiply, and divide mixed numbers, fractions, and whole numbers with detailed step-by-step solutions. Perfect for students, teachers, and anyone learning fractions.
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A mixed numbers calculator is a mathematical tool that helps you perform arithmetic operations (addition, subtraction, multiplication, and division) with mixed numbers, proper fractions, improper fractions, whole numbers, and decimals. Mixed numbers consist of a whole number and a proper fraction, like 2 ¾ or 5 ⅓.
Our calculator provides step-by-step solutions using two different methods: separating parts (breaking down whole numbers and fractions separately) and using formulas (converting to improper fractions first). This educational approach helps students understand not just the answer, but the complete solving process.
The calculator automatically simplifies fractions to their lowest terms, finds the least common denominator (LCD) for addition and subtraction, handles negative numbers correctly, and displays results in the most readable format. Whether you're checking homework, teaching fractions, or solving real-world problems involving measurements and quantities, this tool provides accurate results with detailed explanations.
Method 1 - Separate Parts: Add/subtract whole numbers and fractions separately. Find common denominators for fractions.
Method 2 - Improper Fractions: Convert mixed numbers to improper fractions, find LCD, then add/subtract.
Example: 2 ¾ + 1 ½
= 2 + 1 + ¾ + ½
= 3 + ¾ + 2/4
= 3 + 5/4 = 4 ¼
Always convert to improper fractions first. Then multiply numerators and denominators, or flip and multiply for division.
Multiply: 2 ½ × 1 ⅓
= 5/2 × 4/3
= 20/6 = 10/3 = 3 ⅓
Divide: 3 ¾ ÷ 1 ¼
= 15/4 ÷ 5/4
= 15/4 × 4/5 = 3
See exactly how to solve each problem with detailed steps. Two different methods help you understand which approach works best for each situation - perfect for homework and exam preparation.
Verify your answers immediately and understand mistakes. The calculator shows the correct process, helping students learn from errors rather than just getting marked wrong.
Enter mixed numbers (2 ¾), fractions (¾), decimals (0.75), or whole numbers (3). The calculator handles all formats, making it flexible for any problem type or personal preference.
Results are automatically reduced to lowest terms. No need to manually find GCD or simplify - the calculator does it for you and shows the simplification process.
Perfect for cooking (recipe adjustments), construction (measurements), sewing (fabric calculations), and any task requiring fractional calculations. Practical beyond just schoolwork.
Uses standard mathematical approaches taught in schools. Both solution methods align with Common Core standards and traditional fraction instruction methodologies.
💡 Pro Tip: When adding or subtracting, use Method 1 (separate parts) for easier mental math. For multiplication and division, Method 2 (improper fractions) is always required!
Problem: A recipe calls for 2 ¾ cups flour, but you want to make 1 ½ times the recipe.
Solution: 2 ¾ × 1 ½ = 11/4 × 3/2 = 33/8 = 4 ⅛ cups flour needed
Result: You need 4 ⅛ cups of flour for the adjusted recipe
Problem: You need to cut boards that are 5 ¾ inches wide. How many can you cut from a 46-inch wide plank?
Solution: 46 ÷ 5 ¾ = 46 ÷ 23/4 = 46 × 4/23 = 184/23 = 8 boards
Result: You can cut exactly 8 boards from the plank
Problem: You have 12 ½ yards of fabric. Each dress requires 3 ¾ yards. How many dresses can you make?
Solution: 12 ½ ÷ 3 ¾ = 25/2 ÷ 15/4 = 25/2 × 4/15 = 100/30 = 3 ⅓ → 3 complete dresses
Result: You can make 3 complete dresses with fabric left over
Problem: Sarah walked 2 ⅔ miles on Monday and 1 ¾ miles on Tuesday. How far did she walk total?
Solution: 2 ⅔ + 1 ¾ = (2+1) + (⅔ + ¾) = 3 + (8/12 + 9/12) = 3 + 17/12 = 4 5/12 miles
Result: Sarah walked 4 5/12 miles in total
Method 1: Add whole numbers separately, then add fractions by finding the LCD (Least Common Denominator). For example, 2 ¾ + 1 ½: Add wholes (2+1=3), find LCD of 4 and 2 (which is 4), convert ½ to 2/4, add fractions (¾ + 2/4 = 5/4 = 1¼), then combine (3 + 1¼ = 4¼).
Always convert to improper fractions first, then multiply numerators together and denominators together. For example: 2 ½ × 1 ⅓ = 5/2 × 4/3 = (5×4)/(2×3) = 20/6 = 10/3 = 3 ⅓. Never try to multiply mixed numbers directly without converting first.
Use the formula: (whole number × denominator) + numerator, keep the same denominator. Example: 2 ¾ = (2 × 4 + 3) / 4 = (8 + 3) / 4 = 11/4. For negative numbers, apply the negative sign to the final result: -2 ¾ = -11/4.
You can only add or subtract fractions with the same denominator. The LCD (Least Common Denominator) is the smallest number that both denominators divide into evenly. For example, to add ¾ + ⅔, find LCD of 4 and 3 (which is 12), convert to 9/12 + 8/12 = 17/12 = 1 5/12.
Yes! Enter decimals like 1.75 or 0.5 and the calculator automatically converts them to fractions. For example, 1.75 becomes 1 ¾ and 0.5 becomes ½. This is useful when you have decimal measurements that need to be calculated with fractions.
Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. Example: 17/4 → 17 ÷ 4 = 4 remainder 1, so 17/4 = 4 ¼.
The calculator automatically converts improper fractions to mixed numbers in the final answer. However, if the improper fraction is already in lowest terms (like 5/4), it will show as a mixed number (1 ¼). In mathematics, either form is correct, but mixed numbers are usually preferred for final answers.
Put a minus sign before the number (e.g., -2 ¾). When calculating, the negative applies to the entire mixed number. For example: -2 ¾ = -11/4 (not -2 and ¾ separately). The calculator handles all negative number operations automatically.
Different students learn differently! Method 1 (Separating Parts) is intuitive for beginners and good for mental math with addition/subtraction. Method 2 (Formulas) is the standard algebraic approach, required for multiplication/division, and preferred for complex problems. Both methods give the same answer.
Yes! The calculator automatically reduces all fractions to lowest terms using the GCD (Greatest Common Divisor). For example, 6/8 automatically becomes ¾. This ensures all answers are in their simplest, most readable form as required in mathematics.
Always simplify your final answer: Teachers expect fractions in lowest terms. Use GCD to reduce: for 12/16, find GCD(12,16)=4, divide both by 4 to get ¾. The calculator does this automatically, but knowing how helps you check your work.
For multiplication/division, convert first: Never multiply or divide mixed numbers directly. Always convert to improper fractions first. This prevents errors and makes the calculation much simpler. Example: 2½ × 3 = 5/2 × 3/1 = 15/2 = 7½ (not 6½!).
Check if you can reduce before calculating: Sometimes simplifying fractions before operating makes calculation easier. For 8/12 + 6/12, notice both have 12 as denominator AND can be reduced: 8/12=⅔, 6/12=½. But actually here, just add first: 14/12 = 7/6 = 1⅙.
Use cross-multiplication shortcut for common denominators: When adding fractions with denominators that are multiples (like 4 and 2), you don't need LCD. Just multiply the smaller denominator: ¾ + ½ = ¾ + 2/4 = 5/4. This saves time!
Estimate before calculating: Round mixed numbers to check if your answer makes sense. 2¾ × 1½ should be close to 3×2=6? No, closer to 3×1.5=4.5, actual is 4⅛. This catches big mistakes like forgetting to convert or using wrong operations.
Know when whole numbers dominate: In 100¼ + 50⅛, the fractions (¼+⅛=⅜) barely affect the answer (150⅜). But in ¾ + ⅝, the fraction IS the answer (11/8=1⅜). Understanding scale helps with estimation and confidence.
Practice the conversion formula: Memorize "multiply whole by denominator, add numerator": 3¾ = (3×4+3)/4 = 15/4. This becomes automatic with practice and is essential for all fraction operations. Write it down until it's second nature.
Use visual aids for understanding: Draw pie charts or rectangles divided into parts. Seeing 2¾ as 2 whole pies plus ¾ of a third pie makes the concept concrete, especially for addition and subtraction. This builds intuition beyond just formulas.
| Mixed Number | Improper Fraction | Decimal |
|---|---|---|
| 1 ½ | 3/2 | 1.5 |
| 1 ⅓ | 4/3 | 1.333... |
| 1 ¼ | 5/4 | 1.25 |
| 2 ⅔ | 8/3 | 2.666... |
| 2 ¾ | 11/4 | 2.75 |
| 3 ½ | 7/2 | 3.5 |
| 4 ⅕ | 21/5 | 4.2 |
| 5 ⅜ | 43/8 | 5.375 |
Conversion Formula: To convert mixed number to improper: (whole × denominator) + numerator, keep same denominator. To convert back: divide numerator by denominator, quotient = whole, remainder = new numerator.
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