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Add mixed numbers and fractions with step-by-step solutions. Learn how to add fractions with different denominators and convert results to mixed numbers.
• 2 1/4 + 1 3/8 = 3 5/8
• 1 1/2 + 2 1/3 = 3 5/6
• 3 2/5 + 1 1/2 = 4 9/10
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Step 1: Convert: 2 1/4 = 9/4 and 1 3/8 = 11/8
Step 2: LCD of 4 and 8 is 8
Step 3: 9/4 = 18/8
Step 4: 18/8 + 11/8 = 29/8
Step 5: 29/8 = 3 5/8
Converting to improper fractions is more reliable and less prone to errors, especially when denominators are different. The separate method is faster for simple problems with the same denominator.
After adding, always check if your fraction can be simplified. Find the GCF of the numerator and denominator, then divide both by it. This gives you the simplest form.
Keep your work organized. Line up numerators and denominators vertically. This helps prevent mistakes when finding common denominators and adding.
Convert your answer to decimal and add the original values as decimals. If they match, your answer is correct. This is a quick way to verify your work.
While not strictly necessary, converting to improper fractions first is the most reliable method and reduces errors. You can add the whole numbers and fractions separately, but you must still find a common denominator for the fractions and deal with any improper fractions that result.
When denominators are the same, you can simply add the numerators and keep the denominator. For example, 1/4 + 3/4 = 4/4 = 1. With mixed numbers like 2 1/4 + 1 3/4, you can add whole numbers (2+1=3) and fractions (1/4+3/4=1) separately to get 3+1=4.
After adding, if you get an improper fraction like 29/8, convert it to a mixed number. Divide the numerator by the denominator: 29÷8 = 3 remainder 5, so the answer is 3 5/8. The quotient is the whole number and the remainder becomes the new numerator.
For small numbers, list multiples of each denominator until you find a common one. For larger numbers, use the formula: LCD = (denominator1 × denominator2) / GCF. Or factor both numbers into primes and use each prime factor the maximum number of times it appears.
Yes! Convert all mixed numbers to improper fractions, find the LCD of all denominators, convert each fraction to the LCD, then add all numerators together. Finally, simplify and convert back to a mixed number. Adding multiple fractions follows the same principles as adding two.
Simplifying gives you the answer in its simplest, most standard form. In mathematics, fractions should always be reduced to lowest terms. For example, 6/8 should be simplified to 3/4. Teachers and textbooks expect simplified answers, and they're easier to understand and compare.