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FractionsArithmeticElementary schoolabout 0:55

Calculate 3 1/2 + 1 1/4: animated lesson

A narrated, step-by-step fractions video lesson with captions. Final answer: 19/4.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    3 1/2 + 1 1/4
  2. 2. Steps, part 1
    1. 312=723\tfrac{1}{2} = \frac{7}{2}
      Convert the mixed number 3 1/2 to an improper fraction
    2. 114=541\tfrac{1}{4} = \frac{5}{4}
      Convert the mixed number 1 1/4 to an improper fraction
    3. 72+54=144+54\frac{7}{2} + \frac{5}{4} = \frac{14}{4} + \frac{5}{4}
      Rewrite both fractions with the least common denominator
    4. 14+54=194\frac{14 + 5}{4} = \frac{19}{4}
      Add the numerators and keep the denominator
  3. 3. Steps, part 2
    1. 194=434\frac{19}{4} = 4\tfrac{3}{4}
      Final answer in lowest terms
  4. 4. The answer
    194\frac{19}{4}

    3 1/2 + 1 1/4 = 19/4

  5. 5. Check
    • Decimal check: 19/4 ≈ 4.75
    • As a mixed number: 4 3/4

Transcript

The problem. Here is the problem: 3 1 over 2 plus 1 1 over 4. Exact arithmetic with fractions (results kept in lowest terms).

Steps, part 1. Convert the mixed number 3 1 over 2 to an improper fraction. Convert the mixed number 1 1 over 4 to an improper fraction. Rewrite both fractions with the least common denominator. The LCD of 2 and 4 is 4. Add the numerators and keep the denominator.

Steps, part 2. Final answer in lowest terms.

The answer. So the answer is 19 over 4. Fractions are combined over a common denominator for addition and subtraction, multiplied straight across, and divided by multiplying by the reciprocal. The result is reduced by the greatest common factor.

Check. Decimal check: 19 over 4 approximately 4.75. As a mixed number: 4 3 over 4.

About fractions

Add, subtract, multiply and divide fractions, finding common denominators and simplifying the result.

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