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FractionsArithmeticElementary schoolabout 0:54

Calculate 1/(1/2 + 1/3): animated lesson

A narrated, step-by-step fractions video lesson with captions. Final answer: 6/5.

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
    1/(1/2 + 1/3)
  2. 2. Steps, part 1
    1. 12+13=36+26\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6}
      Rewrite both fractions with the least common denominator
    2. 3+26=56\frac{3 + 2}{6} = \frac{5}{6}
      Add the numerators and keep the denominator
    3. 1÷56=1×651 \div \frac{5}{6} = 1 \times \frac{6}{5}
      Dividing by a fraction means multiplying by its reciprocal
    4. 1×65=1×61×5=651 \times \frac{6}{5} = \frac{1 \times 6}{1 \times 5} = \frac{6}{5}
      Multiply numerators and multiply denominators
  3. 3. Steps, part 2
    1. 65=115\frac{6}{5} = 1\tfrac{1}{5}
      Final answer in lowest terms
  4. 4. The answer
    65\frac{6}{5}

    1/(1/2 + 1/3) = 6/5

  5. 5. Check
    • Decimal check: 6/5 ≈ 1.2
    • As a mixed number: 1 1/5

Transcript

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

Steps, part 1. Rewrite both fractions with the least common denominator. The LCD of 2 and 3 is 6. Add the numerators and keep the denominator. Dividing by a fraction means multiplying by its reciprocal. Multiply numerators and multiply denominators.

Steps, part 2. Final answer in lowest terms.

The answer. So the answer is 6 over 5. 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: 6 over 5 approximately 1.2. As a mixed number: 1 1 over 5.

About fractions

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

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Calculate 1/(1/2 + 1/3): Fractions Step-by-Step Lesson