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Order of operationsArithmeticElementary schoolabout 1:03

Evaluate 1 - 1/2 + 1/4 - 1/8: animated lesson

A narrated, step-by-step order of operations video lesson with captions. Final answer: 5/8.

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    1 - 1/2 + 1/4 - 1/8
  2. 2. Steps, part 1
    1. 1−12=22−121 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2}
      Rewrite both fractions with the least common denominator
    2. 2−12=12\frac{2 - 1}{2} = \frac{1}{2}
      Subtract the numerators and keep the denominator
    3. 12+14=24+14\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4}
      Rewrite both fractions with the least common denominator
    4. 2+14=34\frac{2 + 1}{4} = \frac{3}{4}
      Add the numerators and keep the denominator
  3. 3. Steps, part 2
    1. 34−18=68−18\frac{3}{4} - \frac{1}{8} = \frac{6}{8} - \frac{1}{8}
      Rewrite both fractions with the least common denominator
    2. 6−18=58\frac{6 - 1}{8} = \frac{5}{8}
      Subtract the numerators and keep the denominator
    3. 58\frac{5}{8}
      Final answer in lowest terms
  4. 4. The answer
    58\frac{5}{8}

    1 - 1/2 + 1/4 - 1/8 = 5/8

  5. 5. Check
    • Decimal check: 5/8 ≈ 0.625

Transcript

The problem. Here is the problem: 1 minus 1 over 2 plus 1 over 4 minus 1 over 8. Exact arithmetic with fractions (results kept in lowest terms).

Steps, part 1. Rewrite both fractions with the least common denominator. The LCD of 1 and 2 is 2. Subtract the numerators and keep the denominator. 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. Rewrite both fractions with the least common denominator. The LCD of 4 and 8 is 8. Subtract the numerators and keep the denominator. Final answer in lowest terms.

The answer. So the answer is 5 over 8. 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: 5 over 8 approximately 0.625.

About order of operations

Evaluate expressions with brackets, powers, multiplication, division, addition and subtraction in the right order.

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Evaluate 1 - 1/2 + 1/4 - 1/8: Animated Step-by-Step Lesson