What is 5/8 minus 9/21? (Answer: 11/56)

Exact Answer

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Problem: What is 5/8 minus 9/21?
Formula / Expression: 5/8 − 9/21
Final Answer: 11/56
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.
Working: LCD(8, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 5/8 by 21, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.
Working: 5 × 21/8 × 21 = 105/168 and 9 × 8/21 × 8 = 72/168

Step 3: Subtract the Numerators
Now subtract the numerators (105 − 72 = 33) and keep the common denominator 168 unchanged.
Working: 105 − 72/168 = 33/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/168 ÷ 3 = 11/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 56 produces a repeating decimal (approximately 0.196429, or 19.6429%).
Working: 11 ÷ 56 = 0.196429 (19.6429%)

Key Values:
- Simplified Fraction: 11/56
- Mixed Number Form: 11/56
- Decimal Value: 0.196429
- Percentage: 19.6429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-8-minus-9-21/
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5/8 − 9/21 = 11/56

Simplified Fraction

11/56

Mixed Number

Proper (11/56)

Decimal Value

0.196429

Percentage

19.6429%

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Step-by-Step Solution: 5/8 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.

LCD(8, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 5/8 by 21, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.

5 × 21/8 × 21 = 105/168 and 9 × 8/21 × 8 = 72/168

Step 3

Subtract the Numerators

Now subtract the numerators (105 − 72 = 33) and keep the common denominator 168 unchanged.

105 − 72/168 = 33/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 168, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/168 ÷ 3 = 11/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 56 produces a repeating decimal (approximately 0.196429, or 19.6429%).

11 ÷ 56 = 0.196429 (19.6429%)

Visual Representation

The diagram below illustrates 5/8 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/56`
Mixed Number Form	`11/56`
Decimal Form	`0.196429`
Percentage	`19.6429%`

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Frequently Asked Questions

What is 5/8 minus 9/21 as a fraction?

5/8 − 9/21 in simplest fraction form is 11/56.

What is 5/8 minus 9/21 as a decimal?

5/8 − 9/21 converted to a decimal is 0.196429.

What is 5/8 minus 9/21 as a percentage?

5/8 − 9/21 expressed as a percentage is 19.6429%.

Does 5/8 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.196429...) because the denominator contains prime factors other than 2 and 5.