What is 1/5 minus 9/21? (Answer: -8/35)

Exact Answer

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Problem: What is 1/5 minus 9/21?
Formula / Expression: 1/5 − 9/21
Final Answer: -8/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.
Working: LCD(5, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 1/5 by 21, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.
Working: 1 × 21/5 × 21 = 21/105 and 9 × 5/21 × 5 = 45/105

Step 3: Subtract the Numerators
Now subtract the numerators (21 − 45 = -24) and keep the common denominator 105 unchanged.
Working: 21 − 45/105 = -24/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: -24 ÷ 3/105 ÷ 3 = -8/35

Step 5: Decimal & Percentage Representation
Dividing the numerator -8 by denominator 35 produces a repeating decimal (approximately -0.228571, or -22.8571%).
Working: -8 ÷ 35 = -0.228571 (-22.8571%)

Key Values:
- Simplified Fraction: -8/35
- Mixed Number Form: -8/35
- Decimal Value: -0.228571
- Percentage: -22.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-minus-9-21/
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1/5 − 9/21 = -8/35

Simplified Fraction

-8/35

Mixed Number

Proper (-8/35)

Decimal Value

-0.228571

Percentage

-22.8571%

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Step-by-Step Solution: 1/5 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 21 = 105.

LCD(5, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 1/5 by 21, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.

1 × 21/5 × 21 = 21/105 and 9 × 5/21 × 5 = 45/105

Step 3

Subtract the Numerators

Now subtract the numerators (21 − 45 = -24) and keep the common denominator 105 unchanged.

21 − 45/105 = -24/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 105, which is 3. Divide both the numerator and denominator by 3.

-24 ÷ 3/105 ÷ 3 = -8/35

Step 5

Decimal & Percentage Representation

Dividing the numerator -8 by denominator 35 produces a repeating decimal (approximately -0.228571, or -22.8571%).

-8 ÷ 35 = -0.228571 (-22.8571%)

Visual Representation

The diagram below illustrates 1/5 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-8/35`
Mixed Number Form	`-8/35`
Decimal Form	`-0.228571`
Percentage	`-22.8571%`

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Frequently Asked Questions

What is 1/5 minus 9/21 as a fraction?

1/5 − 9/21 in simplest fraction form is -8/35.

What is 1/5 minus 9/21 as a decimal?

1/5 − 9/21 converted to a decimal is -0.228571.

What is 1/5 minus 9/21 as a percentage?

1/5 − 9/21 expressed as a percentage is -22.8571%.

Does 1/5 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.228571...) because the denominator contains prime factors other than 2 and 5.