What is 5/9 minus 7/21? (Answer: 2/9)

Exact Answer

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Problem: What is 5/9 minus 7/21?
Formula / Expression: 5/9 − 7/21
Final Answer: 2/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).
Working: LCD(9, 21) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 5/9 by 7, and multiply the numerator and denominator of 7/21 by 3 so both fractions share the common base 63.
Working: 5 × 7/9 × 7 = 35/63 and 7 × 3/21 × 3 = 21/63

Step 3: Subtract the Numerators
Now subtract the numerators (35 − 21 = 14) and keep the common denominator 63 unchanged.
Working: 35 − 21/63 = 14/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 63, which is 7. Divide both the numerator and denominator by 7.
Working: 14 ÷ 7/63 ÷ 7 = 2/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 9 produces a repeating decimal (approximately 0.222222, or 22.2222%).
Working: 2 ÷ 9 = 0.222222 (22.2222%)

Key Values:
- Simplified Fraction: 2/9
- Mixed Number Form: 2/9
- Decimal Value: 0.222222
- Percentage: 22.2222%

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Solved with FractionsCalc:
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5/9 − 7/21 = 2/9

Simplified Fraction

2/9

Mixed Number

Proper (2/9)

Decimal Value

0.222222

Percentage

22.2222%

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Step-by-Step Solution: 5/9 − 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).

LCD(9, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 5/9 by 7, and multiply the numerator and denominator of 7/21 by 3 so both fractions share the common base 63.

5 × 7/9 × 7 = 35/63 and 7 × 3/21 × 3 = 21/63

Step 3

Subtract the Numerators

Now subtract the numerators (35 − 21 = 14) and keep the common denominator 63 unchanged.

35 − 21/63 = 14/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 63, which is 7. Divide both the numerator and denominator by 7.

14 ÷ 7/63 ÷ 7 = 2/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 9 produces a repeating decimal (approximately 0.222222, or 22.2222%).

2 ÷ 9 = 0.222222 (22.2222%)

Visual Representation

The diagram below illustrates 5/9 minus 7/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/9`
Mixed Number Form	`2/9`
Decimal Form	`0.222222`
Percentage	`22.2222%`

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Frequently Asked Questions

What is 5/9 minus 7/21 as a fraction?

5/9 − 7/21 in simplest fraction form is 2/9.

What is 5/9 minus 7/21 as a decimal?

5/9 − 7/21 converted to a decimal is 0.222222.

What is 5/9 minus 7/21 as a percentage?

5/9 − 7/21 expressed as a percentage is 22.2222%.

Does 5/9 minus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.222222...) because the denominator contains prime factors other than 2 and 5.