What is 2/5 minus 7/9? (Answer: -17/45)

Exact Answer

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Problem: What is 2/5 minus 7/9?
Formula / Expression: 2/5 − 7/9
Final Answer: -17/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.
Working: LCD(5, 9) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 2/5 by 9, and multiply the numerator and denominator of 7/9 by 5 so both fractions share the common base 45.
Working: 2 × 9/5 × 9 = 18/45 and 7 × 5/9 × 5 = 35/45

Step 3: Subtract the Numerators
Now subtract the numerators (18 − 35 = -17) and keep the common denominator 45 unchanged.
Working: 18 − 35/45 = -17/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 45 is 1, confirming that -17/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: -17/45

Step 5: Decimal & Percentage Representation
Dividing the numerator -17 by denominator 45 produces a repeating decimal (approximately -0.377778, or -37.7778%).
Working: -17 ÷ 45 = -0.377778 (-37.7778%)

Key Values:
- Simplified Fraction: -17/45
- Mixed Number Form: -17/45
- Decimal Value: -0.377778
- Percentage: -37.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-5-minus-7-9/
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2/5 − 7/9 = -17/45

Simplified Fraction

-17/45

Mixed Number

Proper (-17/45)

Decimal Value

-0.377778

Percentage

-37.7778%

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Step-by-Step Solution: 2/5 − 7/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 9 = 45.

LCD(5, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 2/5 by 9, and multiply the numerator and denominator of 7/9 by 5 so both fractions share the common base 45.

2 × 9/5 × 9 = 18/45 and 7 × 5/9 × 5 = 35/45

Step 3

Subtract the Numerators

Now subtract the numerators (18 − 35 = -17) and keep the common denominator 45 unchanged.

18 − 35/45 = -17/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 45 is 1, confirming that -17/45 cannot be reduced further—it is already in its simplest irreducible form.

-17/45

Step 5

Decimal & Percentage Representation

Dividing the numerator -17 by denominator 45 produces a repeating decimal (approximately -0.377778, or -37.7778%).

-17 ÷ 45 = -0.377778 (-37.7778%)

Visual Representation

The diagram below illustrates 2/5 minus 7/9 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-17/45`
Mixed Number Form	`-17/45`
Decimal Form	`-0.377778`
Percentage	`-37.7778%`

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Frequently Asked Questions

What is 2/5 minus 7/9 as a fraction?

2/5 − 7/9 in simplest fraction form is -17/45.

What is 2/5 minus 7/9 as a decimal?

2/5 − 7/9 converted to a decimal is -0.377778.

What is 2/5 minus 7/9 as a percentage?

2/5 − 7/9 expressed as a percentage is -37.7778%.

Does 2/5 minus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.377778...) because the denominator contains prime factors other than 2 and 5.