What is 2/35 minus 9/21? (Answer: -13/35)

Exact Answer

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Problem: What is 2/35 minus 9/21?
Formula / Expression: 2/35 − 9/21
Final Answer: -13/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.
Working: 2 × 3/35 × 3 = 6/105 and 9 × 5/21 × 5 = 45/105

Step 3: Subtract the Numerators
Now subtract the numerators (6 − 45 = -39) and keep the common denominator 105 unchanged.
Working: 6 − 45/105 = -39/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: -39 ÷ 3/105 ÷ 3 = -13/35

Step 5: Decimal & Percentage Representation
Dividing the numerator -13 by denominator 35 produces a repeating decimal (approximately -0.371429, or -37.1429%).
Working: -13 ÷ 35 = -0.371429 (-37.1429%)

Key Values:
- Simplified Fraction: -13/35
- Mixed Number Form: -13/35
- Decimal Value: -0.371429
- Percentage: -37.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-35-minus-9-21/
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2/35 − 9/21 = -13/35

Simplified Fraction

-13/35

Mixed Number

Proper (-13/35)

Decimal Value

-0.371429

Percentage

-37.1429%

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Step-by-Step Solution: 2/35 − 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/35 by 3, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.

2 × 3/35 × 3 = 6/105 and 9 × 5/21 × 5 = 45/105

Step 3

Subtract the Numerators

Now subtract the numerators (6 − 45 = -39) and keep the common denominator 105 unchanged.

6 − 45/105 = -39/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 105, which is 3. Divide both the numerator and denominator by 3.

-39 ÷ 3/105 ÷ 3 = -13/35

Step 5

Decimal & Percentage Representation

Dividing the numerator -13 by denominator 35 produces a repeating decimal (approximately -0.371429, or -37.1429%).

-13 ÷ 35 = -0.371429 (-37.1429%)

Visual Representation

The diagram below illustrates 2/35 minus 9/21 visually:

−

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`-13/35`
Mixed Number Form	`-13/35`
Decimal Form	`-0.371429`
Percentage	`-37.1429%`

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Frequently Asked Questions

What is 2/35 minus 9/21 as a fraction?

2/35 − 9/21 in simplest fraction form is -13/35.

What is 2/35 minus 9/21 as a decimal?

2/35 − 9/21 converted to a decimal is -0.371429.

What is 2/35 minus 9/21 as a percentage?

2/35 − 9/21 expressed as a percentage is -37.1429%.

Does 2/35 minus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately -0.371429...) because the denominator contains prime factors other than 2 and 5.