What is 9/21 plus 20/46? (Answer: 139/161)

Exact Answer

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Problem: What is 9/21 plus 20/46?
Formula / Expression: 9/21 + 20/46
Final Answer: 139/161
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 46 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 46 = 966.
Working: LCD(21, 46) = 966

Step 2: Convert to Equivalent Fractions with Common Denominator 966
Multiply the numerator and denominator of 9/21 by 46, and multiply the numerator and denominator of 20/46 by 21 so both fractions share the common base 966.
Working: 9 × 46/21 × 46 = 414/966 and 20 × 21/46 × 21 = 420/966

Step 3: Add the Numerators
Now add the numerators (414 + 420 = 834) and keep the common denominator 966 unchanged.
Working: 414 + 420/966 = 834/966

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 834 and 966, which is 6. Divide both the numerator and denominator by 6.
Working: 834 ÷ 6/966 ÷ 6 = 139/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 161 produces a repeating decimal (approximately 0.863354, or 86.3354%).
Working: 139 ÷ 161 = 0.863354 (86.3354%)

Key Values:
- Simplified Fraction: 139/161
- Mixed Number Form: 139/161
- Decimal Value: 0.863354
- Percentage: 86.3354%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-20-46/
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9/21 + 20/46 = 139/161

Simplified Fraction

139/161

Mixed Number

Proper (139/161)

Decimal Value

0.863354

Percentage

86.3354%

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Step-by-Step Solution: 9/21 + 20/46

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 46 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 46 = 966.

LCD(21, 46) = 966

Step 2

Convert to Equivalent Fractions with Common Denominator 966

Multiply the numerator and denominator of 9/21 by 46, and multiply the numerator and denominator of 20/46 by 21 so both fractions share the common base 966.

9 × 46/21 × 46 = 414/966 and 20 × 21/46 × 21 = 420/966

Step 3

Add the Numerators

Now add the numerators (414 + 420 = 834) and keep the common denominator 966 unchanged.

414 + 420/966 = 834/966

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 834 and 966, which is 6. Divide both the numerator and denominator by 6.

834 ÷ 6/966 ÷ 6 = 139/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 161 produces a repeating decimal (approximately 0.863354, or 86.3354%).

139 ÷ 161 = 0.863354 (86.3354%)

Visual Representation

The diagram below illustrates 9/21 plus 20/46 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/161`
Mixed Number Form	`139/161`
Decimal Form	`0.863354`
Percentage	`86.3354%`

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Frequently Asked Questions

What is 9/21 plus 20/46 as a fraction?

9/21 + 20/46 in simplest fraction form is 139/161.

What is 9/21 plus 20/46 as a decimal?

9/21 + 20/46 converted to a decimal is 0.863354.

What is 9/21 plus 20/46 as a percentage?

9/21 + 20/46 expressed as a percentage is 86.3354%.

Does 9/21 plus 20/46 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.863354...) because the denominator contains prime factors other than 2 and 5.