What is 21/54 plus 9/21? (Answer: 103/126)

Exact Answer

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Problem: What is 21/54 plus 9/21?
Formula / Expression: 21/54 + 9/21
Final Answer: 103/126
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).
Working: LCD(54, 21) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 21/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 21 × 7/54 × 7 = 147/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (147 + 162 = 309) and keep the common denominator 378 unchanged.
Working: 147 + 162/378 = 309/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 309 and 378, which is 3. Divide both the numerator and denominator by 3.
Working: 309 ÷ 3/378 ÷ 3 = 103/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 126 produces a repeating decimal (approximately 0.81746, or 81.746%).
Working: 103 ÷ 126 = 0.81746 (81.746%)

Key Values:
- Simplified Fraction: 103/126
- Mixed Number Form: 103/126
- Decimal Value: 0.81746
- Percentage: 81.746%

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Solved with FractionsCalc:
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21/54 + 9/21 = 103/126

Simplified Fraction

103/126

Mixed Number

Proper (103/126)

Decimal Value

0.81746

Percentage

81.746%

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Step-by-Step Solution: 21/54 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 21/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

21 × 7/54 × 7 = 147/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (147 + 162 = 309) and keep the common denominator 378 unchanged.

147 + 162/378 = 309/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 309 and 378, which is 3. Divide both the numerator and denominator by 3.

309 ÷ 3/378 ÷ 3 = 103/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 126 produces a repeating decimal (approximately 0.81746, or 81.746%).

103 ÷ 126 = 0.81746 (81.746%)

Visual Representation

The diagram below illustrates 21/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/126`
Mixed Number Form	`103/126`
Decimal Form	`0.81746`
Percentage	`81.746%`

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Frequently Asked Questions

What is 21/54 plus 9/21 as a fraction?

21/54 + 9/21 in simplest fraction form is 103/126.

What is 21/54 plus 9/21 as a decimal?

21/54 + 9/21 converted to a decimal is 0.81746.

What is 21/54 plus 9/21 as a percentage?

21/54 + 9/21 expressed as a percentage is 81.746%.

Does 21/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.81746...) because the denominator contains prime factors other than 2 and 5.