What is 8/21 plus 21/54? (Answer: 97/126)

Exact Answer

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Problem: What is 8/21 plus 21/54?
Formula / Expression: 8/21 + 21/54
Final Answer: 97/126
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 8/21 by 18, and multiply the numerator and denominator of 21/54 by 7 so both fractions share the common base 378.
Working: 8 × 18/21 × 18 = 144/378 and 21 × 7/54 × 7 = 147/378

Step 3: Add the Numerators
Now add the numerators (144 + 147 = 291) and keep the common denominator 378 unchanged.
Working: 144 + 147/378 = 291/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 291 and 378, which is 3. Divide both the numerator and denominator by 3.
Working: 291 ÷ 3/378 ÷ 3 = 97/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 126 produces a repeating decimal (approximately 0.769841, or 76.9841%).
Working: 97 ÷ 126 = 0.769841 (76.9841%)

Key Values:
- Simplified Fraction: 97/126
- Mixed Number Form: 97/126
- Decimal Value: 0.769841
- Percentage: 76.9841%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-21-plus-21-54/
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8/21 + 21/54 = 97/126

Simplified Fraction

97/126

Mixed Number

Proper (97/126)

Decimal Value

0.769841

Percentage

76.9841%

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Step-by-Step Solution: 8/21 + 21/54

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 54) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 8/21 by 18, and multiply the numerator and denominator of 21/54 by 7 so both fractions share the common base 378.

8 × 18/21 × 18 = 144/378 and 21 × 7/54 × 7 = 147/378

Step 3

Add the Numerators

Now add the numerators (144 + 147 = 291) and keep the common denominator 378 unchanged.

144 + 147/378 = 291/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 291 and 378, which is 3. Divide both the numerator and denominator by 3.

291 ÷ 3/378 ÷ 3 = 97/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 126 produces a repeating decimal (approximately 0.769841, or 76.9841%).

97 ÷ 126 = 0.769841 (76.9841%)

Visual Representation

The diagram below illustrates 8/21 plus 21/54 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/126`
Mixed Number Form	`97/126`
Decimal Form	`0.769841`
Percentage	`76.9841%`

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Frequently Asked Questions

What is 8/21 plus 21/54 as a fraction?

8/21 + 21/54 in simplest fraction form is 97/126.

What is 8/21 plus 21/54 as a decimal?

8/21 + 21/54 converted to a decimal is 0.769841.

What is 8/21 plus 21/54 as a percentage?

8/21 + 21/54 expressed as a percentage is 76.9841%.

Does 8/21 plus 21/54 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.769841...) because the denominator contains prime factors other than 2 and 5.