What is 7/54 plus 3/21? (Answer: 103/378)

Exact Answer

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Problem: What is 7/54 plus 3/21?
Formula / Expression: 7/54 + 3/21
Final Answer: 103/378
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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 7/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.
Working: 7 × 7/54 × 7 = 49/378 and 3 × 18/21 × 18 = 54/378

Step 3: Add the Numerators
Now add the numerators (49 + 54 = 103) and keep the common denominator 378 unchanged.
Working: 49 + 54/378 = 103/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 378 is 1, confirming that 103/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 378 produces a repeating decimal (approximately 0.272487, or 27.2487%).
Working: 103 ÷ 378 = 0.272487 (27.2487%)

Key Values:
- Simplified Fraction: 103/378
- Mixed Number Form: 103/378
- Decimal Value: 0.272487
- Percentage: 27.2487%

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Solved with FractionsCalc:
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7/54 + 3/21 = 103/378

Simplified Fraction

103/378

Mixed Number

Proper (103/378)

Decimal Value

0.272487

Percentage

27.2487%

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Step-by-Step Solution: 7/54 + 3/21

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 7/54 by 7, and multiply the numerator and denominator of 3/21 by 18 so both fractions share the common base 378.

7 × 7/54 × 7 = 49/378 and 3 × 18/21 × 18 = 54/378

Step 3

Add the Numerators

Now add the numerators (49 + 54 = 103) and keep the common denominator 378 unchanged.

49 + 54/378 = 103/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 378 is 1, confirming that 103/378 cannot be reduced further—it is already in its simplest irreducible form.

103/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 378 produces a repeating decimal (approximately 0.272487, or 27.2487%).

103 ÷ 378 = 0.272487 (27.2487%)

Visual Representation

The diagram below illustrates 7/54 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/378`
Mixed Number Form	`103/378`
Decimal Form	`0.272487`
Percentage	`27.2487%`

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Frequently Asked Questions

What is 7/54 plus 3/21 as a fraction?

7/54 + 3/21 in simplest fraction form is 103/378.

What is 7/54 plus 3/21 as a decimal?

7/54 + 3/21 converted to a decimal is 0.272487.

What is 7/54 plus 3/21 as a percentage?

7/54 + 3/21 expressed as a percentage is 27.2487%.

Does 7/54 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.272487...) because the denominator contains prime factors other than 2 and 5.