What is 7/54 plus 7/21? (Answer: 25/54)

Exact Answer

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Problem: What is 7/54 plus 7/21?
Formula / Expression: 7/54 + 7/21
Final Answer: 25/54
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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 7/21 by 18 so both fractions share the common base 378.
Working: 7 × 7/54 × 7 = 49/378 and 7 × 18/21 × 18 = 126/378

Step 3: Add the Numerators
Now add the numerators (49 + 126 = 175) and keep the common denominator 378 unchanged.
Working: 49 + 126/378 = 175/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 175 and 378, which is 7. Divide both the numerator and denominator by 7.
Working: 175 ÷ 7/378 ÷ 7 = 25/54

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 54 produces a repeating decimal (approximately 0.462963, or 46.2963%).
Working: 25 ÷ 54 = 0.462963 (46.2963%)

Key Values:
- Simplified Fraction: 25/54
- Mixed Number Form: 25/54
- Decimal Value: 0.462963
- Percentage: 46.2963%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-54-plus-7-21/
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7/54 + 7/21 = 25/54

Simplified Fraction

25/54

Mixed Number

Proper (25/54)

Decimal Value

0.462963

Percentage

46.2963%

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

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 7/21 by 18 so both fractions share the common base 378.

7 × 7/54 × 7 = 49/378 and 7 × 18/21 × 18 = 126/378

Step 3

Add the Numerators

Now add the numerators (49 + 126 = 175) and keep the common denominator 378 unchanged.

49 + 126/378 = 175/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 175 and 378, which is 7. Divide both the numerator and denominator by 7.

175 ÷ 7/378 ÷ 7 = 25/54

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 54 produces a repeating decimal (approximately 0.462963, or 46.2963%).

25 ÷ 54 = 0.462963 (46.2963%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/54`
Mixed Number Form	`25/54`
Decimal Form	`0.462963`
Percentage	`46.2963%`

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Frequently Asked Questions

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

7/54 + 7/21 in simplest fraction form is 25/54.

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

7/54 + 7/21 converted to a decimal is 0.462963.

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

7/54 + 7/21 expressed as a percentage is 46.2963%.

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

It results in a repeating decimal (approximately 0.462963...) because the denominator contains prime factors other than 2 and 5.