What is 7/54 plus 8/21? (Answer: 193/378)

Exact Answer

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Problem: What is 7/54 plus 8/21?
Formula / Expression: 7/54 + 8/21
Final Answer: 193/378
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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 8/21 by 18 so both fractions share the common base 378.
Working: 7 × 7/54 × 7 = 49/378 and 8 × 18/21 × 18 = 144/378

Step 3: Add the Numerators
Now add the numerators (49 + 144 = 193) and keep the common denominator 378 unchanged.
Working: 49 + 144/378 = 193/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 193 and 378 is 1, confirming that 193/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 193/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 193 by denominator 378 produces a repeating decimal (approximately 0.510582, or 51.0582%).
Working: 193 ÷ 378 = 0.510582 (51.0582%)

Key Values:
- Simplified Fraction: 193/378
- Mixed Number Form: 193/378
- Decimal Value: 0.510582
- Percentage: 51.0582%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-54-plus-8-21/
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7/54 + 8/21 = 193/378

Simplified Fraction

193/378

Mixed Number

Proper (193/378)

Decimal Value

0.510582

Percentage

51.0582%

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Step-by-Step Solution: 7/54 + 8/21

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 8/21 by 18 so both fractions share the common base 378.

7 × 7/54 × 7 = 49/378 and 8 × 18/21 × 18 = 144/378

Step 3

Add the Numerators

Now add the numerators (49 + 144 = 193) and keep the common denominator 378 unchanged.

49 + 144/378 = 193/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 193 and 378 is 1, confirming that 193/378 cannot be reduced further—it is already in its simplest irreducible form.

193/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 193 by denominator 378 produces a repeating decimal (approximately 0.510582, or 51.0582%).

193 ÷ 378 = 0.510582 (51.0582%)

Visual Representation

The diagram below illustrates 7/54 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`193/378`
Mixed Number Form	`193/378`
Decimal Form	`0.510582`
Percentage	`51.0582%`

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Frequently Asked Questions

What is 7/54 plus 8/21 as a fraction?

7/54 + 8/21 in simplest fraction form is 193/378.

What is 7/54 plus 8/21 as a decimal?

7/54 + 8/21 converted to a decimal is 0.510582.

What is 7/54 plus 8/21 as a percentage?

7/54 + 8/21 expressed as a percentage is 51.0582%.

Does 7/54 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.510582...) because the denominator contains prime factors other than 2 and 5.