What is 7/54 plus 6/21? (Answer: 157/378)

Exact Answer

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Problem: What is 7/54 plus 6/21?
Formula / Expression: 7/54 + 6/21
Final Answer: 157/378
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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 6/21 by 18 so both fractions share the common base 378.
Working: 7 × 7/54 × 7 = 49/378 and 6 × 18/21 × 18 = 108/378

Step 3: Add the Numerators
Now add the numerators (49 + 108 = 157) and keep the common denominator 378 unchanged.
Working: 49 + 108/378 = 157/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 157 and 378 is 1, confirming that 157/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 157/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 157 by denominator 378 produces a repeating decimal (approximately 0.415344, or 41.5344%).
Working: 157 ÷ 378 = 0.415344 (41.5344%)

Key Values:
- Simplified Fraction: 157/378
- Mixed Number Form: 157/378
- Decimal Value: 0.415344
- Percentage: 41.5344%

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Solved with FractionsCalc:
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7/54 + 6/21 = 157/378

Simplified Fraction

157/378

Mixed Number

Proper (157/378)

Decimal Value

0.415344

Percentage

41.5344%

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Step-by-Step Solution: 7/54 + 6/21

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 6/21 by 18 so both fractions share the common base 378.

7 × 7/54 × 7 = 49/378 and 6 × 18/21 × 18 = 108/378

Step 3

Add the Numerators

Now add the numerators (49 + 108 = 157) and keep the common denominator 378 unchanged.

49 + 108/378 = 157/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 157 and 378 is 1, confirming that 157/378 cannot be reduced further—it is already in its simplest irreducible form.

157/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 157 by denominator 378 produces a repeating decimal (approximately 0.415344, or 41.5344%).

157 ÷ 378 = 0.415344 (41.5344%)

Visual Representation

The diagram below illustrates 7/54 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`157/378`
Mixed Number Form	`157/378`
Decimal Form	`0.415344`
Percentage	`41.5344%`

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Frequently Asked Questions

What is 7/54 plus 6/21 as a fraction?

7/54 + 6/21 in simplest fraction form is 157/378.

What is 7/54 plus 6/21 as a decimal?

7/54 + 6/21 converted to a decimal is 0.415344.

What is 7/54 plus 6/21 as a percentage?

7/54 + 6/21 expressed as a percentage is 41.5344%.

Does 7/54 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.415344...) because the denominator contains prime factors other than 2 and 5.