What is 10/54 plus 7/21? (Answer: 14/27)

Exact Answer

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Problem: What is 10/54 plus 7/21?
Formula / Expression: 10/54 + 7/21
Final Answer: 14/27
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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 10/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.
Working: 10 × 7/54 × 7 = 70/378 and 7 × 18/21 × 18 = 126/378

Step 3: Add the Numerators
Now add the numerators (70 + 126 = 196) and keep the common denominator 378 unchanged.
Working: 70 + 126/378 = 196/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 196 and 378, which is 14. Divide both the numerator and denominator by 14.
Working: 196 ÷ 14/378 ÷ 14 = 14/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 27 produces a repeating decimal (approximately 0.518519, or 51.8519%).
Working: 14 ÷ 27 = 0.518519 (51.8519%)

Key Values:
- Simplified Fraction: 14/27
- Mixed Number Form: 14/27
- Decimal Value: 0.518519
- Percentage: 51.8519%

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Solved with FractionsCalc:
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10/54 + 7/21 = 14/27

Simplified Fraction

14/27

Mixed Number

Proper (14/27)

Decimal Value

0.518519

Percentage

51.8519%

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Step-by-Step Solution: 10/54 + 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 10/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.

10 × 7/54 × 7 = 70/378 and 7 × 18/21 × 18 = 126/378

Step 3

Add the Numerators

Now add the numerators (70 + 126 = 196) and keep the common denominator 378 unchanged.

70 + 126/378 = 196/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 196 and 378, which is 14. Divide both the numerator and denominator by 14.

196 ÷ 14/378 ÷ 14 = 14/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 27 produces a repeating decimal (approximately 0.518519, or 51.8519%).

14 ÷ 27 = 0.518519 (51.8519%)

Visual Representation

The diagram below illustrates 10/54 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/27`
Mixed Number Form	`14/27`
Decimal Form	`0.518519`
Percentage	`51.8519%`

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Frequently Asked Questions

What is 10/54 plus 7/21 as a fraction?

10/54 + 7/21 in simplest fraction form is 14/27.

What is 10/54 plus 7/21 as a decimal?

10/54 + 7/21 converted to a decimal is 0.518519.

What is 10/54 plus 7/21 as a percentage?

10/54 + 7/21 expressed as a percentage is 51.8519%.

Does 10/54 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.518519...) because the denominator contains prime factors other than 2 and 5.