What is 3/54 plus 7/21? (Answer: 7/18)

Exact Answer

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Problem: What is 3/54 plus 7/21?
Formula / Expression: 3/54 + 7/21
Final Answer: 7/18
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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 3/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.
Working: 3 × 7/54 × 7 = 21/378 and 7 × 18/21 × 18 = 126/378

Step 3: Add the Numerators
Now add the numerators (21 + 126 = 147) and keep the common denominator 378 unchanged.
Working: 21 + 126/378 = 147/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 378, which is 21. Divide both the numerator and denominator by 21.
Working: 147 ÷ 21/378 ÷ 21 = 7/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 18 produces a repeating decimal (approximately 0.388889, or 38.8889%).
Working: 7 ÷ 18 = 0.388889 (38.8889%)

Key Values:
- Simplified Fraction: 7/18
- Mixed Number Form: 7/18
- Decimal Value: 0.388889
- Percentage: 38.8889%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-54-plus-7-21/
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3/54 + 7/21 = 7/18

Simplified Fraction

7/18

Mixed Number

Proper (7/18)

Decimal Value

0.388889

Percentage

38.8889%

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

3 × 7/54 × 7 = 21/378 and 7 × 18/21 × 18 = 126/378

Step 3

Add the Numerators

Now add the numerators (21 + 126 = 147) and keep the common denominator 378 unchanged.

21 + 126/378 = 147/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 378, which is 21. Divide both the numerator and denominator by 21.

147 ÷ 21/378 ÷ 21 = 7/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 18 produces a repeating decimal (approximately 0.388889, or 38.8889%).

7 ÷ 18 = 0.388889 (38.8889%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/18`
Mixed Number Form	`7/18`
Decimal Form	`0.388889`
Percentage	`38.8889%`

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Frequently Asked Questions

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

3/54 + 7/21 in simplest fraction form is 7/18.

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

3/54 + 7/21 converted to a decimal is 0.388889.

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

3/54 + 7/21 expressed as a percentage is 38.8889%.

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

It results in a repeating decimal (approximately 0.388889...) because the denominator contains prime factors other than 2 and 5.