What is 9/54 plus 4/21? (Answer: 5/14)

Exact Answer

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Problem: What is 9/54 plus 4/21?
Formula / Expression: 9/54 + 4/21
Final Answer: 5/14
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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 9/54 by 7, and multiply the numerator and denominator of 4/21 by 18 so both fractions share the common base 378.
Working: 9 × 7/54 × 7 = 63/378 and 4 × 18/21 × 18 = 72/378

Step 3: Add the Numerators
Now add the numerators (63 + 72 = 135) and keep the common denominator 378 unchanged.
Working: 63 + 72/378 = 135/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 378, which is 27. Divide both the numerator and denominator by 27.
Working: 135 ÷ 27/378 ÷ 27 = 5/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).
Working: 5 ÷ 14 = 0.357143 (35.7143%)

Key Values:
- Simplified Fraction: 5/14
- Mixed Number Form: 5/14
- Decimal Value: 0.357143
- Percentage: 35.7143%

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Solved with FractionsCalc:
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9/54 + 4/21 = 5/14

Simplified Fraction

5/14

Mixed Number

Proper (5/14)

Decimal Value

0.357143

Percentage

35.7143%

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Step-by-Step Solution: 9/54 + 4/21

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 9/54 by 7, and multiply the numerator and denominator of 4/21 by 18 so both fractions share the common base 378.

9 × 7/54 × 7 = 63/378 and 4 × 18/21 × 18 = 72/378

Step 3

Add the Numerators

Now add the numerators (63 + 72 = 135) and keep the common denominator 378 unchanged.

63 + 72/378 = 135/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 378, which is 27. Divide both the numerator and denominator by 27.

135 ÷ 27/378 ÷ 27 = 5/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).

5 ÷ 14 = 0.357143 (35.7143%)

Visual Representation

The diagram below illustrates 9/54 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/14`
Mixed Number Form	`5/14`
Decimal Form	`0.357143`
Percentage	`35.7143%`

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Frequently Asked Questions

What is 9/54 plus 4/21 as a fraction?

9/54 + 4/21 in simplest fraction form is 5/14.

What is 9/54 plus 4/21 as a decimal?

9/54 + 4/21 converted to a decimal is 0.357143.

What is 9/54 plus 4/21 as a percentage?

9/54 + 4/21 expressed as a percentage is 35.7143%.

Does 9/54 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.357143...) because the denominator contains prime factors other than 2 and 5.