What is 16/54 plus 9/21? (Answer: 137/189)

Exact Answer

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Problem: What is 16/54 plus 9/21?
Formula / Expression: 16/54 + 9/21
Final Answer: 137/189
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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 16/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 16 × 7/54 × 7 = 112/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (112 + 162 = 274) and keep the common denominator 378 unchanged.
Working: 112 + 162/378 = 274/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 274 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 274 ÷ 2/378 ÷ 2 = 137/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 137 by denominator 189 produces a repeating decimal (approximately 0.724868, or 72.4868%).
Working: 137 ÷ 189 = 0.724868 (72.4868%)

Key Values:
- Simplified Fraction: 137/189
- Mixed Number Form: 137/189
- Decimal Value: 0.724868
- Percentage: 72.4868%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-54-plus-9-21/
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16/54 + 9/21 = 137/189

Simplified Fraction

137/189

Mixed Number

Proper (137/189)

Decimal Value

0.724868

Percentage

72.4868%

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Step-by-Step Solution: 16/54 + 9/21

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 16/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

16 × 7/54 × 7 = 112/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (112 + 162 = 274) and keep the common denominator 378 unchanged.

112 + 162/378 = 274/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 274 and 378, which is 2. Divide both the numerator and denominator by 2.

274 ÷ 2/378 ÷ 2 = 137/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 137 by denominator 189 produces a repeating decimal (approximately 0.724868, or 72.4868%).

137 ÷ 189 = 0.724868 (72.4868%)

Visual Representation

The diagram below illustrates 16/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`137/189`
Mixed Number Form	`137/189`
Decimal Form	`0.724868`
Percentage	`72.4868%`

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Frequently Asked Questions

What is 16/54 plus 9/21 as a fraction?

16/54 + 9/21 in simplest fraction form is 137/189.

What is 16/54 plus 9/21 as a decimal?

16/54 + 9/21 converted to a decimal is 0.724868.

What is 16/54 plus 9/21 as a percentage?

16/54 + 9/21 expressed as a percentage is 72.4868%.

Does 16/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.724868...) because the denominator contains prime factors other than 2 and 5.