What is 15/54 plus 9/21? (Answer: 89/126)

Exact Answer

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Problem: What is 15/54 plus 9/21?
Formula / Expression: 15/54 + 9/21
Final Answer: 89/126
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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 15/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 15 × 7/54 × 7 = 105/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (105 + 162 = 267) and keep the common denominator 378 unchanged.
Working: 105 + 162/378 = 267/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 267 and 378, which is 3. Divide both the numerator and denominator by 3.
Working: 267 ÷ 3/378 ÷ 3 = 89/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 126 produces a repeating decimal (approximately 0.706349, or 70.6349%).
Working: 89 ÷ 126 = 0.706349 (70.6349%)

Key Values:
- Simplified Fraction: 89/126
- Mixed Number Form: 89/126
- Decimal Value: 0.706349
- Percentage: 70.6349%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-54-plus-9-21/
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15/54 + 9/21 = 89/126

Simplified Fraction

89/126

Mixed Number

Proper (89/126)

Decimal Value

0.706349

Percentage

70.6349%

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Step-by-Step Solution: 15/54 + 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 15/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

15 × 7/54 × 7 = 105/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (105 + 162 = 267) and keep the common denominator 378 unchanged.

105 + 162/378 = 267/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 267 and 378, which is 3. Divide both the numerator and denominator by 3.

267 ÷ 3/378 ÷ 3 = 89/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 126 produces a repeating decimal (approximately 0.706349, or 70.6349%).

89 ÷ 126 = 0.706349 (70.6349%)

Visual Representation

The diagram below illustrates 15/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/126`
Mixed Number Form	`89/126`
Decimal Form	`0.706349`
Percentage	`70.6349%`

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Frequently Asked Questions

What is 15/54 plus 9/21 as a fraction?

15/54 + 9/21 in simplest fraction form is 89/126.

What is 15/54 plus 9/21 as a decimal?

15/54 + 9/21 converted to a decimal is 0.706349.

What is 15/54 plus 9/21 as a percentage?

15/54 + 9/21 expressed as a percentage is 70.6349%.

Does 15/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.706349...) because the denominator contains prime factors other than 2 and 5.