What is 10/54 plus 5/21? (Answer: 80/189)

Exact Answer

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Problem: What is 10/54 plus 5/21?
Formula / Expression: 10/54 + 5/21
Final Answer: 80/189
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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 10/54 by 7, and multiply the numerator and denominator of 5/21 by 18 so both fractions share the common base 378.
Working: 10 × 7/54 × 7 = 70/378 and 5 × 18/21 × 18 = 90/378

Step 3: Add the Numerators
Now add the numerators (70 + 90 = 160) and keep the common denominator 378 unchanged.
Working: 70 + 90/378 = 160/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 160 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 160 ÷ 2/378 ÷ 2 = 80/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 189 produces a repeating decimal (approximately 0.42328, or 42.328%).
Working: 80 ÷ 189 = 0.42328 (42.328%)

Key Values:
- Simplified Fraction: 80/189
- Mixed Number Form: 80/189
- Decimal Value: 0.42328
- Percentage: 42.328%

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Solved with FractionsCalc:
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10/54 + 5/21 = 80/189

Simplified Fraction

80/189

Mixed Number

Proper (80/189)

Decimal Value

0.42328

Percentage

42.328%

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Step-by-Step Solution: 10/54 + 5/21

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 5/21 by 18 so both fractions share the common base 378.

10 × 7/54 × 7 = 70/378 and 5 × 18/21 × 18 = 90/378

Step 3

Add the Numerators

Now add the numerators (70 + 90 = 160) and keep the common denominator 378 unchanged.

70 + 90/378 = 160/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 160 and 378, which is 2. Divide both the numerator and denominator by 2.

160 ÷ 2/378 ÷ 2 = 80/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 189 produces a repeating decimal (approximately 0.42328, or 42.328%).

80 ÷ 189 = 0.42328 (42.328%)

Visual Representation

The diagram below illustrates 10/54 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/189`
Mixed Number Form	`80/189`
Decimal Form	`0.42328`
Percentage	`42.328%`

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Frequently Asked Questions

What is 10/54 plus 5/21 as a fraction?

10/54 + 5/21 in simplest fraction form is 80/189.

What is 10/54 plus 5/21 as a decimal?

10/54 + 5/21 converted to a decimal is 0.42328.

What is 10/54 plus 5/21 as a percentage?

10/54 + 5/21 expressed as a percentage is 42.328%.

Does 10/54 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.42328...) because the denominator contains prime factors other than 2 and 5.