What is 10/27 plus 9/21? (Answer: 151/189)

Exact Answer

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Problem: What is 10/27 plus 9/21?
Formula / Expression: 10/27 + 9/21
Final Answer: 151/189
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 10/27 by 7, and multiply the numerator and denominator of 9/21 by 9 so both fractions share the common base 189.
Working: 10 × 7/27 × 7 = 70/189 and 9 × 9/21 × 9 = 81/189

Step 3: Add the Numerators
Now add the numerators (70 + 81 = 151) and keep the common denominator 189 unchanged.
Working: 70 + 81/189 = 151/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 151 and 189 is 1, confirming that 151/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 151/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 151 by denominator 189 produces a repeating decimal (approximately 0.798942, or 79.8942%).
Working: 151 ÷ 189 = 0.798942 (79.8942%)

Key Values:
- Simplified Fraction: 151/189
- Mixed Number Form: 151/189
- Decimal Value: 0.798942
- Percentage: 79.8942%

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Solved with FractionsCalc:
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10/27 + 9/21 = 151/189

Simplified Fraction

151/189

Mixed Number

Proper (151/189)

Decimal Value

0.798942

Percentage

79.8942%

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Step-by-Step Solution: 10/27 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 10/27 by 7, and multiply the numerator and denominator of 9/21 by 9 so both fractions share the common base 189.

10 × 7/27 × 7 = 70/189 and 9 × 9/21 × 9 = 81/189

Step 3

Add the Numerators

Now add the numerators (70 + 81 = 151) and keep the common denominator 189 unchanged.

70 + 81/189 = 151/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 151 and 189 is 1, confirming that 151/189 cannot be reduced further—it is already in its simplest irreducible form.

151/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 151 by denominator 189 produces a repeating decimal (approximately 0.798942, or 79.8942%).

151 ÷ 189 = 0.798942 (79.8942%)

Visual Representation

The diagram below illustrates 10/27 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`151/189`
Mixed Number Form	`151/189`
Decimal Form	`0.798942`
Percentage	`79.8942%`

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Frequently Asked Questions

What is 10/27 plus 9/21 as a fraction?

10/27 + 9/21 in simplest fraction form is 151/189.

What is 10/27 plus 9/21 as a decimal?

10/27 + 9/21 converted to a decimal is 0.798942.

What is 10/27 plus 9/21 as a percentage?

10/27 + 9/21 expressed as a percentage is 79.8942%.

Does 10/27 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.798942...) because the denominator contains prime factors other than 2 and 5.