What is 5/12 plus 9/21? (Answer: 71/84)

Exact Answer

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Problem: What is 5/12 plus 9/21?
Formula / Expression: 5/12 + 9/21
Final Answer: 71/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).
Working: LCD(12, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 5/12 by 7, and multiply the numerator and denominator of 9/21 by 4 so both fractions share the common base 84.
Working: 5 × 7/12 × 7 = 35/84 and 9 × 4/21 × 4 = 36/84

Step 3: Add the Numerators
Now add the numerators (35 + 36 = 71) and keep the common denominator 84 unchanged.
Working: 35 + 36/84 = 71/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 84 is 1, confirming that 71/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 84 produces a repeating decimal (approximately 0.845238, or 84.5238%).
Working: 71 ÷ 84 = 0.845238 (84.5238%)

Key Values:
- Simplified Fraction: 71/84
- Mixed Number Form: 71/84
- Decimal Value: 0.845238
- Percentage: 84.5238%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-12-plus-9-21/
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5/12 + 9/21 = 71/84

Simplified Fraction

71/84

Mixed Number

Proper (71/84)

Decimal Value

0.845238

Percentage

84.5238%

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Step-by-Step Solution: 5/12 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).

LCD(12, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 5/12 by 7, and multiply the numerator and denominator of 9/21 by 4 so both fractions share the common base 84.

5 × 7/12 × 7 = 35/84 and 9 × 4/21 × 4 = 36/84

Step 3

Add the Numerators

Now add the numerators (35 + 36 = 71) and keep the common denominator 84 unchanged.

35 + 36/84 = 71/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 84 is 1, confirming that 71/84 cannot be reduced further—it is already in its simplest irreducible form.

71/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 84 produces a repeating decimal (approximately 0.845238, or 84.5238%).

71 ÷ 84 = 0.845238 (84.5238%)

Visual Representation

The diagram below illustrates 5/12 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/84`
Mixed Number Form	`71/84`
Decimal Form	`0.845238`
Percentage	`84.5238%`

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Frequently Asked Questions

What is 5/12 plus 9/21 as a fraction?

5/12 + 9/21 in simplest fraction form is 71/84.

What is 5/12 plus 9/21 as a decimal?

5/12 + 9/21 converted to a decimal is 0.845238.

What is 5/12 plus 9/21 as a percentage?

5/12 + 9/21 expressed as a percentage is 84.5238%.

Does 5/12 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.845238...) because the denominator contains prime factors other than 2 and 5.