What is 8/21 plus 5/12? (Answer: 67/84)

Exact Answer

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Problem: What is 8/21 plus 5/12?
Formula / Expression: 8/21 + 5/12
Final Answer: 67/84
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 8/21 by 4, and multiply the numerator and denominator of 5/12 by 7 so both fractions share the common base 84.
Working: 8 × 4/21 × 4 = 32/84 and 5 × 7/12 × 7 = 35/84

Step 3: Add the Numerators
Now add the numerators (32 + 35 = 67) and keep the common denominator 84 unchanged.
Working: 32 + 35/84 = 67/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 84 is 1, confirming that 67/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 84 produces a repeating decimal (approximately 0.797619, or 79.7619%).
Working: 67 ÷ 84 = 0.797619 (79.7619%)

Key Values:
- Simplified Fraction: 67/84
- Mixed Number Form: 67/84
- Decimal Value: 0.797619
- Percentage: 79.7619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-21-plus-5-12/
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8/21 + 5/12 = 67/84

Simplified Fraction

67/84

Mixed Number

Proper (67/84)

Decimal Value

0.797619

Percentage

79.7619%

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Step-by-Step Solution: 8/21 + 5/12

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 12) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 8/21 by 4, and multiply the numerator and denominator of 5/12 by 7 so both fractions share the common base 84.

8 × 4/21 × 4 = 32/84 and 5 × 7/12 × 7 = 35/84

Step 3

Add the Numerators

Now add the numerators (32 + 35 = 67) and keep the common denominator 84 unchanged.

32 + 35/84 = 67/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 84 is 1, confirming that 67/84 cannot be reduced further—it is already in its simplest irreducible form.

67/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 84 produces a repeating decimal (approximately 0.797619, or 79.7619%).

67 ÷ 84 = 0.797619 (79.7619%)

Visual Representation

The diagram below illustrates 8/21 plus 5/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/84`
Mixed Number Form	`67/84`
Decimal Form	`0.797619`
Percentage	`79.7619%`

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Frequently Asked Questions

What is 8/21 plus 5/12 as a fraction?

8/21 + 5/12 in simplest fraction form is 67/84.

What is 8/21 plus 5/12 as a decimal?

8/21 + 5/12 converted to a decimal is 0.797619.

What is 8/21 plus 5/12 as a percentage?

8/21 + 5/12 expressed as a percentage is 79.7619%.

Does 8/21 plus 5/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.797619...) because the denominator contains prime factors other than 2 and 5.