What is 1/12 plus 8/21? (Answer: 13/28)

Exact Answer

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Problem: What is 1/12 plus 8/21?
Formula / Expression: 1/12 + 8/21
Final Answer: 13/28
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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 1/12 by 7, and multiply the numerator and denominator of 8/21 by 4 so both fractions share the common base 84.
Working: 1 × 7/12 × 7 = 7/84 and 8 × 4/21 × 4 = 32/84

Step 3: Add the Numerators
Now add the numerators (7 + 32 = 39) and keep the common denominator 84 unchanged.
Working: 7 + 32/84 = 39/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/84 ÷ 3 = 13/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).
Working: 13 ÷ 28 = 0.464286 (46.4286%)

Key Values:
- Simplified Fraction: 13/28
- Mixed Number Form: 13/28
- Decimal Value: 0.464286
- Percentage: 46.4286%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-12-plus-8-21/
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1/12 + 8/21 = 13/28

Simplified Fraction

13/28

Mixed Number

Proper (13/28)

Decimal Value

0.464286

Percentage

46.4286%

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Step-by-Step Solution: 1/12 + 8/21

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 1/12 by 7, and multiply the numerator and denominator of 8/21 by 4 so both fractions share the common base 84.

1 × 7/12 × 7 = 7/84 and 8 × 4/21 × 4 = 32/84

Step 3

Add the Numerators

Now add the numerators (7 + 32 = 39) and keep the common denominator 84 unchanged.

7 + 32/84 = 39/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 84, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/84 ÷ 3 = 13/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).

13 ÷ 28 = 0.464286 (46.4286%)

Visual Representation

The diagram below illustrates 1/12 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/28`
Mixed Number Form	`13/28`
Decimal Form	`0.464286`
Percentage	`46.4286%`

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Frequently Asked Questions

What is 1/12 plus 8/21 as a fraction?

1/12 + 8/21 in simplest fraction form is 13/28.

What is 1/12 plus 8/21 as a decimal?

1/12 + 8/21 converted to a decimal is 0.464286.

What is 1/12 plus 8/21 as a percentage?

1/12 + 8/21 expressed as a percentage is 46.4286%.

Does 1/12 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464286...) because the denominator contains prime factors other than 2 and 5.