What is 1/12 plus 10/21? (Answer: 47/84)

Exact Answer

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Problem: What is 1/12 plus 10/21?
Formula / Expression: 1/12 + 10/21
Final Answer: 47/84
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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 1/12 by 7, and multiply the numerator and denominator of 10/21 by 4 so both fractions share the common base 84.
Working: 1 × 7/12 × 7 = 7/84 and 10 × 4/21 × 4 = 40/84

Step 3: Add the Numerators
Now add the numerators (7 + 40 = 47) and keep the common denominator 84 unchanged.
Working: 7 + 40/84 = 47/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 47 and 84 is 1, confirming that 47/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 47/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 84 produces a repeating decimal (approximately 0.559524, or 55.9524%).
Working: 47 ÷ 84 = 0.559524 (55.9524%)

Key Values:
- Simplified Fraction: 47/84
- Mixed Number Form: 47/84
- Decimal Value: 0.559524
- Percentage: 55.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-12-plus-10-21/
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1/12 + 10/21 = 47/84

Simplified Fraction

47/84

Mixed Number

Proper (47/84)

Decimal Value

0.559524

Percentage

55.9524%

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Step-by-Step Solution: 1/12 + 10/21

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 10/21 by 4 so both fractions share the common base 84.

1 × 7/12 × 7 = 7/84 and 10 × 4/21 × 4 = 40/84

Step 3

Add the Numerators

Now add the numerators (7 + 40 = 47) and keep the common denominator 84 unchanged.

7 + 40/84 = 47/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 47 and 84 is 1, confirming that 47/84 cannot be reduced further—it is already in its simplest irreducible form.

47/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 84 produces a repeating decimal (approximately 0.559524, or 55.9524%).

47 ÷ 84 = 0.559524 (55.9524%)

Visual Representation

The diagram below illustrates 1/12 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/84`
Mixed Number Form	`47/84`
Decimal Form	`0.559524`
Percentage	`55.9524%`

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Frequently Asked Questions

What is 1/12 plus 10/21 as a fraction?

1/12 + 10/21 in simplest fraction form is 47/84.

What is 1/12 plus 10/21 as a decimal?

1/12 + 10/21 converted to a decimal is 0.559524.

What is 1/12 plus 10/21 as a percentage?

1/12 + 10/21 expressed as a percentage is 55.9524%.

Does 1/12 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.559524...) because the denominator contains prime factors other than 2 and 5.