What is 10/21 plus 6/12? (Answer: 41/42)

Exact Answer

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Problem: What is 10/21 plus 6/12?
Formula / Expression: 10/21 + 6/12
Final Answer: 41/42
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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 10/21 by 4, and multiply the numerator and denominator of 6/12 by 7 so both fractions share the common base 84.
Working: 10 × 4/21 × 4 = 40/84 and 6 × 7/12 × 7 = 42/84

Step 3: Add the Numerators
Now add the numerators (40 + 42 = 82) and keep the common denominator 84 unchanged.
Working: 40 + 42/84 = 82/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/84 ÷ 2 = 41/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).
Working: 41 ÷ 42 = 0.97619 (97.619%)

Key Values:
- Simplified Fraction: 41/42
- Mixed Number Form: 41/42
- Decimal Value: 0.97619
- Percentage: 97.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-21-plus-6-12/
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10/21 + 6/12 = 41/42

Simplified Fraction

41/42

Mixed Number

Proper (41/42)

Decimal Value

0.97619

Percentage

97.619%

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Step-by-Step Solution: 10/21 + 6/12

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 10/21 by 4, and multiply the numerator and denominator of 6/12 by 7 so both fractions share the common base 84.

10 × 4/21 × 4 = 40/84 and 6 × 7/12 × 7 = 42/84

Step 3

Add the Numerators

Now add the numerators (40 + 42 = 82) and keep the common denominator 84 unchanged.

40 + 42/84 = 82/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 84, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/84 ÷ 2 = 41/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).

41 ÷ 42 = 0.97619 (97.619%)

Visual Representation

The diagram below illustrates 10/21 plus 6/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/42`
Mixed Number Form	`41/42`
Decimal Form	`0.97619`
Percentage	`97.619%`

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Frequently Asked Questions

What is 10/21 plus 6/12 as a fraction?

10/21 + 6/12 in simplest fraction form is 41/42.

What is 10/21 plus 6/12 as a decimal?

10/21 + 6/12 converted to a decimal is 0.97619.

What is 10/21 plus 6/12 as a percentage?

10/21 + 6/12 expressed as a percentage is 97.619%.

Does 10/21 plus 6/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.97619...) because the denominator contains prime factors other than 2 and 5.