What is 10/18 plus 12/21? (Answer: 71/63)

Exact Answer

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Problem: What is 10/18 plus 12/21?
Formula / Expression: 10/18 + 12/21
Final Answer: 1 8/63 (71/63)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 10/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.
Working: 10 × 7/18 × 7 = 70/126 and 12 × 6/21 × 6 = 72/126

Step 3: Add the Numerators
Now add the numerators (70 + 72 = 142) and keep the common denominator 126 unchanged.
Working: 70 + 72/126 = 142/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/126 ÷ 2 = 71/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (63), divide 71 by 63: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/63.
Working: 71/63 = 1 8/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 63 produces a repeating decimal (approximately 1.126984, or 112.6984%).
Working: 71 ÷ 63 = 1.126984 (112.6984%)

Key Values:
- Simplified Fraction: 71/63
- Mixed Number Form: 1 8/63
- Decimal Value: 1.126984
- Percentage: 112.6984%

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Solved with FractionsCalc:
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10/18 + 12/21 = 71/63

Simplified Fraction

71/63

Mixed Number

1 8/63

Decimal Value

1.126984

Percentage

112.6984%

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Step-by-Step Solution: 10/18 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 10/18 by 7, and multiply the numerator and denominator of 12/21 by 6 so both fractions share the common base 126.

10 × 7/18 × 7 = 70/126 and 12 × 6/21 × 6 = 72/126

Step 3

Add the Numerators

Now add the numerators (70 + 72 = 142) and keep the common denominator 126 unchanged.

70 + 72/126 = 142/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 126, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/126 ÷ 2 = 71/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (63), divide 71 by 63: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/63.

71/63 = 18/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 63 produces a repeating decimal (approximately 1.126984, or 112.6984%).

71 ÷ 63 = 1.126984 (112.6984%)

Visual Representation

The diagram below illustrates 10/18 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/63`
Mixed Number Form	`1 8/63`
Decimal Form	`1.126984`
Percentage	`112.6984%`

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Frequently Asked Questions

What is 10/18 plus 12/21 as a fraction?

10/18 + 12/21 in simplest fraction form is 71/63 (or 1 8/63 as a mixed number).

What is 10/18 plus 12/21 as a decimal?

10/18 + 12/21 converted to a decimal is 1.126984.

What is 10/18 plus 12/21 as a percentage?

10/18 + 12/21 expressed as a percentage is 112.6984%.

How do you write 10/18 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/63 can be written as the mixed number 1 8/63.

Does 10/18 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.126984...) because the denominator contains prime factors other than 2 and 5.