What is 7/18 plus 10/21? (Answer: 109/126)

Exact Answer

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Problem: What is 7/18 plus 10/21?
Formula / Expression: 7/18 + 10/21
Final Answer: 109/126
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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 7/18 by 7, and multiply the numerator and denominator of 10/21 by 6 so both fractions share the common base 126.
Working: 7 × 7/18 × 7 = 49/126 and 10 × 6/21 × 6 = 60/126

Step 3: Add the Numerators
Now add the numerators (49 + 60 = 109) and keep the common denominator 126 unchanged.
Working: 49 + 60/126 = 109/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 126 is 1, confirming that 109/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 126 produces a repeating decimal (approximately 0.865079, or 86.5079%).
Working: 109 ÷ 126 = 0.865079 (86.5079%)

Key Values:
- Simplified Fraction: 109/126
- Mixed Number Form: 109/126
- Decimal Value: 0.865079
- Percentage: 86.5079%

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7/18 + 10/21 = 109/126

Simplified Fraction

109/126

Mixed Number

Proper (109/126)

Decimal Value

0.865079

Percentage

86.5079%

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Step-by-Step Solution: 7/18 + 10/21

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

7 × 7/18 × 7 = 49/126 and 10 × 6/21 × 6 = 60/126

Step 3

Add the Numerators

Now add the numerators (49 + 60 = 109) and keep the common denominator 126 unchanged.

49 + 60/126 = 109/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 126 is 1, confirming that 109/126 cannot be reduced further—it is already in its simplest irreducible form.

109/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 126 produces a repeating decimal (approximately 0.865079, or 86.5079%).

109 ÷ 126 = 0.865079 (86.5079%)

Visual Representation

The diagram below illustrates 7/18 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/126`
Mixed Number Form	`109/126`
Decimal Form	`0.865079`
Percentage	`86.5079%`

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Frequently Asked Questions

What is 7/18 plus 10/21 as a fraction?

7/18 + 10/21 in simplest fraction form is 109/126.

What is 7/18 plus 10/21 as a decimal?

7/18 + 10/21 converted to a decimal is 0.865079.

What is 7/18 plus 10/21 as a percentage?

7/18 + 10/21 expressed as a percentage is 86.5079%.

Does 7/18 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.865079...) because the denominator contains prime factors other than 2 and 5.