What is 2/7 plus 10/22? (Answer: 57/77)

Exact Answer

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Problem: What is 2/7 plus 10/22?
Formula / Expression: 2/7 + 10/22
Final Answer: 57/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.
Working: LCD(7, 22) = 154

Step 2: Convert to Equivalent Fractions with Common Denominator 154
Multiply the numerator and denominator of 2/7 by 22, and multiply the numerator and denominator of 10/22 by 7 so both fractions share the common base 154.
Working: 2 × 22/7 × 22 = 44/154 and 10 × 7/22 × 7 = 70/154

Step 3: Add the Numerators
Now add the numerators (44 + 70 = 114) and keep the common denominator 154 unchanged.
Working: 44 + 70/154 = 114/154

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 154, which is 2. Divide both the numerator and denominator by 2.
Working: 114 ÷ 2/154 ÷ 2 = 57/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 77 produces a repeating decimal (approximately 0.74026, or 74.026%).
Working: 57 ÷ 77 = 0.74026 (74.026%)

Key Values:
- Simplified Fraction: 57/77
- Mixed Number Form: 57/77
- Decimal Value: 0.74026
- Percentage: 74.026%

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Solved with FractionsCalc:
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2/7 + 10/22 = 57/77

Simplified Fraction

57/77

Mixed Number

Proper (57/77)

Decimal Value

0.74026

Percentage

74.026%

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Step-by-Step Solution: 2/7 + 10/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.

LCD(7, 22) = 154

Step 2

Convert to Equivalent Fractions with Common Denominator 154

Multiply the numerator and denominator of 2/7 by 22, and multiply the numerator and denominator of 10/22 by 7 so both fractions share the common base 154.

2 × 22/7 × 22 = 44/154 and 10 × 7/22 × 7 = 70/154

Step 3

Add the Numerators

Now add the numerators (44 + 70 = 114) and keep the common denominator 154 unchanged.

44 + 70/154 = 114/154

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 154, which is 2. Divide both the numerator and denominator by 2.

114 ÷ 2/154 ÷ 2 = 57/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 77 produces a repeating decimal (approximately 0.74026, or 74.026%).

57 ÷ 77 = 0.74026 (74.026%)

Visual Representation

The diagram below illustrates 2/7 plus 10/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/77`
Mixed Number Form	`57/77`
Decimal Form	`0.74026`
Percentage	`74.026%`

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Frequently Asked Questions

What is 2/7 plus 10/22 as a fraction?

2/7 + 10/22 in simplest fraction form is 57/77.

What is 2/7 plus 10/22 as a decimal?

2/7 + 10/22 converted to a decimal is 0.74026.

What is 2/7 plus 10/22 as a percentage?

2/7 + 10/22 expressed as a percentage is 74.026%.

Does 2/7 plus 10/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.74026...) because the denominator contains prime factors other than 2 and 5.