What is 2/22 plus 4/7? (Answer: 51/77)

Exact Answer

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Problem: What is 2/22 plus 4/7?
Formula / Expression: 2/22 + 4/7
Final Answer: 51/77
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 154
Multiply the numerator and denominator of 2/22 by 7, and multiply the numerator and denominator of 4/7 by 22 so both fractions share the common base 154.
Working: 2 × 7/22 × 7 = 14/154 and 4 × 22/7 × 22 = 88/154

Step 3: Add the Numerators
Now add the numerators (14 + 88 = 102) and keep the common denominator 154 unchanged.
Working: 14 + 88/154 = 102/154

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 154, which is 2. Divide both the numerator and denominator by 2.
Working: 102 ÷ 2/154 ÷ 2 = 51/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 77 produces a repeating decimal (approximately 0.662338, or 66.2338%).
Working: 51 ÷ 77 = 0.662338 (66.2338%)

Key Values:
- Simplified Fraction: 51/77
- Mixed Number Form: 51/77
- Decimal Value: 0.662338
- Percentage: 66.2338%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-22-plus-4-7/
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2/22 + 4/7 = 51/77

Simplified Fraction

51/77

Mixed Number

Proper (51/77)

Decimal Value

0.662338

Percentage

66.2338%

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Step-by-Step Solution: 2/22 + 4/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(22, 7) = 154

Step 2

Convert to Equivalent Fractions with Common Denominator 154

Multiply the numerator and denominator of 2/22 by 7, and multiply the numerator and denominator of 4/7 by 22 so both fractions share the common base 154.

2 × 7/22 × 7 = 14/154 and 4 × 22/7 × 22 = 88/154

Step 3

Add the Numerators

Now add the numerators (14 + 88 = 102) and keep the common denominator 154 unchanged.

14 + 88/154 = 102/154

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 154, which is 2. Divide both the numerator and denominator by 2.

102 ÷ 2/154 ÷ 2 = 51/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 77 produces a repeating decimal (approximately 0.662338, or 66.2338%).

51 ÷ 77 = 0.662338 (66.2338%)

Visual Representation

The diagram below illustrates 2/22 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/77`
Mixed Number Form	`51/77`
Decimal Form	`0.662338`
Percentage	`66.2338%`

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Frequently Asked Questions

What is 2/22 plus 4/7 as a fraction?

2/22 + 4/7 in simplest fraction form is 51/77.

What is 2/22 plus 4/7 as a decimal?

2/22 + 4/7 converted to a decimal is 0.662338.

What is 2/22 plus 4/7 as a percentage?

2/22 + 4/7 expressed as a percentage is 66.2338%.

Does 2/22 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.662338...) because the denominator contains prime factors other than 2 and 5.