What is 4/22 plus 3/7? (Answer: 47/77)

Exact Answer

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Problem: What is 4/22 plus 3/7?
Formula / Expression: 4/22 + 3/7
Final Answer: 47/77
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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 4/22 by 7, and multiply the numerator and denominator of 3/7 by 22 so both fractions share the common base 154.
Working: 4 × 7/22 × 7 = 28/154 and 3 × 22/7 × 22 = 66/154

Step 3: Add the Numerators
Now add the numerators (28 + 66 = 94) and keep the common denominator 154 unchanged.
Working: 28 + 66/154 = 94/154

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 94 and 154, which is 2. Divide both the numerator and denominator by 2.
Working: 94 ÷ 2/154 ÷ 2 = 47/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 77 produces a repeating decimal (approximately 0.61039, or 61.039%).
Working: 47 ÷ 77 = 0.61039 (61.039%)

Key Values:
- Simplified Fraction: 47/77
- Mixed Number Form: 47/77
- Decimal Value: 0.61039
- Percentage: 61.039%

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Solved with FractionsCalc:
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4/22 + 3/7 = 47/77

Simplified Fraction

47/77

Mixed Number

Proper (47/77)

Decimal Value

0.61039

Percentage

61.039%

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Step-by-Step Solution: 4/22 + 3/7

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 4/22 by 7, and multiply the numerator and denominator of 3/7 by 22 so both fractions share the common base 154.

4 × 7/22 × 7 = 28/154 and 3 × 22/7 × 22 = 66/154

Step 3

Add the Numerators

Now add the numerators (28 + 66 = 94) and keep the common denominator 154 unchanged.

28 + 66/154 = 94/154

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 94 and 154, which is 2. Divide both the numerator and denominator by 2.

94 ÷ 2/154 ÷ 2 = 47/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 77 produces a repeating decimal (approximately 0.61039, or 61.039%).

47 ÷ 77 = 0.61039 (61.039%)

Visual Representation

The diagram below illustrates 4/22 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/77`
Mixed Number Form	`47/77`
Decimal Form	`0.61039`
Percentage	`61.039%`

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Frequently Asked Questions

What is 4/22 plus 3/7 as a fraction?

4/22 + 3/7 in simplest fraction form is 47/77.

What is 4/22 plus 3/7 as a decimal?

4/22 + 3/7 converted to a decimal is 0.61039.

What is 4/22 plus 3/7 as a percentage?

4/22 + 3/7 expressed as a percentage is 61.039%.

Does 4/22 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.61039...) because the denominator contains prime factors other than 2 and 5.