What is 3/22 plus 4/7? (Answer: 109/154)

Exact Answer

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Problem: What is 3/22 plus 4/7?
Formula / Expression: 3/22 + 4/7
Final Answer: 109/154
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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 3/22 by 7, and multiply the numerator and denominator of 4/7 by 22 so both fractions share the common base 154.
Working: 3 × 7/22 × 7 = 21/154 and 4 × 22/7 × 22 = 88/154

Step 3: Add the Numerators
Now add the numerators (21 + 88 = 109) and keep the common denominator 154 unchanged.
Working: 21 + 88/154 = 109/154

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 154 is 1, confirming that 109/154 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/154

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 154 produces a repeating decimal (approximately 0.707792, or 70.7792%).
Working: 109 ÷ 154 = 0.707792 (70.7792%)

Key Values:
- Simplified Fraction: 109/154
- Mixed Number Form: 109/154
- Decimal Value: 0.707792
- Percentage: 70.7792%

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Solved with FractionsCalc:
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3/22 + 4/7 = 109/154

Simplified Fraction

109/154

Mixed Number

Proper (109/154)

Decimal Value

0.707792

Percentage

70.7792%

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

3 × 7/22 × 7 = 21/154 and 4 × 22/7 × 22 = 88/154

Step 3

Add the Numerators

Now add the numerators (21 + 88 = 109) and keep the common denominator 154 unchanged.

21 + 88/154 = 109/154

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 154 is 1, confirming that 109/154 cannot be reduced further—it is already in its simplest irreducible form.

109/154

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 154 produces a repeating decimal (approximately 0.707792, or 70.7792%).

109 ÷ 154 = 0.707792 (70.7792%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/154`
Mixed Number Form	`109/154`
Decimal Form	`0.707792`
Percentage	`70.7792%`

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Frequently Asked Questions

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

3/22 + 4/7 in simplest fraction form is 109/154.

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

3/22 + 4/7 converted to a decimal is 0.707792.

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

3/22 + 4/7 expressed as a percentage is 70.7792%.

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

It results in a repeating decimal (approximately 0.707792...) because the denominator contains prime factors other than 2 and 5.