What is 2/16 plus 7/22? (Answer: 39/88)

Exact Answer

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Problem: What is 2/16 plus 7/22?
Formula / Expression: 2/16 + 7/22
Final Answer: 39/88
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 176 (which is smaller than their product 16 × 22 = 352, keeping the calculation simpler).
Working: LCD(16, 22) = 176

Step 2: Convert to Equivalent Fractions with Common Denominator 176
Multiply the numerator and denominator of 2/16 by 11, and multiply the numerator and denominator of 7/22 by 8 so both fractions share the common base 176.
Working: 2 × 11/16 × 11 = 22/176 and 7 × 8/22 × 8 = 56/176

Step 3: Add the Numerators
Now add the numerators (22 + 56 = 78) and keep the common denominator 176 unchanged.
Working: 22 + 56/176 = 78/176

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 176, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/176 ÷ 2 = 39/88

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 88 produces a repeating decimal (approximately 0.443182, or 44.3182%).
Working: 39 ÷ 88 = 0.443182 (44.3182%)

Key Values:
- Simplified Fraction: 39/88
- Mixed Number Form: 39/88
- Decimal Value: 0.443182
- Percentage: 44.3182%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-16-plus-7-22/
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2/16 + 7/22 = 39/88

Simplified Fraction

39/88

Mixed Number

Proper (39/88)

Decimal Value

0.443182

Percentage

44.3182%

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Step-by-Step Solution: 2/16 + 7/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 22 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 176 (which is smaller than their product 16 × 22 = 352, keeping the calculation simpler).

LCD(16, 22) = 176

Step 2

Convert to Equivalent Fractions with Common Denominator 176

Multiply the numerator and denominator of 2/16 by 11, and multiply the numerator and denominator of 7/22 by 8 so both fractions share the common base 176.

2 × 11/16 × 11 = 22/176 and 7 × 8/22 × 8 = 56/176

Step 3

Add the Numerators

Now add the numerators (22 + 56 = 78) and keep the common denominator 176 unchanged.

22 + 56/176 = 78/176

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 176, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/176 ÷ 2 = 39/88

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 88 produces a repeating decimal (approximately 0.443182, or 44.3182%).

39 ÷ 88 = 0.443182 (44.3182%)

Visual Representation

The diagram below illustrates 2/16 plus 7/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/88`
Mixed Number Form	`39/88`
Decimal Form	`0.443182`
Percentage	`44.3182%`

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Frequently Asked Questions

What is 2/16 plus 7/22 as a fraction?

2/16 + 7/22 in simplest fraction form is 39/88.

What is 2/16 plus 7/22 as a decimal?

2/16 + 7/22 converted to a decimal is 0.443182.

What is 2/16 plus 7/22 as a percentage?

2/16 + 7/22 expressed as a percentage is 44.3182%.

Does 2/16 plus 7/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.443182...) because the denominator contains prime factors other than 2 and 5.