What is 2/6 plus 7/16? (Answer: 37/48)

Exact Answer

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Problem: What is 2/6 plus 7/16?
Formula / Expression: 2/6 + 7/16
Final Answer: 37/48
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 48 (which is smaller than their product 6 × 16 = 96, keeping the calculation simpler).
Working: LCD(6, 16) = 48

Step 2: Convert to Equivalent Fractions with Common Denominator 48
Multiply the numerator and denominator of 2/6 by 8, and multiply the numerator and denominator of 7/16 by 3 so both fractions share the common base 48.
Working: 2 × 8/6 × 8 = 16/48 and 7 × 3/16 × 3 = 21/48

Step 3: Add the Numerators
Now add the numerators (16 + 21 = 37) and keep the common denominator 48 unchanged.
Working: 16 + 21/48 = 37/48

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 48 is 1, confirming that 37/48 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 48 produces a repeating decimal (approximately 0.770833, or 77.0833%).
Working: 37 ÷ 48 = 0.770833 (77.0833%)

Key Values:
- Simplified Fraction: 37/48
- Mixed Number Form: 37/48
- Decimal Value: 0.770833
- Percentage: 77.0833%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-7-16/
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2/6 + 7/16 = 37/48

Simplified Fraction

37/48

Mixed Number

Proper (37/48)

Decimal Value

0.770833

Percentage

77.0833%

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Step-by-Step Solution: 2/6 + 7/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 48 (which is smaller than their product 6 × 16 = 96, keeping the calculation simpler).

LCD(6, 16) = 48

Step 2

Convert to Equivalent Fractions with Common Denominator 48

Multiply the numerator and denominator of 2/6 by 8, and multiply the numerator and denominator of 7/16 by 3 so both fractions share the common base 48.

2 × 8/6 × 8 = 16/48 and 7 × 3/16 × 3 = 21/48

Step 3

Add the Numerators

Now add the numerators (16 + 21 = 37) and keep the common denominator 48 unchanged.

16 + 21/48 = 37/48

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 48 is 1, confirming that 37/48 cannot be reduced further—it is already in its simplest irreducible form.

37/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 48 produces a repeating decimal (approximately 0.770833, or 77.0833%).

37 ÷ 48 = 0.770833 (77.0833%)

Visual Representation

The diagram below illustrates 2/6 plus 7/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/48`
Mixed Number Form	`37/48`
Decimal Form	`0.770833`
Percentage	`77.0833%`

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Frequently Asked Questions

What is 2/6 plus 7/16 as a fraction?

2/6 + 7/16 in simplest fraction form is 37/48.

What is 2/6 plus 7/16 as a decimal?

2/6 + 7/16 converted to a decimal is 0.770833.

What is 2/6 plus 7/16 as a percentage?

2/6 + 7/16 expressed as a percentage is 77.0833%.

Does 2/6 plus 7/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.770833...) because the denominator contains prime factors other than 2 and 5.