What is 7/16 plus 2/3? (Answer: 53/48)

Exact Answer

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Problem: What is 7/16 plus 2/3?
Formula / Expression: 7/16 + 2/3
Final Answer: 1 5/48 (53/48)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 3 = 48.
Working: LCD(16, 3) = 48

Step 2: Convert to Equivalent Fractions with Common Denominator 48
Multiply the numerator and denominator of 7/16 by 3, and multiply the numerator and denominator of 2/3 by 16 so both fractions share the common base 48.
Working: 7 × 3/16 × 3 = 21/48 and 2 × 16/3 × 16 = 32/48

Step 3: Add the Numerators
Now add the numerators (21 + 32 = 53) and keep the common denominator 48 unchanged.
Working: 21 + 32/48 = 53/48

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 48 is 1, confirming that 53/48 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/48

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (48), divide 53 by 48: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/48.
Working: 53/48 = 1 5/48

Step 6: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 48 produces a repeating decimal (approximately 1.104167, or 110.4167%).
Working: 53 ÷ 48 = 1.104167 (110.4167%)

Key Values:
- Simplified Fraction: 53/48
- Mixed Number Form: 1 5/48
- Decimal Value: 1.104167
- Percentage: 110.4167%

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Solved with FractionsCalc:
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7/16 + 2/3 = 53/48

Simplified Fraction

53/48

Mixed Number

1 5/48

Decimal Value

1.104167

Percentage

110.4167%

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Step-by-Step Solution: 7/16 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 3 = 48.

LCD(16, 3) = 48

Step 2

Convert to Equivalent Fractions with Common Denominator 48

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

7 × 3/16 × 3 = 21/48 and 2 × 16/3 × 16 = 32/48

Step 3

Add the Numerators

Now add the numerators (21 + 32 = 53) and keep the common denominator 48 unchanged.

21 + 32/48 = 53/48

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 48 is 1, confirming that 53/48 cannot be reduced further—it is already in its simplest irreducible form.

53/48

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (53) is greater than the denominator (48), divide 53 by 48: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/48.

53/48 = 15/48

Step 6

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 48 produces a repeating decimal (approximately 1.104167, or 110.4167%).

53 ÷ 48 = 1.104167 (110.4167%)

Visual Representation

The diagram below illustrates 7/16 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/48`
Mixed Number Form	`1 5/48`
Decimal Form	`1.104167`
Percentage	`110.4167%`

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Frequently Asked Questions

What is 7/16 plus 2/3 as a fraction?

7/16 + 2/3 in simplest fraction form is 53/48 (or 1 5/48 as a mixed number).

What is 7/16 plus 2/3 as a decimal?

7/16 + 2/3 converted to a decimal is 1.104167.

What is 7/16 plus 2/3 as a percentage?

7/16 + 2/3 expressed as a percentage is 110.4167%.

How do you write 7/16 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 53/48 can be written as the mixed number 1 5/48.

Does 7/16 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.104167...) because the denominator contains prime factors other than 2 and 5.