What is 3/7 plus 9/16? (Answer: 111/112)

Exact Answer

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Problem: What is 3/7 plus 9/16?
Formula / Expression: 3/7 + 9/16
Final Answer: 111/112
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 16 = 112.
Working: LCD(7, 16) = 112

Step 2: Convert to Equivalent Fractions with Common Denominator 112
Multiply the numerator and denominator of 3/7 by 16, and multiply the numerator and denominator of 9/16 by 7 so both fractions share the common base 112.
Working: 3 × 16/7 × 16 = 48/112 and 9 × 7/16 × 7 = 63/112

Step 3: Add the Numerators
Now add the numerators (48 + 63 = 111) and keep the common denominator 112 unchanged.
Working: 48 + 63/112 = 111/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 111 and 112 is 1, confirming that 111/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 111/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 111 by denominator 112 produces a repeating decimal (approximately 0.991071, or 99.1071%).
Working: 111 ÷ 112 = 0.991071 (99.1071%)

Key Values:
- Simplified Fraction: 111/112
- Mixed Number Form: 111/112
- Decimal Value: 0.991071
- Percentage: 99.1071%

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Solved with FractionsCalc:
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3/7 + 9/16 = 111/112

Simplified Fraction

111/112

Mixed Number

Proper (111/112)

Decimal Value

0.991071

Percentage

99.1071%

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Step-by-Step Solution: 3/7 + 9/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 16 = 112.

LCD(7, 16) = 112

Step 2

Convert to Equivalent Fractions with Common Denominator 112

Multiply the numerator and denominator of 3/7 by 16, and multiply the numerator and denominator of 9/16 by 7 so both fractions share the common base 112.

3 × 16/7 × 16 = 48/112 and 9 × 7/16 × 7 = 63/112

Step 3

Add the Numerators

Now add the numerators (48 + 63 = 111) and keep the common denominator 112 unchanged.

48 + 63/112 = 111/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 111 and 112 is 1, confirming that 111/112 cannot be reduced further—it is already in its simplest irreducible form.

111/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 111 by denominator 112 produces a repeating decimal (approximately 0.991071, or 99.1071%).

111 ÷ 112 = 0.991071 (99.1071%)

Visual Representation

The diagram below illustrates 3/7 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`111/112`
Mixed Number Form	`111/112`
Decimal Form	`0.991071`
Percentage	`99.1071%`

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Frequently Asked Questions

What is 3/7 plus 9/16 as a fraction?

3/7 + 9/16 in simplest fraction form is 111/112.

What is 3/7 plus 9/16 as a decimal?

3/7 + 9/16 converted to a decimal is 0.991071.

What is 3/7 plus 9/16 as a percentage?

3/7 + 9/16 expressed as a percentage is 99.1071%.

Does 3/7 plus 9/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.991071...) because the denominator contains prime factors other than 2 and 5.