What is 5/16 plus 4/7? (Answer: 99/112)

Exact Answer

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Problem: What is 5/16 plus 4/7?
Formula / Expression: 5/16 + 4/7
Final Answer: 99/112
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 112
Multiply the numerator and denominator of 5/16 by 7, and multiply the numerator and denominator of 4/7 by 16 so both fractions share the common base 112.
Working: 5 × 7/16 × 7 = 35/112 and 4 × 16/7 × 16 = 64/112

Step 3: Add the Numerators
Now add the numerators (35 + 64 = 99) and keep the common denominator 112 unchanged.
Working: 35 + 64/112 = 99/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 99 and 112 is 1, confirming that 99/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 99/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 99 by denominator 112 produces a repeating decimal (approximately 0.883929, or 88.3929%).
Working: 99 ÷ 112 = 0.883929 (88.3929%)

Key Values:
- Simplified Fraction: 99/112
- Mixed Number Form: 99/112
- Decimal Value: 0.883929
- Percentage: 88.3929%

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Solved with FractionsCalc:
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5/16 + 4/7 = 99/112

Simplified Fraction

99/112

Mixed Number

Proper (99/112)

Decimal Value

0.883929

Percentage

88.3929%

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Step-by-Step Solution: 5/16 + 4/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(16, 7) = 112

Step 2

Convert to Equivalent Fractions with Common Denominator 112

Multiply the numerator and denominator of 5/16 by 7, and multiply the numerator and denominator of 4/7 by 16 so both fractions share the common base 112.

5 × 7/16 × 7 = 35/112 and 4 × 16/7 × 16 = 64/112

Step 3

Add the Numerators

Now add the numerators (35 + 64 = 99) and keep the common denominator 112 unchanged.

35 + 64/112 = 99/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 99 and 112 is 1, confirming that 99/112 cannot be reduced further—it is already in its simplest irreducible form.

99/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 99 by denominator 112 produces a repeating decimal (approximately 0.883929, or 88.3929%).

99 ÷ 112 = 0.883929 (88.3929%)

Visual Representation

The diagram below illustrates 5/16 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`99/112`
Mixed Number Form	`99/112`
Decimal Form	`0.883929`
Percentage	`88.3929%`

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Frequently Asked Questions

What is 5/16 plus 4/7 as a fraction?

5/16 + 4/7 in simplest fraction form is 99/112.

What is 5/16 plus 4/7 as a decimal?

5/16 + 4/7 converted to a decimal is 0.883929.

What is 5/16 plus 4/7 as a percentage?

5/16 + 4/7 expressed as a percentage is 88.3929%.

Does 5/16 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.883929...) because the denominator contains prime factors other than 2 and 5.