What is 7/16 plus 4/7? (Answer: 113/112)

Exact Answer

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Problem: What is 7/16 plus 4/7?
Formula / Expression: 7/16 + 4/7
Final Answer: 1 1/112 (113/112)
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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 7/16 by 7, and multiply the numerator and denominator of 4/7 by 16 so both fractions share the common base 112.
Working: 7 × 7/16 × 7 = 49/112 and 4 × 16/7 × 16 = 64/112

Step 3: Add the Numerators
Now add the numerators (49 + 64 = 113) and keep the common denominator 112 unchanged.
Working: 49 + 64/112 = 113/112

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 112 is 1, confirming that 113/112 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/112

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (113) is greater than the denominator (112), divide 113 by 112: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/112.
Working: 113/112 = 1 1/112

Step 6: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 112 produces a repeating decimal (approximately 1.008929, or 100.8929%).
Working: 113 ÷ 112 = 1.008929 (100.8929%)

Key Values:
- Simplified Fraction: 113/112
- Mixed Number Form: 1 1/112
- Decimal Value: 1.008929
- Percentage: 100.8929%

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Solved with FractionsCalc:
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7/16 + 4/7 = 113/112

Simplified Fraction

113/112

Mixed Number

1 1/112

Decimal Value

1.008929

Percentage

100.8929%

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Step-by-Step Solution: 7/16 + 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 7/16 by 7, and multiply the numerator and denominator of 4/7 by 16 so both fractions share the common base 112.

7 × 7/16 × 7 = 49/112 and 4 × 16/7 × 16 = 64/112

Step 3

Add the Numerators

Now add the numerators (49 + 64 = 113) and keep the common denominator 112 unchanged.

49 + 64/112 = 113/112

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 112 is 1, confirming that 113/112 cannot be reduced further—it is already in its simplest irreducible form.

113/112

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (113) is greater than the denominator (112), divide 113 by 112: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/112.

113/112 = 11/112

Step 6

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 112 produces a repeating decimal (approximately 1.008929, or 100.8929%).

113 ÷ 112 = 1.008929 (100.8929%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/112`
Mixed Number Form	`1 1/112`
Decimal Form	`1.008929`
Percentage	`100.8929%`

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Frequently Asked Questions

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

7/16 + 4/7 in simplest fraction form is 113/112 (or 1 1/112 as a mixed number).

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

7/16 + 4/7 converted to a decimal is 1.008929.

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

7/16 + 4/7 expressed as a percentage is 100.8929%.

How do you write 7/16 plus 4/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 113/112 can be written as the mixed number 1 1/112.

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

It results in a repeating decimal (approximately 1.008929...) because the denominator contains prime factors other than 2 and 5.