What is 4/16 plus 3/7? (Answer: 19/28)

Exact Answer

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Problem: What is 4/16 plus 3/7?
Formula / Expression: 4/16 + 3/7
Final Answer: 19/28
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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 4/16 by 7, and multiply the numerator and denominator of 3/7 by 16 so both fractions share the common base 112.
Working: 4 × 7/16 × 7 = 28/112 and 3 × 16/7 × 16 = 48/112

Step 3: Add the Numerators
Now add the numerators (28 + 48 = 76) and keep the common denominator 112 unchanged.
Working: 28 + 48/112 = 76/112

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 76 and 112, which is 4. Divide both the numerator and denominator by 4.
Working: 76 ÷ 4/112 ÷ 4 = 19/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 28 produces a repeating decimal (approximately 0.678571, or 67.8571%).
Working: 19 ÷ 28 = 0.678571 (67.8571%)

Key Values:
- Simplified Fraction: 19/28
- Mixed Number Form: 19/28
- Decimal Value: 0.678571
- Percentage: 67.8571%

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Solved with FractionsCalc:
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4/16 + 3/7 = 19/28

Simplified Fraction

19/28

Mixed Number

Proper (19/28)

Decimal Value

0.678571

Percentage

67.8571%

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Step-by-Step Solution: 4/16 + 3/7

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 4/16 by 7, and multiply the numerator and denominator of 3/7 by 16 so both fractions share the common base 112.

4 × 7/16 × 7 = 28/112 and 3 × 16/7 × 16 = 48/112

Step 3

Add the Numerators

Now add the numerators (28 + 48 = 76) and keep the common denominator 112 unchanged.

28 + 48/112 = 76/112

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 76 and 112, which is 4. Divide both the numerator and denominator by 4.

76 ÷ 4/112 ÷ 4 = 19/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 28 produces a repeating decimal (approximately 0.678571, or 67.8571%).

19 ÷ 28 = 0.678571 (67.8571%)

Visual Representation

The diagram below illustrates 4/16 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/28`
Mixed Number Form	`19/28`
Decimal Form	`0.678571`
Percentage	`67.8571%`

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Frequently Asked Questions

What is 4/16 plus 3/7 as a fraction?

4/16 + 3/7 in simplest fraction form is 19/28.

What is 4/16 plus 3/7 as a decimal?

4/16 + 3/7 converted to a decimal is 0.678571.

What is 4/16 plus 3/7 as a percentage?

4/16 + 3/7 expressed as a percentage is 67.8571%.

Does 4/16 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.678571...) because the denominator contains prime factors other than 2 and 5.