What is 2/7 plus 10/16? (Answer: 51/56)

Exact Answer

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Problem: What is 2/7 plus 10/16?
Formula / Expression: 2/7 + 10/16
Final Answer: 51/56
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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 2/7 by 16, and multiply the numerator and denominator of 10/16 by 7 so both fractions share the common base 112.
Working: 2 × 16/7 × 16 = 32/112 and 10 × 7/16 × 7 = 70/112

Step 3: Add the Numerators
Now add the numerators (32 + 70 = 102) and keep the common denominator 112 unchanged.
Working: 32 + 70/112 = 102/112

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 112, which is 2. Divide both the numerator and denominator by 2.
Working: 102 ÷ 2/112 ÷ 2 = 51/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 56 produces a repeating decimal (approximately 0.910714, or 91.0714%).
Working: 51 ÷ 56 = 0.910714 (91.0714%)

Key Values:
- Simplified Fraction: 51/56
- Mixed Number Form: 51/56
- Decimal Value: 0.910714
- Percentage: 91.0714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-10-16/
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2/7 + 10/16 = 51/56

Simplified Fraction

51/56

Mixed Number

Proper (51/56)

Decimal Value

0.910714

Percentage

91.0714%

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Step-by-Step Solution: 2/7 + 10/16

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 2/7 by 16, and multiply the numerator and denominator of 10/16 by 7 so both fractions share the common base 112.

2 × 16/7 × 16 = 32/112 and 10 × 7/16 × 7 = 70/112

Step 3

Add the Numerators

Now add the numerators (32 + 70 = 102) and keep the common denominator 112 unchanged.

32 + 70/112 = 102/112

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 112, which is 2. Divide both the numerator and denominator by 2.

102 ÷ 2/112 ÷ 2 = 51/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 56 produces a repeating decimal (approximately 0.910714, or 91.0714%).

51 ÷ 56 = 0.910714 (91.0714%)

Visual Representation

The diagram below illustrates 2/7 plus 10/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/56`
Mixed Number Form	`51/56`
Decimal Form	`0.910714`
Percentage	`91.0714%`

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Frequently Asked Questions

What is 2/7 plus 10/16 as a fraction?

2/7 + 10/16 in simplest fraction form is 51/56.

What is 2/7 plus 10/16 as a decimal?

2/7 + 10/16 converted to a decimal is 0.910714.

What is 2/7 plus 10/16 as a percentage?

2/7 + 10/16 expressed as a percentage is 91.0714%.

Does 2/7 plus 10/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.910714...) because the denominator contains prime factors other than 2 and 5.