What is 2/10 plus 9/14? (Answer: 59/70)

Exact Answer

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Problem: What is 2/10 plus 9/14?
Formula / Expression: 2/10 + 9/14
Final Answer: 59/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 14 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 70 (which is smaller than their product 10 × 14 = 140, keeping the calculation simpler).
Working: LCD(10, 14) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/10 by 7, and multiply the numerator and denominator of 9/14 by 5 so both fractions share the common base 70.
Working: 2 × 7/10 × 7 = 14/70 and 9 × 5/14 × 5 = 45/70

Step 3: Add the Numerators
Now add the numerators (14 + 45 = 59) and keep the common denominator 70 unchanged.
Working: 14 + 45/70 = 59/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 70 is 1, confirming that 59/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 70 produces a repeating decimal (approximately 0.842857, or 84.2857%).
Working: 59 ÷ 70 = 0.842857 (84.2857%)

Key Values:
- Simplified Fraction: 59/70
- Mixed Number Form: 59/70
- Decimal Value: 0.842857
- Percentage: 84.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-9-14/
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2/10 + 9/14 = 59/70

Simplified Fraction

59/70

Mixed Number

Proper (59/70)

Decimal Value

0.842857

Percentage

84.2857%

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Step-by-Step Solution: 2/10 + 9/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 14 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 70 (which is smaller than their product 10 × 14 = 140, keeping the calculation simpler).

LCD(10, 14) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 2/10 by 7, and multiply the numerator and denominator of 9/14 by 5 so both fractions share the common base 70.

2 × 7/10 × 7 = 14/70 and 9 × 5/14 × 5 = 45/70

Step 3

Add the Numerators

Now add the numerators (14 + 45 = 59) and keep the common denominator 70 unchanged.

14 + 45/70 = 59/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 70 is 1, confirming that 59/70 cannot be reduced further—it is already in its simplest irreducible form.

59/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 70 produces a repeating decimal (approximately 0.842857, or 84.2857%).

59 ÷ 70 = 0.842857 (84.2857%)

Visual Representation

The diagram below illustrates 2/10 plus 9/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/70`
Mixed Number Form	`59/70`
Decimal Form	`0.842857`
Percentage	`84.2857%`

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Frequently Asked Questions

What is 2/10 plus 9/14 as a fraction?

2/10 + 9/14 in simplest fraction form is 59/70.

What is 2/10 plus 9/14 as a decimal?

2/10 + 9/14 converted to a decimal is 0.842857.

What is 2/10 plus 9/14 as a percentage?

2/10 + 9/14 expressed as a percentage is 84.2857%.

Does 2/10 plus 9/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.842857...) because the denominator contains prime factors other than 2 and 5.