What is 2/5 plus 7/14? (Answer: 9/10)

Exact Answer

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Problem: What is 2/5 plus 7/14?
Formula / Expression: 2/5 + 7/14
Final Answer: 9/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 14 = 70.
Working: LCD(5, 14) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 2/5 by 14, and multiply the numerator and denominator of 7/14 by 5 so both fractions share the common base 70.
Working: 2 × 14/5 × 14 = 28/70 and 7 × 5/14 × 5 = 35/70

Step 3: Add the Numerators
Now add the numerators (28 + 35 = 63) and keep the common denominator 70 unchanged.
Working: 28 + 35/70 = 63/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 70, which is 7. Divide both the numerator and denominator by 7.
Working: 63 ÷ 7/70 ÷ 7 = 9/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 10 yields an exact terminating decimal of 0.9 (or 90%).
Working: 9 ÷ 10 = 0.9 (90%)

Key Values:
- Simplified Fraction: 9/10
- Mixed Number Form: 9/10
- Decimal Value: 0.9
- Percentage: 90%

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Solved with FractionsCalc:
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2/5 + 7/14 = 9/10

Simplified Fraction

9/10

Mixed Number

Proper (9/10)

Decimal Value

0.9

Percentage

90%

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Step-by-Step Solution: 2/5 + 7/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 14 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 14 = 70.

LCD(5, 14) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

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

2 × 14/5 × 14 = 28/70 and 7 × 5/14 × 5 = 35/70

Step 3

Add the Numerators

Now add the numerators (28 + 35 = 63) and keep the common denominator 70 unchanged.

28 + 35/70 = 63/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 70, which is 7. Divide both the numerator and denominator by 7.

63 ÷ 7/70 ÷ 7 = 9/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 10 yields an exact terminating decimal of 0.9 (or 90%).

9 ÷ 10 = 0.9 (90%)

Visual Representation

The diagram below illustrates 2/5 plus 7/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/10`
Mixed Number Form	`9/10`
Decimal Form	`0.9`
Percentage	`90%`

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Frequently Asked Questions

What is 2/5 plus 7/14 as a fraction?

2/5 + 7/14 in simplest fraction form is 9/10.

What is 2/5 plus 7/14 as a decimal?

2/5 + 7/14 converted to a decimal is 0.9.

What is 2/5 plus 7/14 as a percentage?

2/5 + 7/14 expressed as a percentage is 90%.

Does 2/5 plus 7/14 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.9) because the denominator in simplest terms contains only prime factors 2 and/or 5.