What is 7/30 plus 2/3? (Answer: 9/10)

Exact Answer

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Problem: What is 7/30 plus 2/3?
Formula / Expression: 7/30 + 2/3
Final Answer: 9/10
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 30 is an exact multiple of 3 (3 × 10 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.
Working: LCD(30, 3) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 7/30 by 1, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.
Working: 7 × 1/30 × 1 = 7/30 and 2 × 10/3 × 10 = 20/30

Step 3: Add the Numerators
Now add the numerators (7 + 20 = 27) and keep the common denominator 30 unchanged.
Working: 7 + 20/30 = 27/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 30, which is 3. Divide both the numerator and denominator by 3.
Working: 27 ÷ 3/30 ÷ 3 = 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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7/30 + 2/3 = 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: 7/30 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 30 is an exact multiple of 3 (3 × 10 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.

LCD(30, 3) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 7/30 by 1, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.

7 × 1/30 × 1 = 7/30 and 2 × 10/3 × 10 = 20/30

Step 3

Add the Numerators

Now add the numerators (7 + 20 = 27) and keep the common denominator 30 unchanged.

7 + 20/30 = 27/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 30, which is 3. Divide both the numerator and denominator by 3.

27 ÷ 3/30 ÷ 3 = 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 7/30 plus 2/3 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 7/30 plus 2/3 as a fraction?

7/30 + 2/3 in simplest fraction form is 9/10.

What is 7/30 plus 2/3 as a decimal?

7/30 + 2/3 converted to a decimal is 0.9.

What is 7/30 plus 2/3 as a percentage?

7/30 + 2/3 expressed as a percentage is 90%.

Does 7/30 plus 2/3 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.