What is 3/5 plus 7/10? (Answer: 13/10)

Exact Answer

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Problem: What is 3/5 plus 7/10?
Formula / Expression: 3/5 + 7/10
Final Answer: 1 3/10 (13/10)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 10 is an exact multiple of 5 (5 × 2 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.
Working: LCD(5, 10) = 10

Step 2: Convert to Equivalent Fractions with Common Denominator 10
Multiply the numerator and denominator of 3/5 by 2, and multiply the numerator and denominator of 7/10 by 1 so both fractions share the common base 10.
Working: 3 × 2/5 × 2 = 6/10 and 7 × 1/10 × 1 = 7/10

Step 3: Add the Numerators
Now add the numerators (6 + 7 = 13) and keep the common denominator 10 unchanged.
Working: 6 + 7/10 = 13/10

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 10 is 1, confirming that 13/10 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/10

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (13) is greater than the denominator (10), divide 13 by 10: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/10.
Working: 13/10 = 1 3/10

Step 6: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 10 yields an exact terminating decimal of 1.3 (or 130%).
Working: 13 ÷ 10 = 1.3 (130%)

Key Values:
- Simplified Fraction: 13/10
- Mixed Number Form: 1 3/10
- Decimal Value: 1.3
- Percentage: 130%

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3/5 + 7/10 = 13/10

Simplified Fraction

13/10

Mixed Number

1 3/10

Decimal Value

1.3

Percentage

130%

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Step-by-Step Solution: 3/5 + 7/10

Step 1

Find the Least Common Denominator (LCD)

Notice that 10 is an exact multiple of 5 (5 × 2 = 10). The Least Common Denominator (LCD) is simply 10, meaning we only need to scale one fraction.

LCD(5, 10) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

Multiply the numerator and denominator of 3/5 by 2, and multiply the numerator and denominator of 7/10 by 1 so both fractions share the common base 10.

3 × 2/5 × 2 = 6/10 and 7 × 1/10 × 1 = 7/10

Step 3

Add the Numerators

Now add the numerators (6 + 7 = 13) and keep the common denominator 10 unchanged.

6 + 7/10 = 13/10

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 10 is 1, confirming that 13/10 cannot be reduced further—it is already in its simplest irreducible form.

13/10

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (13) is greater than the denominator (10), divide 13 by 10: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/10.

13/10 = 13/10

Step 6

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 10 yields an exact terminating decimal of 1.3 (or 130%).

13 ÷ 10 = 1.3 (130%)

Visual Representation

The diagram below illustrates 3/5 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/10`
Mixed Number Form	`1 3/10`
Decimal Form	`1.3`
Percentage	`130%`

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Frequently Asked Questions

What is 3/5 plus 7/10 as a fraction?

3/5 + 7/10 in simplest fraction form is 13/10 (or 1 3/10 as a mixed number).

What is 3/5 plus 7/10 as a decimal?

3/5 + 7/10 converted to a decimal is 1.3.

What is 3/5 plus 7/10 as a percentage?

3/5 + 7/10 expressed as a percentage is 130%.

How do you write 3/5 plus 7/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 13/10 can be written as the mixed number 1 3/10.

Does 3/5 plus 7/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.3) because the denominator in simplest terms contains only prime factors 2 and/or 5.