What is 3/10 plus 3/4? (Answer: 21/20)

Exact Answer

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Problem: What is 3/10 plus 3/4?
Formula / Expression: 3/10 + 3/4
Final Answer: 1 1/20 (21/20)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 10 × 4 = 40, keeping the calculation simpler).
Working: LCD(10, 4) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 3/10 by 2, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.
Working: 3 × 2/10 × 2 = 6/20 and 3 × 5/4 × 5 = 15/20

Step 3: Add the Numerators
Now add the numerators (6 + 15 = 21) and keep the common denominator 20 unchanged.
Working: 6 + 15/20 = 21/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 20 is 1, confirming that 21/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/20

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (21) is greater than the denominator (20), divide 21 by 20: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/20.
Working: 21/20 = 1 1/20

Step 6: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 20 yields an exact terminating decimal of 1.05 (or 105%).
Working: 21 ÷ 20 = 1.05 (105%)

Key Values:
- Simplified Fraction: 21/20
- Mixed Number Form: 1 1/20
- Decimal Value: 1.05
- Percentage: 105%

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3/10 + 3/4 = 21/20

Simplified Fraction

21/20

Mixed Number

1 1/20

Decimal Value

1.05

Percentage

105%

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Step-by-Step Solution: 3/10 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 20 (which is smaller than their product 10 × 4 = 40, keeping the calculation simpler).

LCD(10, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 3/10 by 2, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.

3 × 2/10 × 2 = 6/20 and 3 × 5/4 × 5 = 15/20

Step 3

Add the Numerators

Now add the numerators (6 + 15 = 21) and keep the common denominator 20 unchanged.

6 + 15/20 = 21/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 20 is 1, confirming that 21/20 cannot be reduced further—it is already in its simplest irreducible form.

21/20

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (21) is greater than the denominator (20), divide 21 by 20: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/20.

21/20 = 11/20

Step 6

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 20 yields an exact terminating decimal of 1.05 (or 105%).

21 ÷ 20 = 1.05 (105%)

Visual Representation

The diagram below illustrates 3/10 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/20`
Mixed Number Form	`1 1/20`
Decimal Form	`1.05`
Percentage	`105%`

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Frequently Asked Questions

What is 3/10 plus 3/4 as a fraction?

3/10 + 3/4 in simplest fraction form is 21/20 (or 1 1/20 as a mixed number).

What is 3/10 plus 3/4 as a decimal?

3/10 + 3/4 converted to a decimal is 1.05.

What is 3/10 plus 3/4 as a percentage?

3/10 + 3/4 expressed as a percentage is 105%.

How do you write 3/10 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 21/20 can be written as the mixed number 1 1/20.

Does 3/10 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.05) because the denominator in simplest terms contains only prime factors 2 and/or 5.