What is 7/14 plus 3/4? (Answer: 5/4)

Exact Answer

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Problem: What is 7/14 plus 3/4?
Formula / Expression: 7/14 + 3/4
Final Answer: 1 1/4 (5/4)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 28 (which is smaller than their product 14 × 4 = 56, keeping the calculation simpler).
Working: LCD(14, 4) = 28

Step 2: Convert to Equivalent Fractions with Common Denominator 28
Multiply the numerator and denominator of 7/14 by 2, and multiply the numerator and denominator of 3/4 by 7 so both fractions share the common base 28.
Working: 7 × 2/14 × 2 = 14/28 and 3 × 7/4 × 7 = 21/28

Step 3: Add the Numerators
Now add the numerators (14 + 21 = 35) and keep the common denominator 28 unchanged.
Working: 14 + 21/28 = 35/28

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 28, which is 7. Divide both the numerator and denominator by 7.
Working: 35 ÷ 7/28 ÷ 7 = 5/4

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.
Working: 5/4 = 1 1/4

Step 6: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).
Working: 5 ÷ 4 = 1.25 (125%)

Key Values:
- Simplified Fraction: 5/4
- Mixed Number Form: 1 1/4
- Decimal Value: 1.25
- Percentage: 125%

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7/14 + 3/4 = 5/4

Simplified Fraction

5/4

Mixed Number

1 1/4

Decimal Value

1.25

Percentage

125%

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Step-by-Step Solution: 7/14 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 4 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 28 (which is smaller than their product 14 × 4 = 56, keeping the calculation simpler).

LCD(14, 4) = 28

Step 2

Convert to Equivalent Fractions with Common Denominator 28

Multiply the numerator and denominator of 7/14 by 2, and multiply the numerator and denominator of 3/4 by 7 so both fractions share the common base 28.

7 × 2/14 × 2 = 14/28 and 3 × 7/4 × 7 = 21/28

Step 3

Add the Numerators

Now add the numerators (14 + 21 = 35) and keep the common denominator 28 unchanged.

14 + 21/28 = 35/28

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 28, which is 7. Divide both the numerator and denominator by 7.

35 ÷ 7/28 ÷ 7 = 5/4

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (5) is greater than the denominator (4), divide 5 by 4: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/4.

5/4 = 11/4

Step 6

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 4 yields an exact terminating decimal of 1.25 (or 125%).

5 ÷ 4 = 1.25 (125%)

Visual Representation

The diagram below illustrates 7/14 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/4`
Mixed Number Form	`1 1/4`
Decimal Form	`1.25`
Percentage	`125%`

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Frequently Asked Questions

What is 7/14 plus 3/4 as a fraction?

7/14 + 3/4 in simplest fraction form is 5/4 (or 1 1/4 as a mixed number).

What is 7/14 plus 3/4 as a decimal?

7/14 + 3/4 converted to a decimal is 1.25.

What is 7/14 plus 3/4 as a percentage?

7/14 + 3/4 expressed as a percentage is 125%.

How do you write 7/14 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 5/4 can be written as the mixed number 1 1/4.

Does 7/14 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.