What is 1/2 plus 4/7? (Answer: 15/14)

Exact Answer

==================================================
Problem: What is 1/2 plus 4/7?
Formula / Expression: 1/2 + 4/7
Final Answer: 1 1/14 (15/14)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 7 = 14.
Working: LCD(2, 7) = 14

Step 2: Convert to Equivalent Fractions with Common Denominator 14
Multiply the numerator and denominator of 1/2 by 7, and multiply the numerator and denominator of 4/7 by 2 so both fractions share the common base 14.
Working: 1 × 7/2 × 7 = 7/14 and 4 × 2/7 × 2 = 8/14

Step 3: Add the Numerators
Now add the numerators (7 + 8 = 15) and keep the common denominator 14 unchanged.
Working: 7 + 8/14 = 15/14

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 15 and 14 is 1, confirming that 15/14 cannot be reduced further—it is already in its simplest irreducible form.
Working: 15/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.
Working: 15/14 = 1 1/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).
Working: 15 ÷ 14 = 1.071429 (107.1429%)

Key Values:
- Simplified Fraction: 15/14
- Mixed Number Form: 1 1/14
- Decimal Value: 1.071429
- Percentage: 107.1429%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-4-7/
==================================================

1/2 + 4/7 = 15/14

Simplified Fraction

15/14

Mixed Number

1 1/14

Decimal Value

1.071429

Percentage

107.1429%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/2 + 4/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 7 = 14.

LCD(2, 7) = 14

Step 2

Convert to Equivalent Fractions with Common Denominator 14

Multiply the numerator and denominator of 1/2 by 7, and multiply the numerator and denominator of 4/7 by 2 so both fractions share the common base 14.

1 × 7/2 × 7 = 7/14 and 4 × 2/7 × 2 = 8/14

Step 3

Add the Numerators

Now add the numerators (7 + 8 = 15) and keep the common denominator 14 unchanged.

7 + 8/14 = 15/14

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 15 and 14 is 1, confirming that 15/14 cannot be reduced further—it is already in its simplest irreducible form.

15/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.

15/14 = 11/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).

15 ÷ 14 = 1.071429 (107.1429%)

Visual Representation

The diagram below illustrates 1/2 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/14`
Mixed Number Form	`1 1/14`
Decimal Form	`1.071429`
Percentage	`107.1429%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/2 plus 4/7 as a fraction?

1/2 + 4/7 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).

What is 1/2 plus 4/7 as a decimal?

1/2 + 4/7 converted to a decimal is 1.071429.

What is 1/2 plus 4/7 as a percentage?

1/2 + 4/7 expressed as a percentage is 107.1429%.

How do you write 1/2 plus 4/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 15/14 can be written as the mixed number 1 1/14.

Does 1/2 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.071429...) because the denominator contains prime factors other than 2 and 5.