What is 5/10 plus 4/7? (Answer: 15/14)

Exact Answer

==================================================
Problem: What is 5/10 plus 4/7?
Formula / Expression: 5/10 + 4/7
Final Answer: 1 1/14 (15/14)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.
Working: LCD(10, 7) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 5/10 by 7, and multiply the numerator and denominator of 4/7 by 10 so both fractions share the common base 70.
Working: 5 × 7/10 × 7 = 35/70 and 4 × 10/7 × 10 = 40/70

Step 3: Add the Numerators
Now add the numerators (35 + 40 = 75) and keep the common denominator 70 unchanged.
Working: 35 + 40/70 = 75/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 70, which is 5. Divide both the numerator and denominator by 5.
Working: 75 ÷ 5/70 ÷ 5 = 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-5-10-plus-4-7/
==================================================

5/10 + 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: 5/10 + 4/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.

LCD(10, 7) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 5/10 by 7, and multiply the numerator and denominator of 4/7 by 10 so both fractions share the common base 70.

5 × 7/10 × 7 = 35/70 and 4 × 10/7 × 10 = 40/70

Step 3

Add the Numerators

Now add the numerators (35 + 40 = 75) and keep the common denominator 70 unchanged.

35 + 40/70 = 75/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 70, which is 5. Divide both the numerator and denominator by 5.

75 ÷ 5/70 ÷ 5 = 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 5/10 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 5/10 plus 4/7 as a fraction?

5/10 + 4/7 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).

What is 5/10 plus 4/7 as a decimal?

5/10 + 4/7 converted to a decimal is 1.071429.

What is 5/10 plus 4/7 as a percentage?

5/10 + 4/7 expressed as a percentage is 107.1429%.

How do you write 5/10 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 5/10 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.