What is 4/10 plus 5/7? (Answer: 39/35)

Exact Answer

==================================================
Problem: What is 4/10 plus 5/7?
Formula / Expression: 4/10 + 5/7
Final Answer: 1 4/35 (39/35)
==================================================

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 4/10 by 7, and multiply the numerator and denominator of 5/7 by 10 so both fractions share the common base 70.
Working: 4 × 7/10 × 7 = 28/70 and 5 × 10/7 × 10 = 50/70

Step 3: Add the Numerators
Now add the numerators (28 + 50 = 78) and keep the common denominator 70 unchanged.
Working: 28 + 50/70 = 78/70

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 70, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/70 ÷ 2 = 39/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (39) is greater than the denominator (35), divide 39 by 35: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/35.
Working: 39/35 = 1 4/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 35 produces a repeating decimal (approximately 1.114286, or 111.4286%).
Working: 39 ÷ 35 = 1.114286 (111.4286%)

Key Values:
- Simplified Fraction: 39/35
- Mixed Number Form: 1 4/35
- Decimal Value: 1.114286
- Percentage: 111.4286%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-10-plus-5-7/
==================================================

4/10 + 5/7 = 39/35

Simplified Fraction

39/35

Mixed Number

1 4/35

Decimal Value

1.114286

Percentage

111.4286%

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: 4/10 + 5/7

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

4 × 7/10 × 7 = 28/70 and 5 × 10/7 × 10 = 50/70

Step 3

Add the Numerators

Now add the numerators (28 + 50 = 78) and keep the common denominator 70 unchanged.

28 + 50/70 = 78/70

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 70, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/70 ÷ 2 = 39/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (39) is greater than the denominator (35), divide 39 by 35: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/35.

39/35 = 14/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 35 produces a repeating decimal (approximately 1.114286, or 111.4286%).

39 ÷ 35 = 1.114286 (111.4286%)

Visual Representation

The diagram below illustrates 4/10 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/35`
Mixed Number Form	`1 4/35`
Decimal Form	`1.114286`
Percentage	`111.4286%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

4/10 + 5/7 in simplest fraction form is 39/35 (or 1 4/35 as a mixed number).

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

4/10 + 5/7 converted to a decimal is 1.114286.

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

4/10 + 5/7 expressed as a percentage is 111.4286%.

How do you write 4/10 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 39/35 can be written as the mixed number 1 4/35.

Does 4/10 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.114286...) because the denominator contains prime factors other than 2 and 5.