What is 4/7 plus 7/10? (Answer: 89/70)

Exact Answer

==================================================
Problem: What is 4/7 plus 7/10?
Formula / Expression: 4/7 + 7/10
Final Answer: 1 19/70 (89/70)
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 4/7 by 10, and multiply the numerator and denominator of 7/10 by 7 so both fractions share the common base 70.
Working: 4 × 10/7 × 10 = 40/70 and 7 × 7/10 × 7 = 49/70

Step 3: Add the Numerators
Now add the numerators (40 + 49 = 89) and keep the common denominator 70 unchanged.
Working: 40 + 49/70 = 89/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 70 is 1, confirming that 89/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/70

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (89) is greater than the denominator (70), divide 89 by 70: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/70.
Working: 89/70 = 1 19/70

Step 6: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 70 produces a repeating decimal (approximately 1.271429, or 127.1429%).
Working: 89 ÷ 70 = 1.271429 (127.1429%)

Key Values:
- Simplified Fraction: 89/70
- Mixed Number Form: 1 19/70
- Decimal Value: 1.271429
- Percentage: 127.1429%

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

4/7 + 7/10 = 89/70

Simplified Fraction

89/70

Mixed Number

1 19/70

Decimal Value

1.271429

Percentage

127.1429%

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: 4/7 + 7/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 10) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

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

4 × 10/7 × 10 = 40/70 and 7 × 7/10 × 7 = 49/70

Step 3

Add the Numerators

Now add the numerators (40 + 49 = 89) and keep the common denominator 70 unchanged.

40 + 49/70 = 89/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 70 is 1, confirming that 89/70 cannot be reduced further—it is already in its simplest irreducible form.

89/70

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (89) is greater than the denominator (70), divide 89 by 70: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/70.

89/70 = 119/70

Step 6

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 70 produces a repeating decimal (approximately 1.271429, or 127.1429%).

89 ÷ 70 = 1.271429 (127.1429%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/70`
Mixed Number Form	`1 19/70`
Decimal Form	`1.271429`
Percentage	`127.1429%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

4/7 + 7/10 in simplest fraction form is 89/70 (or 1 19/70 as a mixed number).

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

4/7 + 7/10 converted to a decimal is 1.271429.

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

4/7 + 7/10 expressed as a percentage is 127.1429%.

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

Because the numerator is greater than the denominator, the improper fraction 89/70 can be written as the mixed number 1 19/70.

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

It results in a repeating decimal (approximately 1.271429...) because the denominator contains prime factors other than 2 and 5.