What is 7/34 plus 10/21? (Answer: 487/714)

Exact Answer

==================================================
Problem: What is 7/34 plus 10/21?
Formula / Expression: 7/34 + 10/21
Final Answer: 487/714
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 21 = 714.
Working: LCD(34, 21) = 714

Step 2: Convert to Equivalent Fractions with Common Denominator 714
Multiply the numerator and denominator of 7/34 by 21, and multiply the numerator and denominator of 10/21 by 34 so both fractions share the common base 714.
Working: 7 × 21/34 × 21 = 147/714 and 10 × 34/21 × 34 = 340/714

Step 3: Add the Numerators
Now add the numerators (147 + 340 = 487) and keep the common denominator 714 unchanged.
Working: 147 + 340/714 = 487/714

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 487 and 714 is 1, confirming that 487/714 cannot be reduced further—it is already in its simplest irreducible form.
Working: 487/714

Step 5: Decimal & Percentage Representation
Dividing the numerator 487 by denominator 714 produces a repeating decimal (approximately 0.682073, or 68.2073%).
Working: 487 ÷ 714 = 0.682073 (68.2073%)

Key Values:
- Simplified Fraction: 487/714
- Mixed Number Form: 487/714
- Decimal Value: 0.682073
- Percentage: 68.2073%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-34-plus-10-21/
==================================================

7/34 + 10/21 = 487/714

Simplified Fraction

487/714

Mixed Number

Proper (487/714)

Decimal Value

0.682073

Percentage

68.2073%

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: 7/34 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 21 = 714.

LCD(34, 21) = 714

Step 2

Convert to Equivalent Fractions with Common Denominator 714

Multiply the numerator and denominator of 7/34 by 21, and multiply the numerator and denominator of 10/21 by 34 so both fractions share the common base 714.

7 × 21/34 × 21 = 147/714 and 10 × 34/21 × 34 = 340/714

Step 3

Add the Numerators

Now add the numerators (147 + 340 = 487) and keep the common denominator 714 unchanged.

147 + 340/714 = 487/714

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 487 and 714 is 1, confirming that 487/714 cannot be reduced further—it is already in its simplest irreducible form.

487/714

Step 5

Decimal & Percentage Representation

Dividing the numerator 487 by denominator 714 produces a repeating decimal (approximately 0.682073, or 68.2073%).

487 ÷ 714 = 0.682073 (68.2073%)

Visual Representation

The diagram below illustrates 7/34 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`487/714`
Mixed Number Form	`487/714`
Decimal Form	`0.682073`
Percentage	`68.2073%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/34 plus 10/21 as a fraction?

7/34 + 10/21 in simplest fraction form is 487/714.

What is 7/34 plus 10/21 as a decimal?

7/34 + 10/21 converted to a decimal is 0.682073.

What is 7/34 plus 10/21 as a percentage?

7/34 + 10/21 expressed as a percentage is 68.2073%.

Does 7/34 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.682073...) because the denominator contains prime factors other than 2 and 5.