What is 10/34 plus 10/21? (Answer: 275/357)

Exact Answer

==================================================
Problem: What is 10/34 plus 10/21?
Formula / Expression: 10/34 + 10/21
Final Answer: 275/357
==================================================

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 10/34 by 21, and multiply the numerator and denominator of 10/21 by 34 so both fractions share the common base 714.
Working: 10 × 21/34 × 21 = 210/714 and 10 × 34/21 × 34 = 340/714

Step 3: Add the Numerators
Now add the numerators (210 + 340 = 550) and keep the common denominator 714 unchanged.
Working: 210 + 340/714 = 550/714

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 550 and 714, which is 2. Divide both the numerator and denominator by 2.
Working: 550 ÷ 2/714 ÷ 2 = 275/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 275 by denominator 357 produces a repeating decimal (approximately 0.770308, or 77.0308%).
Working: 275 ÷ 357 = 0.770308 (77.0308%)

Key Values:
- Simplified Fraction: 275/357
- Mixed Number Form: 275/357
- Decimal Value: 0.770308
- Percentage: 77.0308%

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

10/34 + 10/21 = 275/357

Simplified Fraction

275/357

Mixed Number

Proper (275/357)

Decimal Value

0.770308

Percentage

77.0308%

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

10 × 21/34 × 21 = 210/714 and 10 × 34/21 × 34 = 340/714

Step 3

Add the Numerators

Now add the numerators (210 + 340 = 550) and keep the common denominator 714 unchanged.

210 + 340/714 = 550/714

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 550 and 714, which is 2. Divide both the numerator and denominator by 2.

550 ÷ 2/714 ÷ 2 = 275/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 275 by denominator 357 produces a repeating decimal (approximately 0.770308, or 77.0308%).

275 ÷ 357 = 0.770308 (77.0308%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`275/357`
Mixed Number Form	`275/357`
Decimal Form	`0.770308`
Percentage	`77.0308%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

10/34 + 10/21 in simplest fraction form is 275/357.

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

10/34 + 10/21 converted to a decimal is 0.770308.

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

10/34 + 10/21 expressed as a percentage is 77.0308%.

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

It results in a repeating decimal (approximately 0.770308...) because the denominator contains prime factors other than 2 and 5.