What is 10/51 plus 7/21? (Answer: 9/17)

Exact Answer

==================================================
Problem: What is 10/51 plus 7/21?
Formula / Expression: 10/51 + 7/21
Final Answer: 9/17
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).
Working: LCD(51, 21) = 357

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 10/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 10 × 7/51 × 7 = 70/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (70 + 119 = 189) and keep the common denominator 357 unchanged.
Working: 70 + 119/357 = 189/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 189 and 357, which is 21. Divide both the numerator and denominator by 21.
Working: 189 ÷ 21/357 ÷ 21 = 9/17

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 17 produces a repeating decimal (approximately 0.529412, or 52.9412%).
Working: 9 ÷ 17 = 0.529412 (52.9412%)

Key Values:
- Simplified Fraction: 9/17
- Mixed Number Form: 9/17
- Decimal Value: 0.529412
- Percentage: 52.9412%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-51-plus-7-21/
==================================================

10/51 + 7/21 = 9/17

Simplified Fraction

9/17

Mixed Number

Proper (9/17)

Decimal Value

0.529412

Percentage

52.9412%

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: 10/51 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).

LCD(51, 21) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 10/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

10 × 7/51 × 7 = 70/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (70 + 119 = 189) and keep the common denominator 357 unchanged.

70 + 119/357 = 189/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 189 and 357, which is 21. Divide both the numerator and denominator by 21.

189 ÷ 21/357 ÷ 21 = 9/17

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 17 produces a repeating decimal (approximately 0.529412, or 52.9412%).

9 ÷ 17 = 0.529412 (52.9412%)

Visual Representation

The diagram below illustrates 10/51 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/17`
Mixed Number Form	`9/17`
Decimal Form	`0.529412`
Percentage	`52.9412%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/51 plus 7/21 as a fraction?

10/51 + 7/21 in simplest fraction form is 9/17.

What is 10/51 plus 7/21 as a decimal?

10/51 + 7/21 converted to a decimal is 0.529412.

What is 10/51 plus 7/21 as a percentage?

10/51 + 7/21 expressed as a percentage is 52.9412%.

Does 10/51 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.529412...) because the denominator contains prime factors other than 2 and 5.