What is 10/27 plus 10/21? (Answer: 160/189)

Exact Answer

==================================================
Problem: What is 10/27 plus 10/21?
Formula / Expression: 10/27 + 10/21
Final Answer: 160/189
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 10/27 by 7, and multiply the numerator and denominator of 10/21 by 9 so both fractions share the common base 189.
Working: 10 × 7/27 × 7 = 70/189 and 10 × 9/21 × 9 = 90/189

Step 3: Add the Numerators
Now add the numerators (70 + 90 = 160) and keep the common denominator 189 unchanged.
Working: 70 + 90/189 = 160/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 160 and 189 is 1, confirming that 160/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 160/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 160 by denominator 189 produces a repeating decimal (approximately 0.846561, or 84.6561%).
Working: 160 ÷ 189 = 0.846561 (84.6561%)

Key Values:
- Simplified Fraction: 160/189
- Mixed Number Form: 160/189
- Decimal Value: 0.846561
- Percentage: 84.6561%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-27-plus-10-21/
==================================================

10/27 + 10/21 = 160/189

Simplified Fraction

160/189

Mixed Number

Proper (160/189)

Decimal Value

0.846561

Percentage

84.6561%

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: 10/27 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 10/27 by 7, and multiply the numerator and denominator of 10/21 by 9 so both fractions share the common base 189.

10 × 7/27 × 7 = 70/189 and 10 × 9/21 × 9 = 90/189

Step 3

Add the Numerators

Now add the numerators (70 + 90 = 160) and keep the common denominator 189 unchanged.

70 + 90/189 = 160/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 160 and 189 is 1, confirming that 160/189 cannot be reduced further—it is already in its simplest irreducible form.

160/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 160 by denominator 189 produces a repeating decimal (approximately 0.846561, or 84.6561%).

160 ÷ 189 = 0.846561 (84.6561%)

Visual Representation

The diagram below illustrates 10/27 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`160/189`
Mixed Number Form	`160/189`
Decimal Form	`0.846561`
Percentage	`84.6561%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/27 plus 10/21 as a fraction?

10/27 + 10/21 in simplest fraction form is 160/189.

What is 10/27 plus 10/21 as a decimal?

10/27 + 10/21 converted to a decimal is 0.846561.

What is 10/27 plus 10/21 as a percentage?

10/27 + 10/21 expressed as a percentage is 84.6561%.

Does 10/27 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.846561...) because the denominator contains prime factors other than 2 and 5.