What is 10/54 plus 4/21? (Answer: 71/189)

Exact Answer

==================================================
Problem: What is 10/54 plus 4/21?
Formula / Expression: 10/54 + 4/21
Final Answer: 71/189
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).
Working: LCD(54, 21) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 10/54 by 7, and multiply the numerator and denominator of 4/21 by 18 so both fractions share the common base 378.
Working: 10 × 7/54 × 7 = 70/378 and 4 × 18/21 × 18 = 72/378

Step 3: Add the Numerators
Now add the numerators (70 + 72 = 142) and keep the common denominator 378 unchanged.
Working: 70 + 72/378 = 142/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 142 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 142 ÷ 2/378 ÷ 2 = 71/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 189 produces a repeating decimal (approximately 0.375661, or 37.5661%).
Working: 71 ÷ 189 = 0.375661 (37.5661%)

Key Values:
- Simplified Fraction: 71/189
- Mixed Number Form: 71/189
- Decimal Value: 0.375661
- Percentage: 37.5661%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-54-plus-4-21/
==================================================

10/54 + 4/21 = 71/189

Simplified Fraction

71/189

Mixed Number

Proper (71/189)

Decimal Value

0.375661

Percentage

37.5661%

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: 10/54 + 4/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 54 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 54 × 21 = 1134, keeping the calculation simpler).

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 10/54 by 7, and multiply the numerator and denominator of 4/21 by 18 so both fractions share the common base 378.

10 × 7/54 × 7 = 70/378 and 4 × 18/21 × 18 = 72/378

Step 3

Add the Numerators

Now add the numerators (70 + 72 = 142) and keep the common denominator 378 unchanged.

70 + 72/378 = 142/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 142 and 378, which is 2. Divide both the numerator and denominator by 2.

142 ÷ 2/378 ÷ 2 = 71/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 189 produces a repeating decimal (approximately 0.375661, or 37.5661%).

71 ÷ 189 = 0.375661 (37.5661%)

Visual Representation

The diagram below illustrates 10/54 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/189`
Mixed Number Form	`71/189`
Decimal Form	`0.375661`
Percentage	`37.5661%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/54 plus 4/21 as a fraction?

10/54 + 4/21 in simplest fraction form is 71/189.

What is 10/54 plus 4/21 as a decimal?

10/54 + 4/21 converted to a decimal is 0.375661.

What is 10/54 plus 4/21 as a percentage?

10/54 + 4/21 expressed as a percentage is 37.5661%.

Does 10/54 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.375661...) because the denominator contains prime factors other than 2 and 5.