What is 10/30 plus 9/21? (Answer: 16/21)

Exact Answer

==================================================
Problem: What is 10/30 plus 9/21?
Formula / Expression: 10/30 + 9/21
Final Answer: 16/21
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 10/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.
Working: 10 × 7/30 × 7 = 70/210 and 9 × 10/21 × 10 = 90/210

Step 3: Add the Numerators
Now add the numerators (70 + 90 = 160) and keep the common denominator 210 unchanged.
Working: 70 + 90/210 = 160/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 160 and 210, which is 10. Divide both the numerator and denominator by 10.
Working: 160 ÷ 10/210 ÷ 10 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-30-plus-9-21/
==================================================

10/30 + 9/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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: 10/30 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 10/30 by 7, and multiply the numerator and denominator of 9/21 by 10 so both fractions share the common base 210.

10 × 7/30 × 7 = 70/210 and 9 × 10/21 × 10 = 90/210

Step 3

Add the Numerators

Now add the numerators (70 + 90 = 160) and keep the common denominator 210 unchanged.

70 + 90/210 = 160/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 160 and 210, which is 10. Divide both the numerator and denominator by 10.

160 ÷ 10/210 ÷ 10 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 10/30 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/30 plus 9/21 as a fraction?

10/30 + 9/21 in simplest fraction form is 16/21.

What is 10/30 plus 9/21 as a decimal?

10/30 + 9/21 converted to a decimal is 0.761905.

What is 10/30 plus 9/21 as a percentage?

10/30 + 9/21 expressed as a percentage is 76.1905%.

Does 10/30 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.