What is 3/21 plus 5/30? (Answer: 13/42)

Exact Answer

==================================================
Problem: What is 3/21 plus 5/30?
Formula / Expression: 3/21 + 5/30
Final Answer: 13/42
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 3/21 by 10, and multiply the numerator and denominator of 5/30 by 7 so both fractions share the common base 210.
Working: 3 × 10/21 × 10 = 30/210 and 5 × 7/30 × 7 = 35/210

Step 3: Add the Numerators
Now add the numerators (30 + 35 = 65) and keep the common denominator 210 unchanged.
Working: 30 + 35/210 = 65/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 65 and 210, which is 5. Divide both the numerator and denominator by 5.
Working: 65 ÷ 5/210 ÷ 5 = 13/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).
Working: 13 ÷ 42 = 0.309524 (30.9524%)

Key Values:
- Simplified Fraction: 13/42
- Mixed Number Form: 13/42
- Decimal Value: 0.309524
- Percentage: 30.9524%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-5-30/
==================================================

3/21 + 5/30 = 13/42

Simplified Fraction

13/42

Mixed Number

Proper (13/42)

Decimal Value

0.309524

Percentage

30.9524%

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: 3/21 + 5/30

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 30) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 3/21 by 10, and multiply the numerator and denominator of 5/30 by 7 so both fractions share the common base 210.

3 × 10/21 × 10 = 30/210 and 5 × 7/30 × 7 = 35/210

Step 3

Add the Numerators

Now add the numerators (30 + 35 = 65) and keep the common denominator 210 unchanged.

30 + 35/210 = 65/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 65 and 210, which is 5. Divide both the numerator and denominator by 5.

65 ÷ 5/210 ÷ 5 = 13/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 42 produces a repeating decimal (approximately 0.309524, or 30.9524%).

13 ÷ 42 = 0.309524 (30.9524%)

Visual Representation

The diagram below illustrates 3/21 plus 5/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/42`
Mixed Number Form	`13/42`
Decimal Form	`0.309524`
Percentage	`30.9524%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/21 plus 5/30 as a fraction?

3/21 + 5/30 in simplest fraction form is 13/42.

What is 3/21 plus 5/30 as a decimal?

3/21 + 5/30 converted to a decimal is 0.309524.

What is 3/21 plus 5/30 as a percentage?

3/21 + 5/30 expressed as a percentage is 30.9524%.

Does 3/21 plus 5/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.309524...) because the denominator contains prime factors other than 2 and 5.