What is 4/30 plus 8/21? (Answer: 18/35)

Exact Answer

==================================================
Problem: What is 4/30 plus 8/21?
Formula / Expression: 4/30 + 8/21
Final Answer: 18/35
==================================================

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 4/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.
Working: 4 × 7/30 × 7 = 28/210 and 8 × 10/21 × 10 = 80/210

Step 3: Add the Numerators
Now add the numerators (28 + 80 = 108) and keep the common denominator 210 unchanged.
Working: 28 + 80/210 = 108/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 108 and 210, which is 6. Divide both the numerator and denominator by 6.
Working: 108 ÷ 6/210 ÷ 6 = 18/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 18 by denominator 35 produces a repeating decimal (approximately 0.514286, or 51.4286%).
Working: 18 ÷ 35 = 0.514286 (51.4286%)

Key Values:
- Simplified Fraction: 18/35
- Mixed Number Form: 18/35
- Decimal Value: 0.514286
- Percentage: 51.4286%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-30-plus-8-21/
==================================================

4/30 + 8/21 = 18/35

Simplified Fraction

18/35

Mixed Number

Proper (18/35)

Decimal Value

0.514286

Percentage

51.4286%

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: 4/30 + 8/21

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 4/30 by 7, and multiply the numerator and denominator of 8/21 by 10 so both fractions share the common base 210.

4 × 7/30 × 7 = 28/210 and 8 × 10/21 × 10 = 80/210

Step 3

Add the Numerators

Now add the numerators (28 + 80 = 108) and keep the common denominator 210 unchanged.

28 + 80/210 = 108/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 108 and 210, which is 6. Divide both the numerator and denominator by 6.

108 ÷ 6/210 ÷ 6 = 18/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 18 by denominator 35 produces a repeating decimal (approximately 0.514286, or 51.4286%).

18 ÷ 35 = 0.514286 (51.4286%)

Visual Representation

The diagram below illustrates 4/30 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`18/35`
Mixed Number Form	`18/35`
Decimal Form	`0.514286`
Percentage	`51.4286%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/30 plus 8/21 as a fraction?

4/30 + 8/21 in simplest fraction form is 18/35.

What is 4/30 plus 8/21 as a decimal?

4/30 + 8/21 converted to a decimal is 0.514286.

What is 4/30 plus 8/21 as a percentage?

4/30 + 8/21 expressed as a percentage is 51.4286%.

Does 4/30 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.514286...) because the denominator contains prime factors other than 2 and 5.