What is 5/30 plus 4/21? (Answer: 5/14)

Exact Answer

==================================================
Problem: What is 5/30 plus 4/21?
Formula / Expression: 5/30 + 4/21
Final Answer: 5/14
==================================================

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 5/30 by 7, and multiply the numerator and denominator of 4/21 by 10 so both fractions share the common base 210.
Working: 5 × 7/30 × 7 = 35/210 and 4 × 10/21 × 10 = 40/210

Step 3: Add the Numerators
Now add the numerators (35 + 40 = 75) and keep the common denominator 210 unchanged.
Working: 35 + 40/210 = 75/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 210, which is 15. Divide both the numerator and denominator by 15.
Working: 75 ÷ 15/210 ÷ 15 = 5/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).
Working: 5 ÷ 14 = 0.357143 (35.7143%)

Key Values:
- Simplified Fraction: 5/14
- Mixed Number Form: 5/14
- Decimal Value: 0.357143
- Percentage: 35.7143%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-30-plus-4-21/
==================================================

5/30 + 4/21 = 5/14

Simplified Fraction

5/14

Mixed Number

Proper (5/14)

Decimal Value

0.357143

Percentage

35.7143%

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: 5/30 + 4/21

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 5/30 by 7, and multiply the numerator and denominator of 4/21 by 10 so both fractions share the common base 210.

5 × 7/30 × 7 = 35/210 and 4 × 10/21 × 10 = 40/210

Step 3

Add the Numerators

Now add the numerators (35 + 40 = 75) and keep the common denominator 210 unchanged.

35 + 40/210 = 75/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 210, which is 15. Divide both the numerator and denominator by 15.

75 ÷ 15/210 ÷ 15 = 5/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 14 produces a repeating decimal (approximately 0.357143, or 35.7143%).

5 ÷ 14 = 0.357143 (35.7143%)

Visual Representation

The diagram below illustrates 5/30 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/14`
Mixed Number Form	`5/14`
Decimal Form	`0.357143`
Percentage	`35.7143%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/30 plus 4/21 as a fraction?

5/30 + 4/21 in simplest fraction form is 5/14.

What is 5/30 plus 4/21 as a decimal?

5/30 + 4/21 converted to a decimal is 0.357143.

What is 5/30 plus 4/21 as a percentage?

5/30 + 4/21 expressed as a percentage is 35.7143%.

Does 5/30 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.357143...) because the denominator contains prime factors other than 2 and 5.