What is 6/21 plus 10/35? (Answer: 4/7)

Exact Answer

==================================================
Problem: What is 6/21 plus 10/35?
Formula / Expression: 6/21 + 10/35
Final Answer: 4/7
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).
Working: LCD(21, 35) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 6/21 by 5, and multiply the numerator and denominator of 10/35 by 3 so both fractions share the common base 105.
Working: 6 × 5/21 × 5 = 30/105 and 10 × 3/35 × 3 = 30/105

Step 3: Add the Numerators
Now add the numerators (30 + 30 = 60) and keep the common denominator 105 unchanged.
Working: 30 + 30/105 = 60/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 105, which is 15. Divide both the numerator and denominator by 15.
Working: 60 ÷ 15/105 ÷ 15 = 4/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).
Working: 4 ÷ 7 = 0.571429 (57.1429%)

Key Values:
- Simplified Fraction: 4/7
- Mixed Number Form: 4/7
- Decimal Value: 0.571429
- Percentage: 57.1429%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-21-plus-10-35/
==================================================

6/21 + 10/35 = 4/7

Simplified Fraction

4/7

Mixed Number

Proper (4/7)

Decimal Value

0.571429

Percentage

57.1429%

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: 6/21 + 10/35

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).

LCD(21, 35) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 6/21 by 5, and multiply the numerator and denominator of 10/35 by 3 so both fractions share the common base 105.

6 × 5/21 × 5 = 30/105 and 10 × 3/35 × 3 = 30/105

Step 3

Add the Numerators

Now add the numerators (30 + 30 = 60) and keep the common denominator 105 unchanged.

30 + 30/105 = 60/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 60 and 105, which is 15. Divide both the numerator and denominator by 15.

60 ÷ 15/105 ÷ 15 = 4/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 7 produces a repeating decimal (approximately 0.571429, or 57.1429%).

4 ÷ 7 = 0.571429 (57.1429%)

Visual Representation

The diagram below illustrates 6/21 plus 10/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/7`
Mixed Number Form	`4/7`
Decimal Form	`0.571429`
Percentage	`57.1429%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 6/21 plus 10/35 as a fraction?

6/21 + 10/35 in simplest fraction form is 4/7.

What is 6/21 plus 10/35 as a decimal?

6/21 + 10/35 converted to a decimal is 0.571429.

What is 6/21 plus 10/35 as a percentage?

6/21 + 10/35 expressed as a percentage is 57.1429%.

Does 6/21 plus 10/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.571429...) because the denominator contains prime factors other than 2 and 5.