What is 20/35 plus 15/21? (Answer: 9/7)

Exact Answer

==================================================
Problem: What is 20/35 plus 15/21?
Formula / Expression: 20/35 + 15/21
Final Answer: 1 2/7 (9/7)
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 20/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.
Working: 20 × 3/35 × 3 = 60/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (60 + 75 = 135) and keep the common denominator 105 unchanged.
Working: 60 + 75/105 = 135/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 105, which is 15. Divide both the numerator and denominator by 15.
Working: 135 ÷ 15/105 ÷ 15 = 9/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (9) is greater than the denominator (7), divide 9 by 7: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/7.
Working: 9/7 = 1 2/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 7 produces a repeating decimal (approximately 1.285714, or 128.5714%).
Working: 9 ÷ 7 = 1.285714 (128.5714%)

Key Values:
- Simplified Fraction: 9/7
- Mixed Number Form: 1 2/7
- Decimal Value: 1.285714
- Percentage: 128.5714%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-20-35-plus-15-21/
==================================================

20/35 + 15/21 = 9/7

Simplified Fraction

9/7

Mixed Number

1 2/7

Decimal Value

1.285714

Percentage

128.5714%

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: 20/35 + 15/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 20/35 by 3, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.

20 × 3/35 × 3 = 60/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (60 + 75 = 135) and keep the common denominator 105 unchanged.

60 + 75/105 = 135/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 105, which is 15. Divide both the numerator and denominator by 15.

135 ÷ 15/105 ÷ 15 = 9/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (9) is greater than the denominator (7), divide 9 by 7: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/7.

9/7 = 12/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 7 produces a repeating decimal (approximately 1.285714, or 128.5714%).

9 ÷ 7 = 1.285714 (128.5714%)

Visual Representation

The diagram below illustrates 20/35 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/7`
Mixed Number Form	`1 2/7`
Decimal Form	`1.285714`
Percentage	`128.5714%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 20/35 plus 15/21 as a fraction?

20/35 + 15/21 in simplest fraction form is 9/7 (or 1 2/7 as a mixed number).

What is 20/35 plus 15/21 as a decimal?

20/35 + 15/21 converted to a decimal is 1.285714.

What is 20/35 plus 15/21 as a percentage?

20/35 + 15/21 expressed as a percentage is 128.5714%.

How do you write 20/35 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 9/7 can be written as the mixed number 1 2/7.

Does 20/35 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.285714...) because the denominator contains prime factors other than 2 and 5.