What is 13/35 plus 9/21? (Answer: 4/5)

Exact Answer

==================================================
Problem: What is 13/35 plus 9/21?
Formula / Expression: 13/35 + 9/21
Final Answer: 4/5
==================================================

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 13/35 by 3, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.
Working: 13 × 3/35 × 3 = 39/105 and 9 × 5/21 × 5 = 45/105

Step 3: Add the Numerators
Now add the numerators (39 + 45 = 84) and keep the common denominator 105 unchanged.
Working: 39 + 45/105 = 84/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 105, which is 21. Divide both the numerator and denominator by 21.
Working: 84 ÷ 21/105 ÷ 21 = 4/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).
Working: 4 ÷ 5 = 0.8 (80%)

Key Values:
- Simplified Fraction: 4/5
- Mixed Number Form: 4/5
- Decimal Value: 0.8
- Percentage: 80%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-35-plus-9-21/
==================================================

13/35 + 9/21 = 4/5

Simplified Fraction

4/5

Mixed Number

Proper (4/5)

Decimal Value

0.8

Percentage

80%

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: 13/35 + 9/21

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 13/35 by 3, and multiply the numerator and denominator of 9/21 by 5 so both fractions share the common base 105.

13 × 3/35 × 3 = 39/105 and 9 × 5/21 × 5 = 45/105

Step 3

Add the Numerators

Now add the numerators (39 + 45 = 84) and keep the common denominator 105 unchanged.

39 + 45/105 = 84/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 105, which is 21. Divide both the numerator and denominator by 21.

84 ÷ 21/105 ÷ 21 = 4/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).

4 ÷ 5 = 0.8 (80%)

Visual Representation

The diagram below illustrates 13/35 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/5`
Mixed Number Form	`4/5`
Decimal Form	`0.8`
Percentage	`80%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 13/35 plus 9/21 as a fraction?

13/35 + 9/21 in simplest fraction form is 4/5.

What is 13/35 plus 9/21 as a decimal?

13/35 + 9/21 converted to a decimal is 0.8.

What is 13/35 plus 9/21 as a percentage?

13/35 + 9/21 expressed as a percentage is 80%.

Does 13/35 plus 9/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.8) because the denominator in simplest terms contains only prime factors 2 and/or 5.