What is 1/48 plus 7/21? (Answer: 17/48)

Exact Answer

==================================================
Problem: What is 1/48 plus 7/21?
Formula / Expression: 1/48 + 7/21
Final Answer: 17/48
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).
Working: LCD(48, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 1/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.
Working: 1 × 7/48 × 7 = 7/336 and 7 × 16/21 × 16 = 112/336

Step 3: Add the Numerators
Now add the numerators (7 + 112 = 119) and keep the common denominator 336 unchanged.
Working: 7 + 112/336 = 119/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 119 and 336, which is 7. Divide both the numerator and denominator by 7.
Working: 119 ÷ 7/336 ÷ 7 = 17/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 48 produces a repeating decimal (approximately 0.354167, or 35.4167%).
Working: 17 ÷ 48 = 0.354167 (35.4167%)

Key Values:
- Simplified Fraction: 17/48
- Mixed Number Form: 17/48
- Decimal Value: 0.354167
- Percentage: 35.4167%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-48-plus-7-21/
==================================================

1/48 + 7/21 = 17/48

Simplified Fraction

17/48

Mixed Number

Proper (17/48)

Decimal Value

0.354167

Percentage

35.4167%

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: 1/48 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).

LCD(48, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 1/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.

1 × 7/48 × 7 = 7/336 and 7 × 16/21 × 16 = 112/336

Step 3

Add the Numerators

Now add the numerators (7 + 112 = 119) and keep the common denominator 336 unchanged.

7 + 112/336 = 119/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 119 and 336, which is 7. Divide both the numerator and denominator by 7.

119 ÷ 7/336 ÷ 7 = 17/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 48 produces a repeating decimal (approximately 0.354167, or 35.4167%).

17 ÷ 48 = 0.354167 (35.4167%)

Visual Representation

The diagram below illustrates 1/48 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/48`
Mixed Number Form	`17/48`
Decimal Form	`0.354167`
Percentage	`35.4167%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/48 plus 7/21 as a fraction?

1/48 + 7/21 in simplest fraction form is 17/48.

What is 1/48 plus 7/21 as a decimal?

1/48 + 7/21 converted to a decimal is 0.354167.

What is 1/48 plus 7/21 as a percentage?

1/48 + 7/21 expressed as a percentage is 35.4167%.

Does 1/48 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.354167...) because the denominator contains prime factors other than 2 and 5.