- 33/1,314 + 35 = ? Adding Ordinary (Simple, Common) Math Fractions Calculator, Addition Explained Step by Step

The executed operation (with ordinary fractions):
- 33/1,314 + 35

Result written: As a positive improper fraction (numerator >= denominator). As a mixed number. As a decimal number. As a percentage.

Reduce (simplify) fractions to their lowest terms equivalents:

To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.

Fraction: - 33/1,314 = - (3 × 11)/(2 × 32 × 73) = - ((3 × 11) ÷ 3)/((2 × 32 × 73) ÷ 3) = - 11/438;

Reduce (simplify) fractions to their simplest form, online calculator


Rewrite the equivalent simplified operation:

- 33/1,314 + 35 =


- 11/438 + 35 =


35 - 11/438

Rewrite the expression:

As a positive improper fraction (numerator >= denominator):

35 - 11/438 =


(35 × 438)/438 - 11/438 =


(35 × 438 - 11)/438 =


15,319/438

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.


Proper fraction = numerator smaller than denominator.


15,319 ÷ 438 = 34 and remainder = 427 =>


15,319 = 34 × 438 + 427 =>


15,319/438 =


(34 × 438 + 427)/438 =


(34 × 438)/438 + 427/438 =


34 + 427/438 =


34 427/438

As a decimal number:

34 + 427/438 =


34 + 427 ÷ 438 ≈


34.974885844749 ≈


34.97

As a percentage:

34.974885844749 =


34.974885844749 × 100/100 =


(34.974885844749 × 100)/100 =


3,497.488584474886/100


3,497.488584474886% ≈


3,497.49%

>> Convert fractions to percentages, online calculator


The final answer:
:: written in four ways ::

As a positive improper fraction (numerator >= denominator):
- 33/1,314 + 35 = 15,319/438

As a mixed number (also called a mixed fraction):
- 33/1,314 + 35 = 34 427/438

As a decimal number:
- 33/1,314 + 35 ≈ 34.97

As a percentage:
- 33/1,314 + 35 ≈ 3,497.49%

More operations of this kind:

How to subtract the ordinary fractions:
- 35/1,322 - 46/6


Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case);

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation;

Add ordinary fractions, online calculator

The latest added fractions

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5/1,020 - 33/10 = ? Dec 01 05:19 UTC (GMT)
5/10 + 34/40 = ? Dec 01 05:19 UTC (GMT)
9/62,183 + 2 = ? Dec 01 05:19 UTC (GMT)
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see more... added fractions

How to: Adding ordinary (simple, common) math fractions. Steps.

There are two cases regarding the denominators when we add ordinary fractions:

  • A. the fractions have like denominators;
  • B. the fractions have unlike denominators.

A. How to add ordinary fractions that have like denominators?

  • Simply add the numerators of the fractions.
  • The denominator of the resulting fraction will be the common denominator of the fractions.
  • Reduce the resulting fraction.

An example of adding ordinary fractions that have like denominators, with explanations

  • 3/18 + 4/18 + 5/18 = (3 + 4 + 5)/18 = 12/18;

  • We simply added the numerators of the fractions: 3 + 4 + 5 = 12;
  • The denominator of the resulting fraction is: 18;
  • The resulting fraction is being reduced: 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3.

  • How to reduce (simplify) the common fraction 12/18?

B. To add fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?

  • 1. Reduce the fractions to the lowest terms (simplifying).

  • 2. Calculate the least common multiple, LCM, of all the fractions' new denominators:

    • LCM is going to be the common denominator of the added fractions.
    • Factor all the new denominators of the reduced fractions (run the prime factorization).
    • The least common multiple, LCM, is the product of all the unique prime factors of the denominators, taken by the largest exponents.
    • Calculate LCM, the least common multiple of numbers.

  • 3. Calculate each fraction's expanding number:

    • The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator.
    • Divide the least common multiple, LCM, calculated above, by each fraction's denominator, in order to calculate each fraction's expanding number.
  • 4. Expand each fraction:

    • Multiply each fraction's both numerator and denominator by expanding number.
    • At this point, fractions are built up to the same denominator.
  • 5. Add the fractions:

    • In order to add all the fractions simply add all the fractions' numerators.
    • The end fraction will have as a denominator the least common multiple, LCM, calculated above.
  • 6. Reduce the end fraction to the lowest terms, if needed.

... Read the rest of this article, here: How to add ordinary (common) fractions?

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers