Our free Fraction Calculator with steps helps you solve simple fractions, mixed numbers, and improper fractions instantly. Whether you need to add fractions with different denominators, subtract mixed fractions, multiply rational numbers, or divide fractions using reciprocals, this tool provides fast and accurate results online.
In mathematics, a fraction is a number that represents a part of a whole. It is made up of two components: a numerator and a denominator. The numerator indicates how many equal parts are being considered, while the denominator shows the total number of equal parts that make up the whole.
For example, in the fraction 38 the numerator is 3 and the denominator is 8. To visualize this, imagine a pie divided into 8 equal slices. One slice represents a single part (the numerator), and the entire pie, consisting of 8 slices, represents the whole (the denominator). If someone eats 3 slices, the fraction of the pie that remains is 58 as illustrated in the image on the right.
It is important to note that a fraction’s denominator cannot be 0, because division by zero is undefined. Fractions can be used in various mathematical operations, some of which are discussed below.
Fractions can be added in two main cases:
When the denominators are the same, you simply add the numerators and keep the denominator the same.
2/7 + 3/7 = 5/7
Explanation: Both fractions are parts of the same-sized whole (7 equal parts). Adding 2 parts and 3 parts gives 5 parts out of 7.
If the denominators are different, you first need to find a common denominator (usually the least common multiple of the denominators), then adjust the numerators accordingly before adding.
Example: 1/4 + 2/3
Step 1: Find a common denominator. Denominators are 4 and 3, so the least common denominator (LCD) is 12.
Step 2: Adjust fractions:
1/4 = 3/12, 2/3 = 8/12
Step 3: Add the numerators:
3/12 + 8/12 = 11/12
Answer: 1/4 + 2/3 = 11/12
Subtracting fractions works similarly to addition and also has two main cases:
When the denominators are the same, you simply subtract the numerators and keep the denominator the same.
5/8 - 3/8 = 2/8
Explanation: Both fractions are parts of the same-sized whole (8 equal parts). Subtracting 3 parts from 5 parts leaves 2 parts out of 8.
If the denominators are different, you first need to find a common denominator (usually the least common multiple of the denominators), then adjust the numerators accordingly before subtracting.
Example: 3/4 - 1/3
Step 1: Find a common denominator. Denominators are 4 and 3, so the least common denominator (LCD) is 12.
Step 2: Adjust fractions:
3/4 = 9/12, 1/3 = 4/12
Step 3: Subtract the numerators:
9/12 - 4/12 = 5/12
Answer: 3/4 - 1/3 = 5/12
Multiplying fractions is straightforward. You simply multiply the numerators together and multiply the denominators together.
Example: 2/3 × 3/4
Step 1: Multiply the numerators:
2 × 3 = 6
Step 2: Multiply the denominators:
3 × 4 = 12
Step 3: Write the new fraction:
2/3 × 3/4 = 6/12
Step 4: Simplify if possible:
6/12 = 1/2
For mixed fractions, first convert them into improper fractions, then multiply as usual.
Example: 1 1/2 × 2 1/3
Step 1: Convert to improper fractions:
1 1/2 = 3/2, 2 1/3 = 7/3
Step 2: Multiply numerators and denominators:
3 × 7 = 21, 2 × 3 = 6
Step 3: Write the new fraction:
3/2 × 7/3 = 21/6
Step 4: Simplify or convert to a mixed fraction:
21/6 = 3 3/6 = 3 1/2
Tip: Always simplify the result to its lowest terms for clarity.
Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction.
Example: 3/4 ÷ 2/5
Step 1: Find the reciprocal of the second fraction:
Reciprocal of 2/5 = 5/2
Step 2: Multiply the first fraction by the reciprocal:
3/4 × 5/2
Step 3: Multiply numerators and denominators:
3 × 5 = 15, 4 × 2 = 8
Step 4: Write the new fraction:
3/4 ÷ 2/5 = 15/8
Step 5: Convert to mixed fraction if needed:
15/8 = 1 7/8
For mixed fractions, first convert them into improper fractions, then divide as usual by multiplying with the reciprocal.
Example: 2 1/3 ÷ 1 2/5
Step 1: Convert to improper fractions:
2 1/3 = 7/3, 1 2/5 = 7/5
Step 2: Find the reciprocal of the second fraction:
Reciprocal of 7/5 = 5/7
Step 3: Multiply the first fraction by the reciprocal:
7/3 × 5/7
Step 4: Multiply numerators and denominators:
7 × 5 = 35, 3 × 7 = 21
Step 5: Write the new fraction:
7/3 ÷ 7/5 = 35/21
Step 6: Simplify or convert to mixed fraction:
35/21 = 1 14/21 = 1 2/3
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InCalculator.com was launched in 2020 with the goal of providing fast and accurate online calculators. However, the journey of calculators began in the 17th century, when inventors designed mechanical machines to simplify complex mathematical tasks.
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