Question 1

How do you add fractions with different denominators?

Accepted Answer

To add fractions with different denominators, you must first find a common denominator, typically the Least Common Denominator (LCD). Multiply the numerator and denominator of each fraction by the factor needed to scale its denominator to the LCD. Once the denominators are equal, add the numerators together and write the sum over the common denominator. Finally, simplify the resulting fraction using its Greatest Common Divisor (GCD).

Question 2

How do you simplify a fraction?

Accepted Answer

A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the Greatest Common Divisor (GCD) of the numerator and denominator. Then, divide both the numerator and the denominator by this GCD. For example, for 12/8, the GCD is 4. Dividing 12 by 4 gives 3, and 8 by 4 gives 2, resulting in the simplified fraction 3/2.

Question 3

What is a mixed number and how do I calculate with it?

Accepted Answer

A mixed number consists of a whole number combined with a proper fraction (e.g., 2 3/4). To perform mathematical operations with mixed numbers, it is easiest to convert them into improper fractions first. Multiply the whole number by the denominator, add the numerator, and place that sum over the original denominator. After performing addition, subtraction, multiplication, or division on the improper fractions, simplify the result and convert it back into a mixed number.

Question 4

How do you multiply fractions?

Accepted Answer

Multiplying fractions is straightforward: multiply the numerators straight across to find the new numerator, and multiply the denominators straight across to find the new denominator. For example, (2/3) × (4/5) equals (2 × 4) / (3 × 5), which is 8/15. You do not need common denominators to multiply fractions. Remember to simplify the final answer.

Question 5

How do you divide fractions?

Accepted Answer

To divide fractions, multiply the first fraction (dividend) by the reciprocal of the second fraction (divisor). To find the reciprocal of a fraction, swap its numerator and denominator (e.g., the reciprocal of 2/3 is 3/2). The division (a/b) ÷ (c/d) becomes (a/b) × (d/c) = (ad) / (bc). Simplify the final result if needed.

Question 6

What is the LCD (Lowest Common Denominator)?

Accepted Answer

The Lowest Common Denominator (LCD) is the lowest common multiple of the denominators of a set of fractions. It represents the smallest number that can be divided evenly by all the individual denominators. Finding the LCD is required before adding, subtracting, or comparing fractions with unlike denominators.

Question 7

How do you convert a fraction to a decimal?

Accepted Answer

To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert 3/4, divide 3 by 4 to get 0.75. If the division does not terminate, it will result in a repeating decimal, which can be rounded to a desired number of decimal places.

Question 8

How do you compare two fractions?

Accepted Answer

To compare two fractions, convert them to have a common denominator (LCD) and compare their scaled numerators. Whichever fraction has the larger numerator is the larger fraction. Alternatively, you can convert both fractions to decimals by dividing their numerators by their denominators and comparing the decimal values.

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