Simplifying Mixed Fractions: Mixed fractions are fractions with whole numbers, fractions, and decimals. To simplify a mixed fraction, it is necessary to fir...
Simplifying Mixed Fractions:
Mixed fractions are fractions with whole numbers, fractions, and decimals. To simplify a mixed fraction, it is necessary to first express it in a improper fraction, then combine like fractions by adding the numerators and keeping the denominator the same.
For example, consider the mixed fraction 3 1/2. To convert it to an improper fraction, we can rewrite the whole number as 3 and the fraction as 2/2. Adding the numerators, we get 3 + 2 = 5. Therefore, 3 1/2 can be expressed as 5/2.
Simplifying Decimals:
Similarly, to simplify a decimal, it is crucial to first express it in a fraction with the denominator being 10. This can be done by finding the decimal equivalent of the fraction and then reducing it to its simplest form.
For instance, consider the decimal 0.75. Converting it to a fraction with the denominator 10 gives 0.75 = 75/100. Dividing both numerator and denominator by 25, we get 3/4, which simplifies to 0.75.
Simplifying Mixed Fractions and Decimals in Sums:
When adding fractions with different denominators, we need to find a common denominator for addition. The lowest common multiple of the denominators of the fractions is their greatest common divisor (gcd).
To find the greatest common divisor, we need to determine the largest number that evenly divides both denominators. In our example, the greatest common divisor of 2 and 5 is 1. Therefore, the common denominator for 3/2 and 1/5 is 10.
To add fractions with different denominators, we first convert them to equivalent fractions with the common denominator. Then, we add the numerators and keep the denominator the same. For example, 3/2 + 1/5 can be simplified by finding the least common multiple of 2 and 5, which is 10, and then converting the fractions to 30/20 and 4/20, respectively. Adding these fractions gives 34/20, which simplifies to 17/10.
Similarly, 0.75 + 0.25 can be simplified by finding the least common multiple of 10 and 4, which is 40, and then converting the fractions to 30/40 and 12/40, respectively. Adding these fractions gives 42/40, which simplifies to 1.4