find the LCD 3/4-2/5 9/14-1/8 1/12-3/4 53/7-1/2 3/14-1/15 subtract the numerator then write the different over the common denominator express in simpliest form
Answer (1)
Answer:## Finding the LCD and Subtracting FractionsTo find the LCD (Least Common Denominator) and subtract fractions, we'll follow these steps for each pair of fractions:### 1. 3/4 - 2/5- *Find the LCD*: The denominators are 4 and 5. The LCD is 20.- *Convert fractions to have the LCD*: - 3/4 = (3 × 5) / (4 × 5) = 15/20 - 2/5 = (2 × 4) / (5 × 4) = 8/20- *Subtract the numerators*: 15 - 8 = 7- *Write the difference over the common denominator*: 7/20- *Simplify*: 7/20 is already in simplest form.### 2. 9/14 - 1/8- *Find the LCD*: The denominators are 14 and 8. The LCD is 56.- *Convert fractions to have the LCD*: - 9/14 = (9 × 4) / (14 × 4) = 36/56 - 1/8 = (1 × 7) / (8 × 7) = 7/56- *Subtract the numerators*: 36 - 7 = 29- *Write the difference over the common denominator*: 29/56- *Simplify*: 29/56 is already in simplest form.### 3. 1/12 - 3/4- *Find the LCD*: The denominators are 12 and 4. The LCD is 12.- *Convert fractions to have the LCD*: - 1/12 = 1/12 - 3/4 = (3 × 3) / (4 × 3) = 9/12- *Subtract the numerators*: 1 - 9 = -8- *Write the difference over the common denominator*: -8/12- *Simplify*: -8/12 = -2/3### 4. 53/7 - 1/2- *Find the LCD*: The denominators are 7 and 2. The LCD is 14.- *Convert fractions to have the LCD*: - 53/7 = (53 × 2) / (7 × 2) = 106/14 - 1/2 = (1 × 7) / (2 × 7) = 7/14- *Subtract the numerators*: 106 - 7 = 99- *Write the difference over the common denominator*: 99/14- *Simplify*: 99/14 is already in simplest form.### 5. 3/14 - 1/15- *Find the LCD*: The denominators are 14 and 15. The LCD is 210.- *Convert fractions to have the LCD*: - 3/14 = (3 × 15) / (14 × 15) = 45/210 - 1/15 = (1 × 14) / (15 × 14) = 14/210- *Subtract the numerators*: 45 - 14 = 31- *Write the difference over the common denominator*: 31/210- *Simplify*: 31/210 is already in simplest form.The results are:- 3/4 - 2/5 = 7/20- 9/14 - 1/8 = 29/56- 1/12 - 3/4 = -2/3- 53/7 - 1/2 = 99/14- 3/14 - 1/15 = 31/210
