Question

Сократить дробь и затем проверьте их к наименьшему общему знаменателю:10/15и6/8. 14/42и150/160. 45/400;45/225и72/144

Answer 1

10/15и6/8 .
2/3 и 3/4
8/12 и 9/12

14/42и150/160.
1/3 и 15/16
16/48 и 45/48


45/400= 9/80;

45/225 и 72/144
1/5 и  1/2
2/10 и 5/10

Answer 2

Simplifying and Finding the Least Common Denominator

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. Then, we can find the least common denominator (LCD) by finding the least common multiple (LCM) of the denominators of the fractions involved.

Let's simplify and find the LCD for the given fractions:

1. 10/15 and 6/8: - To simplify 10/15, we can divide both the numerator and denominator by their GCD, which is 5. This gives us 2/3. - To simplify 6/8, we can divide both the numerator and denominator by their GCD, which is 2. This gives us 3/4. - The LCD of 3 and 4 is 12, so we need to convert both fractions to have a denominator of 12. - Multiplying 2/3 by 4/4 gives us 8/12. - Multiplying 3/4 by 3/3 gives us 9/12. - Therefore, the simplified fractions with the LCD of 12 are 8/12 and 9/12.

2. 14/42 and 150/160: - To simplify 14/42, we can divide both the numerator and denominator by their GCD, which is 14. This gives us 1/3. - To simplify 150/160, we can divide both the numerator and denominator by their GCD, which is 10. This gives us 15/16. - The LCD of 3 and 16 is 48, so we need to convert both fractions to have a denominator of 48. - Multiplying 1/3 by 16/16 gives us 16/48. - Multiplying 15/16 by 3/3 gives us 45/48. - Therefore, the simplified fractions with the LCD of 48 are 16/48 and 45/48.

3. 45/400: - To simplify 45/400, we can divide both the numerator and denominator by their GCD, which is 5. This gives us 9/80.

4. 45/225 and 72/144: - To simplify 45/225, we can divide both the numerator and denominator by their GCD, which is 45. This gives us 1/5. - To simplify 72/144, we can divide both the numerator and denominator by their GCD, which is 72. This gives us 1/2. - The LCD of 5 and 2 is 10, so we need to convert both fractions to have a denominator of 10. - Multiplying 1/5 by 2/2 gives us 2/10. - Multiplying 1/2 by 5/5 gives us 5/10. - Therefore, the simplified fractions with the LCD of 10 are 2/10 and 5/10.

Summary:

1. 10/15 and 6/8 simplify to 8/12 and 9/12, respectively, with the LCD of 12. 2. 14/42 and 150/160 simplify to 16/48 and 45/48, respectively, with the LCD of 48. 3. 45/400 simplifies to 9/80. 4. 45/225 and 72/144 simplify to 2/10 and 5/10, respectively, with the LCD of 10.

Please let me know if you need any further assistance!