Question

ПОМОГИТЕ ПОЖАЛУЙСТА 20 баллов!! Сравните дроби или, приведя к наименьшему общему знаменателю, или же,приведя к общему числителю а)1/4 и 1/6 б)3/8 и 4/15 в) 1/12 и 1/18 г)4/9 и 7/12 д) 1/21 и 3/5 е) 1/24 и 1/36 ж) 7/18 и 5/6 з) 2/15 и 11/12 и) 3/10,3/8 и 3/4 к) 1/20 и 1/30 л) 1/9,1/4 и 1/6 м) 3/28,9/14 и 7/8 ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Ответ:

а) 1/4 и 1/6 - общ.знам.12=1/4×3 и 1/6×2= 3/12>2/12

б) 3/8 и 4/15 - общ.знам.120=3/8×15 и 4/15×8= 45/120>32/120

в) 1/12 и 1/18 - общ.знам.36=1/12×3 и 1/18×2= 3/36>2/36

г) 4/9 и 7/12 - общ.знам.36=4/9×4 и 7/12×3= 16/36<21/36

д) 1/21 и 3/5 - общ.знам.105=1/21×5 и 3/5×21= 5/105<63/105

е) 1/24 и 1/36 - общ.знам.72=1/24×3 и 1/36×2= 3/72>2/72

ж) 7/18 и 5/6 - общ.знам.18=7/18×1 и 5/6×3= 7/18<15/18

з) 2/15 и 11/12 - общ.знам.60=2/15×4 и 11/12×5= 8/60<55/60

и) 3/10, 3/8 и 3/4 - общ.знам.40=3/10×4, 3/8×5 и 3/4×10= 12/40<15/40<30/40

к) 1/20 и 1/30 - общ.знам.60=1/20×3 и 1/30×2= 3/60>2/60

л) 1/9, 1/4 и 1/6 - общ.знам.36=1/9×4, 1/4×9 и 1/6×6= 4/36<9/36>6/36

м) 3/28, 9/14 и 7/8 - общ.знам.56= 3/28×2, 9/14×4 и 7/8×7= 6/56<36/56<49/56

Answer 2

Comparing Fractions and Finding the Least Common Denominator

When comparing fractions, we can either find the least common denominator (LCD) or convert the fractions to have a common numerator. Let's compare the given fractions and find the LCD or a common numerator for each pair.

a) Comparing 1/4 and 1/6: To compare 1/4 and 1/6, we can find the least common denominator (LCD) of 4 and 6, which is 12. We can convert both fractions to have a denominator of 12: - 1/4 = 3/12 (multiplied numerator and denominator by 3) - 1/6 = 2/12 (multiplied numerator and denominator by 2)

Therefore, 1/4 is greater than 1/6.

b) Comparing 3/8 and 4/15: To compare 3/8 and 4/15, we can find the least common denominator (LCD) of 8 and 15, which is 120. We can convert both fractions to have a denominator of 120: - 3/8 = 45/120 (multiplied numerator and denominator by 15) - 4/15 = 32/120 (multiplied numerator and denominator by 8)

Therefore, 3/8 is greater than 4/15.

c) Comparing 1/12 and 1/18: To compare 1/12 and 1/18, we can find the least common denominator (LCD) of 12 and 18, which is 36. We can convert both fractions to have a denominator of 36: - 1/12 = 3/36 (multiplied numerator and denominator by 3) - 1/18 = 2/36 (multiplied numerator and denominator by 2)

Therefore, 1/12 is greater than 1/18.

d) Comparing 4/9 and 7/12: To compare 4/9 and 7/12, we can find the least common denominator (LCD) of 9 and 12, which is 36. We can convert both fractions to have a denominator of 36: - 4/9 = 16/36 (multiplied numerator and denominator by 4) - 7/12 = 21/36 (multiplied numerator and denominator by 3)

Therefore, 7/12 is greater than 4/9.

e) Comparing 1/21 and 3/5: To compare 1/21 and 3/5, we can find the least common denominator (LCD) of 21 and 5, which is 105. We can convert both fractions to have a denominator of 105: - 1/21 = 5/105 (multiplied numerator and denominator by 5) - 3/5 = 63/105 (multiplied numerator and denominator by 21)

Therefore, 3/5 is greater than 1/21.

f) Comparing 1/24 and 1/36: To compare 1/24 and 1/36, we can find the least common denominator (LCD) of 24 and 36, which is 72. We can convert both fractions to have a denominator of 72: - 1/24 = 3/72 (multiplied numerator and denominator by 3) - 1/36 = 2/72 (multiplied numerator and denominator by 2)

Therefore, 1/24 is greater than 1/36.

g) Comparing 7/18 and 5/6: To compare 7/18 and 5/6, we can find the least common denominator (LCD) of 18 and 6, which is 18. We can convert both fractions to have a denominator of 18: - 7/18 = 7/18 - 5/6 = 15/18 (multiplied numerator and denominator by 3)

Therefore, 5/6 is greater than 7/18.

h) Comparing 2/15 and 11/12: To compare 2/15 and 11/12, we can find the least common denominator (LCD) of 15 and 12, which is 60. We can convert both fractions to have a denominator of 60: - 2/15 = 8/60 (multiplied numerator and denominator by 4) - 11/12 = 55/60 (multiplied numerator and denominator by 5)

Therefore, 11/12 is greater than 2/15.

i) Comparing 3/10, 3/8, and 3/4: To compare 3/10, 3/8, and 3/4, we can find the least common denominator (LCD) of 10, 8, and 4, which is 40. We can convert all fractions to have a denominator of 40: - 3/10 = 12/40 (multiplied numerator and denominator by 4) - 3/8 = 15/40 (multiplied numerator and denominator by 5) - 3/4 = 30/40 (multiplied numerator and denominator by 10)

Therefore, 3/4 is the greatest, followed by 3/8, and then 3/10.

j) Comparing 1/20 and 1/30: To compare 1/20 and 1/30, we can find the least common denominator (LCD) of 20 and 30, which is 60. We can convert both fractions to have a denominator of 60: - 1/20 = 3/60 (multiplied numerator and denominator by 3) - 1/30 = 2/60 (multiplied numerator and denominator by 2)

Therefore, 1/20 is greater than 1/30.

k) Comparing 1/9, 1/4, and 1/6: To compare 1/9, 1/4, and 1/6, we can find the least common denominator (LCD) of 9, 4, and 6, which is 36. We can convert all fractions to have a denominator of 36: - 1/9 = 4/36 (multiplied numerator and denominator by 4) - 1/4 = 9/36 (multiplied numerator and denominator by 9) - 1/6 = 6/36 (multiplied numerator and denominator by 6)

Therefore, 1/4 is the greatest, followed by 1/6, and then 1/9.

l) Comparing 3/28, 9/14, and 7/8: To compare 3/28, 9/14, and 7/8, we can find the least common denominator (LCD) of 28, 14, and 8, which is 56. We can convert all fractions to have a denominator of 56: - 3/28 = 6/56 (multiplied numerator and denominator by 2) - 9/14 = 18/56 (multiplied numerator and denominator by 2) - 7/8 = 49/56 (multiplied numerator and denominator by 7)

Therefore, 7/8 is the greatest, followed by 9/14, and then 3/28.

I hope this helps! Let me know if you have any further questions.