Реши задание на изображении
Calculating fractions and borrowing
First, I’m figuring out 3 2/14 - 2 3/14. I know that 3 1/7 is equal to 3 2/14, so when I subtract, I get 13/14. For the next part, 2 3/42 - 1 1/7 (which is 6/42) leads me to borrow and convert properly, ending up with 39/42, which is also 13/14. Finally, adding 13/14 and 13/14 gives me 26/14, simplifying to 1 6/7. I need to explain the principles involved, especially about common denominators and borrowing during subtraction.Clarifying fractional subtraction
I’m working through subtracting fractions with mixed numbers, feeling a bit mixed up. So, I start with 2 3/42 minus 1 6/42. Since 3/42 is less than 6/42, I need to borrow. After working it out, I get 1 39/42, which simplifies to 13/14. Then I’m moving on to checking with different denominators, specifically looking at 5 2/8 and 3 7/8. After recalculating, I find out better results, which is encouraging!Recalculating fractions
Wait, I realized I computed something incorrectly earlier! I need to recalculate carefully. So, for 1 1/7, it should break down into 1 plus 1/7, which equals 42/42 plus 6/42, giving 48/42, not 49. Ah, I see now: 1 times 42 plus 6 equals 48! Then I subtract: 87 minus 48 equals 39/42, which simplifies to 13/14. This feels much better now; I’ve got it right!
Краткий ответ:
а) \(3\dfrac{5}{7}\);
б) \(1\dfrac{3}{8}\).а) \(1\dfrac{6}{7}\).
Решение:
1а)
Приведём дроби к знаменателю \(21\):
\[ 1\dfrac47+2\dfrac3{21} =1\dfrac{12}{21}+2\dfrac3{21} =3\dfrac{15}{21} =3\dfrac57. \]
1б)
Приведём дроби к знаменателю \(8\). Так как \(\dfrac28<\dfrac78\), занимаем \(1\) у целой части:
\[ 5\dfrac14-3\dfrac78 =5\dfrac28-3\dfrac78 =4\dfrac{10}{8}-3\dfrac78 =1\dfrac38. \]
2а)
В первой скобке знаменатель \(14\), во второй — \(42\):
\[ 3\dfrac17-2\dfrac3{14} =3\dfrac2{14}-2\dfrac3{14} =\dfrac{13}{14}. \]
\[ 2\dfrac3{42}-1\dfrac17 =2\dfrac3{42}-1\dfrac6{42} =1\dfrac{45}{42}-1\dfrac6{42} =\dfrac{39}{42} =\dfrac{13}{14}. \]
Тогда
\[ \left(3\dfrac17-2\dfrac3{14}\right) +\left(2\dfrac3{42}-1\dfrac17\right) =\dfrac{13}{14}+\dfrac{13}{14} =\dfrac{26}{14} =\dfrac{13}{7} =1\dfrac67. \]
Правило: сначала приводим дробные части к общему знаменателю, затем выполняем действие с числителями; при вычитании, если дробная часть уменьшаемого меньше, занимаем \(1\) у целой части.
Нижняя часть изображения обрезана, поэтому остальные пункты прочитать нельзя.
