第1章有理数–练习1.3 |套装1
问题11.应该从3/7中减去哪个数字以获得5/4?
解决方案：
Let the number be x
3/7 – x = 5/4
-x = 5/4 – 3/7 (Transposing 3/7)
LCM of 4 and 7 is 28
-x = (5 × 7 – 3 × 4)/28
-x = (35 – 12)/28
-x = (23)/28
x = -23/28
Therefore, -23/28 should be subtracted.
问题12.(2/3 + 3/5)应该加上什么才能得到-2/15?
解决方案：
Let the number be x
(2/3 + 3/5) + x = -2/15
LCM of 3 and 5 is 15
(2 × 5 + 3 × 3)/15 + x = -2/15
(10 + 9)/15 + x = -2/15
19/15 + x = -2/15
x = -2/15 – 19/15 (Transposing 19/15)
x = (-2 – 19)/15
x = (-21)/15
x = (-7)/5
Therefore, -7/5 should be added.
问题13.(1/2 + 1/3 + 1/5)应该加上什么才能得到3?
解决方案：
Let the number be x
(1/2 + 1/3 + 1/5) + x = 3
LCM of 2, 3 and 5 is 30
(1 × 15 + 1 × 10 + 1 × 6)/30 + x = 3
(15 + 10 + 6)/30 + x = 3
31/30 + x = 3
x = 3/1 – 31/30 (Transposing 31/30)
LCM of 1 and 30 is 30
x = (3 × 30 – 31)/30
x = (90 – 31)/30
x = (59)/30
Therefore, 59/30 should be added.
问题14.应该从(3/4 – 2/3)中减去哪个数字以获得-1/6?
解决方案：
Let the number be x
(3/4 – 2/3) – x = -1/6
LCM of 4 and 3 is 12
(3 × 3 – 2 × 4)/12 – x = -1/6
(9 – 8)/12 – x = -1/6
1/12 – x = -1/6
-x = -1/6 – 1/12
LCM of 6 and 12 is 12
-x = (-1 × 2 – 1)/12
-x = (-2 – 1)/12
-x = -3/12
x = 1/4
Therefore, 1/4 should be subtracted.
问题15：填写空白：
(i)-4/13 – -3/26 =……。
解决方案：
This can be written as
-4/13 + 3/26
LCM of 13 and 26 is 26
= (-4 × 2 + 3 × 1)/26
= (-8 + 3)/26
= -5/26
Therefore, -5/26 is the required number
(ii)-9/14 +….. = -1
解决方案：
Let the number to be added be x
-9/14 + x = -1
x = -1/1 + 9/14 (Transposing -9/14)
LCM of 1 and 14 is 14
x = (-1 × 14 + 9 × 1)/14
= (-14 + 9)/14
= -5/14
Therefore, the number to be added is -5/14
(iii)-7/9 +…。 = 3
解决方案：
Let the number to be added be x
-7/9 + x = 3
x = 3 – (-7/9)
x = 3/1 + 7/9
LCM of 1 and 9 is 9
x = (3 × 9 + 7 × 1)/9
x = (27 + 7)/9
x = 34/9
Therefore, the number to be added is 34/9
(iv)….. + 15/23 = 4
解决方案：
Let the number be x
x + 15/23 = 4
x = 4/1 – 15/23
LCM of 1 and 23 is 23
x = (4 × 23 – 15 × 1)/23
x = (92 – 15)/23
x = 77/23
Therefore, the number to be added is 77/23