第1章有理数–练习1.7 |套装1
问题11. 2 1/3米的布料成本为75¼卢比。查找每米布料的成本。
解决方案：
2 1 / 3 = 7 / 3 meters of cloth = Rs 301 / 4
Let us consider a number = x
x (7 / 3) = 301 / 4
x = (301 / 4) / (7 / 3)
= (301 / 4) × (3 / 7)
= (301 × 3) / (4 × 7)
7 is the common factor
= (43 × 3) / (4 × 1)
= 129 / 4
= 32.25
Cost of cloth per meter is Rs 32.25
问题12. -33/16应该除以多少以得到-11/4?
解决方案：
Let us consider a number = x
(-33 / 16) / x = -11 / 4
-33 / 16 = x (-11 / 4)
x = (-33 / 16) / (-11 / 4)
= (-33 / 16) × (4 / -11)
4 and 11 are the common factors
= (-33 × 4) / (16 × -11)
= (-3 × 1) / (4 × -1)
= 3 / 4
The number should be divided by 3 / 4
问题13.将-13/5和12/7的总和除以-31/7和-1/2的乘积。
解决方案：
Sum of -13 / 5 and 12 / 7
= -13 / 5 + 12 / 7
LCM is 35
= ((-13 × 7) + (12 × 5)) / 35
= (-91 + 60) / 35
= -31 / 35
Product of -31 / 7 and -1 / 2
= -31 / 7 × -1 / 2
= (-31 × -1) / (7 × 2)
= 31 / 14
Dividing the sum and the product,
= (-31 / 35) / (31 / 14)
= (-31 / 35) × (14 / 31)
= (-31 × 14) / (35 × 31)
31 and 7 is the common factor
= -2 / 5
问题14：将65/12和12/7之和除以它们的差。
解决方案：
Sum = 65 / 12 + 12 / 7
LCM is 84
= (65 × 7 + 12 × 12) / 84
= (455 + 144) / 84
= 599 / 84
Difference i = 65 / 12 – 12 / 7
= (65 × 7 – 12 × 12) / 84
= (455 – 144) / 84
= 311 / 84
After dividing, (599 / 84) / (311 / 84)
= (599 / 84) × (84 / 311)
84 is the common factor
= 599 / 311
问题15.如果可以在54米长的布料中准备24条相同大小的裤子，那么每对裤子需要多少长度的布料?
解决方案：
Total number trousers = 24
The total length of the cloth = 54 m
Length of the cloth required for each trouser = total length of the cloth / number of trousers = 54 / 24
6 is the common factor
Hence it can be written as 9 / 4
9 / 4 meters is required for each trouser.