Question

а) 1 5/7 : 1 1/7 б) 3 1/5 : 2 2/15 в) 5 2/3 : 1/3 - 1 7/12 * 6

Answer 1

а) $1\frac{5}{7}:1\frac{1}{7}=\frac{12}{7}:\frac{8}{7}=\frac{12}{7}\cdot\frac{7}{8}=\frac{3}{2}=1\frac{1}{2}=1,5$

 

б) $3\frac{1}{5}:2\frac{2}{15}=\frac{16}{5}:\frac{32}{15}=\frac{16}{5}\cdot\frac{15}{32} =\frac{3}{2}=1\frac{1}{2}=1,5$                                                                                             

в)  $5\frac{2}{3}:\frac{1}{3}-1\frac{7}{12}\cdot6=7\frac{1}{2}=7,5$

 

1) $5\frac{2}{3}:\frac{1}{3}=\frac{17}{3}:\frac{1}{3}=\frac{17}{3}\cdot\frac{3}{1}=17$

 

2) $1\frac{7}{12}\cdot6=\frac{19}{12}\cdot6=\frac{19}{2}=9\frac{1}{2}=9,5$

 

3) $17-9,5=7,5$

Answer 2

а) 1 5/7 : 1 1/7 =12/7:8/7=12/7*7/8=84/56=3/2=1 1/2=1,5

 

б) 3 1/5 : 2 2/15=16/5:32/15=16/5*15/32=240/160=3/2=1 1/2=1,5

 

в)  5 2/3 : 1/3 - 1 7/12 * 6=7,5

1) 5 2/3 : 1/3=17/3:1/3=17/3*3/1=51/3=17

2) 1 7/12 * 6=19/12*6/1=114/12=19/2=9 1/2=9,5

3) 17-9,5=7,5

 

 

 

Answer 3

a) 1 5/7 : 1 1/7

To solve this division problem, we need to convert the mixed numbers into improper fractions and then divide them.

First, let's convert the mixed numbers into improper fractions: 1 5/7 = (7 * 1 + 5) / 7 = 12/7 1 1/7 = (7 * 1 + 1) / 7 = 8/7

Now, we can divide the fractions: 12/7 : 8/7 = 12/7 * 7/8 (dividing by a fraction is the same as multiplying by its reciprocal) = (12 * 7) / (7 * 8) = 84/56

To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD: GCD(84, 56) = 28 84/56 = 84/28 : 56/28 = 3/2

Therefore, 1 5/7 : 1 1/7 = 3/2.

b) 3 1/5 : 2 2/15

Again, let's convert the mixed numbers into improper fractions: 3 1/5 = (5 * 3 + 1) / 5 = 16/5 2 2/15 = (15 * 2 + 2) / 15 = 32/15

Now, we can divide the fractions: 16/5 : 32/15 = 16/5 * 15/32 = (16 * 15) / (5 * 32) = 240/160

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor: GCD(240, 160) = 80 240/160 = 240/80 : 160/80 = 3/2

Therefore, 3 1/5 : 2 2/15 = 3/2.

c) 5 2/3 : 1/3 - 1 7/12 * 6

Let's break down this expression into smaller steps to solve it:

Step 1: Multiply 1 7/12 by 6 1 7/12 * 6 = (12 * 1 + 7) / 12 * 6 = 19/12 * 6

Step 2: Convert 5 2/3 into an improper fraction 5 2/3 = (3 * 5 + 2) / 3 = 17/3

Step 3: Multiply 19/12 by 6 19/12 * 6 = 19/12 * 6/1 = (19 * 6) / (12 * 1) = 114/12

Step 4: Subtract 1/3 from 114/12 114/12 - 1/3 = (114 * 3) / (12 * 3) - (1 * 12) / (3 * 12) = 342/36 - 12/36 = (342 - 12) / 36 = 330/36

Step 5: Simplify the fraction To simplify 330/36, we can find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD: GCD(330, 36) = 6 330/36 = 330/6 : 36/6 = 55/6

Therefore, 5 2/3 : 1/3 - 1 7/12 * 6 = 55/6.