Question

1/4+2/9=? 31/115-11/185=?3/7-1/10=? 3/8+3/14-1/28=?​

Answer 1

Ответ:

1) 1/4+2/9=?

$\frac{1}{4}+\frac{2}{9}=\frac{9*1+2*4}{36} =\frac{9+8}{36} =\frac{17}{36}$

2) 31/115-11/185=?

$\frac{31}{115} -\frac{11}{185} =\frac{31*37+11*23}{4255} =\frac{1147-253}{4255}=\frac{894}{4255}$

3) 3/7-1/10=?

$\frac{3}{7}-\frac{1}{10}=\frac{3*10-1*7}{70} =\frac{30-7}{70} =\frac{23}{70}$

4)3/8+3/14-1/28=?​

$\frac{3}{8}+\frac{3}{14}-\frac{1}{28}=\frac{3*7+3*4-1*2}{56} =\frac{21+12-2}{56} =\frac{31}{56}$

Answer 2

Ответ:

1)

$\frac{17}{36}$

2)

$\frac{23}{70}$

3)

$\frac{894}{4255}$

4)

$\frac{31}{56}$

Пошаговое объяснение:

1)

$\frac{1}{4} + \frac{2}{9 } = \frac{9}{36} + \frac{8}{36} = \frac{17}{36}$

2)

$\frac{3}{7} - \frac{1}{10} = \frac{30}{70} - \frac{7}{70} = \frac{23}{70}$

3)

$\frac{31}{115} - \frac{11}{185} = \frac{31 \times 37}{115 \times 37} - \frac{11 \times 23}{185 \times 23} = \frac{1147}{4255} - \frac{253}{4255} = \frac{894}{4255}$

4)

$\frac{3}{8} + \frac{3}{14} - \frac{1}{28} = \frac{21}{56} + \frac{12}{56} - \frac{2}{56} = \frac{33}{56} - \frac{2}{56} = \frac{31}{56}$

Answer 3

To solve these equations, we need to perform arithmetic operations on fractions. Let's solve each equation step by step:

1. 1/4 + 2/9: To add fractions, we need to have a common denominator. The common denominator of 4 and 9 is 36. So, we can rewrite the fractions as: 1/4 = 9/36 (by multiplying the numerator and denominator by 9) 2/9 = 8/36 (by multiplying the numerator and denominator by 4) Now, we can add the fractions: 9/36 + 8/36 = 17/36

Therefore, 1/4 + 2/9 = 17/36.

2. 31/115 - 11/185: To subtract fractions, we also need a common denominator. The common denominator of 115 and 185 is 2075. So, we can rewrite the fractions as: 31/115 = 341/2075 (by multiplying the numerator and denominator by 19) 11/185 = 77/2075 (by multiplying the numerator and denominator by 5) Now, we can subtract the fractions: 341/2075 - 77/2075 = 264/2075

Therefore, 31/115 - 11/185 = 264/2075.

3. 3/7 - 1/10: To subtract fractions, we need a common denominator. The common denominator of 7 and 10 is 70. So, we can rewrite the fractions as: 3/7 = 30/70 (by multiplying the numerator and denominator by 10) 1/10 = 7/70 (by multiplying the numerator and denominator by 7) Now, we can subtract the fractions: 30/70 - 7/70 = 23/70

Therefore, 3/7 - 1/10 = 23/70.

4. 3/8 + 3/14 - 1/28: To add or subtract fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 8, 14, and 28 is 56. So, we can rewrite the fractions as: 3/8 = 21/56 (by multiplying the numerator and denominator by 7) 3/14 = 9/56 (by multiplying the numerator and denominator by 4) 1/28 = 2/56 (by multiplying the numerator and denominator by 2) Now, we can add/subtract the fractions: 21/56 + 9/56 - 2/56 = 28/56

Simplifying the fraction 28/56 by dividing both the numerator and denominator by their greatest common divisor (which is 28), we get: 28/56 = 1/2

Therefore, 3/8 + 3/14 - 1/28 = 1/2.

To summarize: 1/4 + 2/9 = 17/36 31/115 - 11/185 = 264/2075 3/7 - 1/10 = 23/70 3/8 + 3/14 - 1/28 = 1/2