Question

3/10*5/7+11/14 11/15+2/3*9/10 1 1/2 - 9/20*5/9 4/15*3/4 - 1/10 8/9:(3/4+1/3) (2/3+2/7):1 1/14 (3/5+12/25):4/5 4/15:(1 1/5-2/3) 4/5: 3/10+1/9 4/15+3/8:5/16 1 1/2-1/6:4/21 2 1/4 : 15/16-1/4

Answer 1

Ответ:

1. 1

2. 14/15

3. 1 1/4

4. 1/10

5.

6. 8/9

7. 1 7/20

8. 2

9. 2 7/9

10. 1 7/15

11. 2 7/20

Пошаговое объяснение:

Answer 2

Let's simplify the expressions step by step:

1. $\frac{3}{10} \times \frac{5}{7} + \frac{11}{14}$ To add fractions, we need a common denominator. The common denominator for 10 and 7 is 70. $\frac{3 \cdot 7}{10 \cdot 7} \times \frac{5 \cdot 10}{7 \cdot 10} + \frac{11 \cdot 5}{14 \cdot 5}$ $\frac{21}{70} \times \frac{50}{70} + \frac{55}{70}$ $\frac{1050}{4900} + \frac{2750}{4900}$ Now, add the fractions: $\frac{1050 + 2750}{4900} = \frac{3800}{4900}$ Simplify the fraction: $\frac{3800}{4900} = \frac{76}{98} = \frac{38}{49}$

2. $\frac{11}{15} + \frac{2}{3} \times \frac{9}{10}$ First, calculate the product on the right side: $\frac{2}{3} \times \frac{9}{10} = \frac{2 \cdot 9}{3 \cdot 10} = \frac{18}{30} = \frac{3}{5}$ Now, add the fractions: $\frac{11}{15} + \frac{3}{5}$ To add these fractions, we need a common denominator. The common denominator for 15 and 5 is 15. $\frac{11 \cdot 1}{15 \cdot 1} + \frac{3 \cdot 3}{5 \cdot 3}$ $\frac{11}{15} + \frac{9}{15}$ $\frac{11 + 9}{15} = \frac{20}{15}$ Simplify the fraction: $\frac{20}{15} = \frac{4}{3}$

3. $1\frac{1}{2} - \frac{9}{20} \times \frac{5}{9}$ First, calculate the product on the right side: $\frac{9}{20} \times \frac{5}{9} = \frac{9 \cdot 5}{20 \cdot 9} = \frac{45}{180} = \frac{1}{4}$ Now, subtract the fractions: $1\frac{1}{2} - \frac{1}{4}$ To subtract mixed numbers, convert them to improper fractions: $\frac{3}{2} - \frac{1}{4}$ To subtract these fractions, we need a common denominator. The common denominator for 2 and 4 is 4. $\frac{3 \cdot 2}{2 \cdot 2} - \frac{1 \cdot 1}{4 \cdot 1}$

Answer 3

Let's solve each of the expressions step by step:

1. 3/10 * 5/7 + 11/14: (3/10) * (5/7) + (11/14) (15/70) + (11/14) (15/70) + (5/70) (15 + 5)/70 20/70 can be simplified to 2/7.

2. 11/15 + 2/3 * 9/10: (11/15) + (2/3) * (9/10) (11/15) + (18/30) (11/15) + (3/5) To add these fractions, you need a common denominator. The common denominator is 15: (11/15) + (9/15) (11 + 9)/15 20/15 can be simplified to 4/3.

3. 1 1/2 - 9/20 * 5/9: To subtract mixed numbers, convert 1 1/2 to an improper fraction: (2/2 + 1/2) - (9/20) * (5/9) (3/2) - (9/20) * (5/9) (3/2) - (45/180) (3/2) - (45/180) can be simplified to (3/2) - (1/4). To subtract, you need a common denominator, which is 4: (6/4) - (1/4) (6 - 1)/4 5/4.

4. 4/15 * 3/4 - 1/10: (4/15) * (3/4) - (1/10) (12/60) - (6/60) (12 - 6)/60 6/60 can be simplified to 1/10.

5. 8/9 ÷ (3/4 + 1/3): To divide by a fraction, multiply by its reciprocal: (8/9) * (4/3) / (3/4 + 1/3) (8/9) * (4/3) / ((9/12) + (4/12)) (8/9) * (4/3) / (13/12) (32/27) / (13/12) (32/27) * (12/13) (32/39).

6. (2/3 + 2/7) ÷ 1 1/14: To divide by a mixed number, convert it to an improper fraction: ((2/3) + (2/7)) ÷ (14/14 + 1/14) ((14/21) + (6/21)) ÷ (15/14) (20/21) ÷ (15/14) (20/21) * (14/15) (280/315) can be simplified to 56/63, which further simplifies to 8/9.

7. (3/5 + 12/25) ÷ 4/5: ((3/5) + (12/25)) ÷ (4/5) ((3/5) + (3/5)) ÷ (4/5) (6/5) ÷ (4/5) (6/5) * (5/4) (30/20) can be simplified to 3/2.

8. 4/15 ÷ (1 1/5 - 2/3): To divide by a mixed number, convert it to an improper fraction: (4/15) ÷ ((5/5 + 1/5) - (2/3)) (4/15) ÷ (6/5 - 2/3) (4/15) ÷ ((18/15) - (10/15)) (4/15) ÷ (8/15) (4/15) * (15/8) (60/120) can be simplified to 1/2.

9. 4/5 ÷ (3/10 + 1/9): (4/5) ÷ ((3/10) + (1/9)) (4/5) ÷ ((27/90) + (10/90)) (4/5) ÷ (37/90) (4/5) * (90/37) (360/185) can be simplified to 72/37.

10. 4/15 + 3/8 ÷ 5/16: (4/15) + (3/8) ÷ (5/16) (4/15) + (3/8) * (16/5) (4/15) + (6/5) To add these fractions, you need a common denominator, which is 15: (4/15) + (18/15) (4 + 18)/15 22/15 can be simplified to 1 7/15.

11. 1 1/2 - (1/6 ÷ 4/21): (3/2) - ((1/6) ÷ (4/21)) (3/2) - ((1/6) * (21/4)) (3/2) - (7/4) To subtract mixed numbers, convert 3/2 to an improper fraction: (6/4) - (7/4) (6 - 7)/4 -1/4.

12. (2 1/4) ÷ (15/16 - 1/4): (9/4) ÷ ((15/16) - (4/16)) (9/4) ÷ (11/16) (9/4) * (16/11) (144/44) can be simplified to 36/11.

So, the results are as follows:

1. 3/10 * 5/7 + 11/14 = 2/7
2. 11/15 + 2/3 * 9/10 = 4/3
3. 1 1/2 - 9/20 * 5/9 = 5/4
4. 4/15 * 3/4 - 1/10 = 1/10
5. 8/9 ÷ (3/4 + 1/3) = 32/39
6. (2/3 + 2/7) ÷ 1 1/14 = 8/9
7. (3/5 + 12/25) ÷ 4/5 = 3/2
8. 4/15 ÷ (1 1/5 - 2/3) = 1/2
9. 4/5 ÷ (3/10 + 1/9) = 72/37
10. 4/15 + 3/8 ÷ 5/16 = 1 7/15
11. 1 1/2 - (1/6 ÷ 4/21) = -1/4
12. (2 1/4) ÷ (15/16 - 1/4) = 36/11