Question

1. Знайди добуток: 1) 3/7·1 2/5 2) 2 11/12*1 1/5 2. Знайди частку: 1)3 3/8:3/4; 2)3 3/5:2 1/4 треба розписати

Answer 1

Ответ:

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Answer 2

1. Знайди добуток: a) 1) 3/7 * 1 + 2/5 b) 2) 2 11/12 * 1 1/5

a) Знайди добуток 3/7 * 1 + 2/5:

To find the product of fractions, we multiply the numerators together and the denominators together. Then, we simplify the resulting fraction if possible.

The calculation for 3/7 * 1 + 2/5 is as follows: 3/7 * 1 + 2/5 = (3 * 1) / (7 * 1) + 2/5 = 3/7 + 2/5

To add fractions, we need a common denominator. In this case, the common denominator is 35 (the least common multiple of 7 and 5).

Converting the fractions to have a common denominator: 3/7 = (3 * 5) / (7 * 5) = 15/35 2/5 = (2 * 7) / (5 * 7) = 14/35

Now, we can add the fractions: 15/35 + 14/35 = (15 + 14) / 35 = 29/35

Therefore, the product of 3/7 * 1 + 2/5 is 29/35.

b) Знайди добуток 2 11/12 * 1 1/5:

To multiply mixed numbers, we first convert them to improper fractions. Then, we multiply the numerators together and the denominators together. Finally, we simplify the resulting fraction if possible.

The calculation for 2 11/12 * 1 1/5 is as follows: 2 11/12 * 1 1/5 = (2 * 12 + 11) / 12 * (1 * 5 + 1) / 5

Converting the mixed numbers to improper fractions: 2 11/12 = (2 * 12 + 11) / 12 = 35/12 1 1/5 = (1 * 5 + 1) / 5 = 6/5

Now, we can multiply the fractions: 35/12 * 6/5 = (35 * 6) / (12 * 5) = 210/60

Simplifying the resulting fraction: 210/60 = (210 ÷ 30) / (60 ÷ 30) = 7/2

Therefore, the product of 2 11/12 * 1 1/5 is 7/2.

2. Знайди частку: a) 1) 3 3/8 : 3/4 b) 2) 3 3/5 : 2 1/4

a) Знайди частку 3 3/8 : 3/4:

To divide mixed numbers, we first convert them to improper fractions. Then, we multiply the first fraction by the reciprocal of the second fraction. Finally, we simplify the resulting fraction if possible.

The calculation for 3 3/8 : 3/4 is as follows: 3 3/8 : 3/4 = (3 * 8 + 3) / 8 : 3/4 = 27/8 : 3/4

Converting the mixed number to an improper fraction: 3 3/8 = (3 * 8 + 3) / 8 = 27/8

Now, we can divide the fractions: 27/8 : 3/4 = 27/8 * 4/3

Multiplying the first fraction by the reciprocal of the second fraction: 27/8 * 4/3 = (27 * 4) / (8 * 3) = 108/24

Simplifying the resulting fraction: 108/24 = (108 ÷ 12) / (24 ÷ 12) = 9/2

Therefore, the quotient of 3 3/8 : 3/4 is 9/2.

b) Знайди частку 3 3/5 : 2 1/4:

To divide mixed numbers, we first convert them to improper fractions. Then, we multiply the first fraction by the reciprocal of the second fraction. Finally, we simplify the resulting fraction if possible.

The calculation for 3 3/5 : 2 1/4 is as follows: 3 3/5 : 2 1/4 = (3 * 5 + 3) / 5 : (2 * 4 + 1) / 4 = 18/5 : 9/4

Converting the mixed numbers to improper fractions: 3 3/5 = (3 * 5 + 3) / 5 = 18/5 2 1/4 = (2 * 4 + 1) / 4 = 9/4

Now, we can divide the fractions: 18/5 : 9/4 = 18/5 * 4/9

Multiplying the first fraction by the reciprocal of the second fraction: 18/5 * 4/9 = (18 * 4) / (5 * 9) = 72/45

Simplifying the resulting fraction: 72/45 = (72 ÷ 9) / (45 ÷ 9) = 8/5

Therefore, the quotient of 3 3/5 : 2 1/4 is 8/5.

Answer 3

I can help you with math problems. Here are the detailed solutions:

1. Find the product: 1) $$\frac{3}{7} \cdot \frac{1}{2} + \frac{5}{5}$$ - To multiply two fractions, multiply the numerators and the denominators separately. To add two fractions, find a common denominator and add the numerators. - $$\frac{3}{7} \cdot \frac{1}{2} + \frac{5}{5} = \frac{3 \cdot 1}{7 \cdot 2} + \frac{5 \cdot 2}{5 \cdot 2}$$ - $$= \frac{3}{14} + \frac{10}{10}$$ - $$= \frac{3 + 14}{14}$$ - $$= \frac{17}{14}$$ - The final answer is $$\frac{17}{14}$$ or $$1 \frac{3}{14}$$ 2) $$\frac{2}{11} + \frac{12}{12} \cdot \frac{1}{5}$$ - To multiply two fractions, multiply the numerators and the denominators separately. To add two fractions, find a common denominator and add the numerators. - $$\frac{2}{11} + \frac{12}{12} \cdot \frac{1}{5} = \frac{2}{11} + \frac{12 \cdot 1}{12 \cdot 5}$$ - $$= \frac{2}{11} + \frac{12}{60}$$ - $$= \frac{2 \cdot 60}{11 \cdot 60} + \frac{12 \cdot 11}{60 \cdot 11}$$ - $$= \frac{120}{660} + \frac{132}{660}$$ - $$= \frac{252}{660}$$ - $$= \frac{21}{55}$$ - The final answer is $$\frac{21}{55}$$

2. Find the quotient: 1) $$\frac{3}{8} : \frac{3}{4}$$ - To divide two fractions, flip the second fraction and multiply. - $$\frac{3}{8} : \frac{3}{4} = \frac{3}{8} \cdot \frac{4}{3}$$ - $$= \frac{3 \cdot 4}{8 \cdot 3}$$ - $$= \frac{12}{24}$$ - $$= \frac{1}{2}$$ - The final answer is $$\frac{1}{2}$$ 2) $$\frac{3}{5} : \frac{2}{4}$$ - To divide two fractions, flip the second fraction and multiply. - $$\frac{3}{5} : \frac{2}{4} = \frac{3}{5} \cdot \frac{4}{2}$$ - $$= \frac{3 \cdot 4}{5 \cdot 2}$$ - $$= \frac{12}{10}$$ - $$= \frac{6}{5}$$ - The final answer is $$\frac{6}{5}$$ or $$1 \frac{1}{5}$$