Question

4\7-3\14 5\14*2 1\3 3-2 7\10 40:5\8 выполни действия найдите значение выражения: 3\4/(5\6+1\4). найдите значение выражения:4-2 2\5*(1 1\3-5\6)/10 иван посадил 2\5 всех саженцев яблонь петр -треть всех саженцев а антон -оставшиеся 8 саженцев яблонь. сколько всего саженцев посажено?

Answer 1

1) $1)\frac{4}{7} -\frac{3}{14} =\frac{8-3}{14} =\frac{5}{14} ; 2)\frac{5}{14} *2\frac{1}{3} =\frac{5}{6} ;\\3) 3-2\frac{7}{10} =\frac{3}{10} ; 4) 40:\frac{5}{8} =40*\frac{8}{5} =64$

2) $\frac{\frac{3}{4} }{\frac{5}{6}+\frac{1}{4} } =\frac{3}{4} *\frac{24}{26} =\frac{9}{13}$

3) 4-(2,4*(4/3-5/6))/10=4-1,2/10=4-0,12=3,88

4)$2/5+1/3=\frac{11}{15};1-\frac{11}{15} =4/15$ -это оставшиеся 8 саженцев, т.е. всего было 8*15/4=30

Answer 2

Let's solve each expression step by step:

1. Expression: 4/7 - 3/14 + 5/14 * 2 + 1/3 - 3 - 2 + 7/10

First, simplify the fractions:

4/7 - 3/14 = (8/14) - (3/14) = 5/14

5/14 * 2 = 5/7

1/3 - 3 = (2/6) - (18/6) = -16/6 = -8/3

Now, add all the terms together:

5/14 + 5/7 - 8/3 + 7/10

To add these fractions, you need to find a common denominator. The least common multiple (LCM) of 14, 7, 3, and 10 is 420.

Now, convert each fraction to have a denominator of 420:

(5/14) * (30/30) = 150/420

(5/7) * (60/60) = 300/420

(-8/3) * (140/140) = -112/420

(7/10) * (42/42) = 294/420

Add them together:

150/420 + 300/420 - 112/420 + 294/420 = 632/420

Simplify the fraction:

632/420 = 158/105

So, the value of the expression is 158/105.

2. Expression: 3/4 / (5/6 + 1/4)

First, find a common denominator for the fractions inside the parentheses, which is 12.

5/6 * (2/2) = 10/12

1/4 * (3/3) = 3/12

Now, the expression becomes:

3/4 / (10/12 + 3/12)

Add the fractions inside the parentheses:

3/4 / (13/12)

To divide by a fraction, invert and multiply:

3/4 * (12/13)

Multiply the numerators and denominators:

(3 * 12) / (4 * 13) = 36/52

Simplify the fraction:

36/52 = 9/13

So, the value of the expression is 9/13.

3. Problem: Ivan planted 2/5 of all apple tree seedlings, Peter planted one-third (1/3) of all the seedlings, and Anton planted the remaining 8 seedlings. We need to find the total number of apple tree seedlings planted.

Let's represent the total number of seedlings with "T."

Ivan planted 2/5 of the seedlings, which is (2/5)T. Peter planted one-third (1/3) of the seedlings, which is (1/3)T. Anton planted the remaining 8 seedlings.

Now, we can set up an equation to find "T":

(2/5)T + (1/3)T + 8 = T

To solve for "T," let's get rid of the fractions:

Multiply the entire equation by the least common multiple (LCM) of 5 and 3, which is 15:

15 * (2/5)T + 15 * (1/3)T + 15 * 8 = 15 * T

Now, simplify:

6T + 5T + 120 = 15T

Combine the "T" terms:

11T + 120 = 15T

Subtract 11T from both sides:

120 = 4T

Now, isolate "T" by dividing both sides by 4:

T = 120 / 4

T = 30

So, the total number of apple tree seedlings planted is 30.