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4 years ago

Simplify the following 3/5×(7/10+2/5)/ 5 2/3+1 3/8-2 1/4

Mathematics

1 answer:

Inessa [10]4 years ago

4 0

Answer:

(-2579)/3400

Step-by-step explanation:

Simplify the following:

3/5 (7/10 + 2/5)/(5 + 2/3) + 1 + 3/8 - (2 + 1/4)

(3 (7/10 + 2/5)/(5 + 2/3))/5 = (3 (7/10 + 2/5))/(5 (5 + 2/3)):

(3 (7/10 + 2/5))/(5 (2/3 + 5)) + 1 + 3/8 - (2 + 1/4)

Put 5 + 2/3 over the common denominator 3. 5 + 2/3 = (3×5)/3 + 2/3:

(3 (7/10 + 2/5))/(5 (3×5)/3 + 2/3) + 1 + 3/8 - (2 + 1/4)

3×5 = 15:

(3 (7/10 + 2/5))/(5 (15/3 + 2/3)) + 1 + 3/8 - (2 + 1/4)

15/3 + 2/3 = (15 + 2)/3:

(3 (7/10 + 2/5))/(5 (15 + 2)/3) + 1 + 3/8 - (2 + 1/4)

15 + 2 = 17:

(3 (7/10 + 2/5))/(5×17/3) + 1 + 3/8 - (2 + 1/4)

Put 7/10 + 2/5 over the common denominator 10. 7/10 + 2/5 = 7/10 + (2×2)/10:

(3 7/10 + (2×2)/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)

2×2 = 4:

(3 (7/10 + 4/10))/((5×17)/3) + 1 + 3/8 - (2 + 1/4)

7/10 + 4/10 = (7 + 4)/10:

(3 (7 + 4)/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)

7 + 4 = 11:

(3×11/10)/(5×17/3) + 1 + 3/8 - (2 + 1/4)

5×17/3 = (5×17)/3:

(3×11/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)

3×11/10 = (3×11)/10:

((3×11)/10)/((5×17)/3) + 1 + 3/8 - (2 + 1/4)

Multiply the numerator by the reciprocal of the denominator, ((3×11)/10)/((5×17)/3) = (3×11)/10×3/(5×17):

(3×11×3)/(5×17×10) + 1 + 3/8 - (2 + 1/4)

5×17 = 85:

(3×11×3)/(85×10) + 1 + 3/8 - (2 + 1/4)

85×10 = 850:

(3×11×3)/850 + 1 + 3/8 - (2 + 1/4)

3×11 = 33:

(33×3)/850 + 1 + 3/8 - (2 + 1/4)

33×3 = 99:

99/850 + 1 + 3/8 - (2 + 1/4)

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

99/850 + 1 + 3/8 - (4×2)/4 + 1/4

4×2 = 8:

99/850 + 1 + 3/8 - (8/4 + 1/4)

8/4 + 1/4 = (8 + 1)/4:

99/850 + 1 + 3/8 - (8 + 1)/4

8 + 1 = 9:

99/850 + 1 + 3/8 - 9/4

Put 99/850 + 1 + 3/8 - 9/4 over the common denominator 3400. 99/850 + 1 + 3/8 - 9/4 = (4×99)/3400 + 3400/3400 + (425×3)/3400 + (850 (-9))/3400:

(4×99)/3400 + 3400/3400 + (425×3)/3400 + (850 (-9))/3400

4×99 = 396:

396/3400 + 3400/3400 + (425×3)/3400 + (850 (-9))/3400

425×3 = 1275:

396/3400 + 3400/3400 + 1275/3400 + (850 (-9))/3400

850 (-9) = -7650:

396/3400 + 3400/3400 + 1275/3400 + (-7650)/3400

396/3400 + 3400/3400 + 1275/3400 - 7650/3400 = (396 + 3400 + 1275 - 7650)/3400:

(396 + 3400 + 1275 - 7650)/3400

| 1 | 1 | 1 |

| 3 | 4 | 0 | 0

| 1 | 2 | 7 | 5

+ | | 3 | 9 | 6

| 5 | 0 | 7 | 1:

(5071 - 7650)/3400

5071 - 7650 = -(7650 - 5071):

(-(7650 - 5071))/3400

| | | 14 |

| | 5 | 4 | 10

| 7 | 6 | 5 | 0

- | 5 | 0 | 7 | 1

| 2 | 5 | 7 | 9:

Answer: (-2579)/3400

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Step-by-step explanation:

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A survey of 500 farmers showed that of the farmers, 129 grew only wheat, 111 grew only corn, 93 grew only oats, 206 grew wh

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Answer:

a) 419

b)34

c)81

d)52

Step-by-step explanation:

Let x represent the number of farmers who grew all three crops and y represent those who grew corn and oath.

This information is represented on a Venn Diagram as shown in the attachment (A)

Let us add all the regions in wheat and equate to 206.

$206 = 129 + 58 - x + x + 53 - x$

$206 = 240 - x$

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We redraw the Venn diagram as shown in the attachment (B).

We can now answer the question using the second diagram:

Those who grew at least one of the three crops =exactly one +exactly two +exactly three

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b) Of the farmers,34 grew all three crops.

c) Of the farmers,81 did not grow any of the three crops.

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4 years ago

Two times the sum of a number and 9 is half the number

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Answer:

Equation:

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Solve:

The umber is:

-12

Step-by-step explanation:

Equation:

2(a+9) = a/2

Solve:

2*a + 2*9 = a/2

2a + 18 = a/2

2a - a/2 = -18

4a/2 - a/2 = -18

3a/2 = -18

a = -18*2/3

a = -12

Check:

2(-12+9) = -12/2

2(-3) = -12/2 = -6

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3 years ago

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Kay [80]

Answer:

B. 2^0 = 1

Step-by-step explanation:

here

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D.) squareroot of 20 = 4.4 something is > 4

and any no like 3^0= also 1,

4^0=1

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ans is

B.) 2^0 = 1 is true

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3 years ago

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3 years ago

Simplify the following 3/5×(7/10+2/5)/ 5 2/3+1 3/8-2 1/4​

Simplify the following 3/5×(7/10+2/5)/ 5 2/3+1 3/8-2 1/4