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mash [69]
2 years ago
8

What is: 3/4 + (1/3 / 1/6) - (-1/2) = a

Mathematics
1 answer:
deff fn [24]2 years ago
6 0

Answer:

We will use the concepts of fractions to solve this.

(a) 2/3 + 1/7

LCM of 3 and 7 = 21

(2 × 7 + 1 × 3) / 21 = (14 + 3) / 21

= 17/21

(b) 3/10 + 7/15

LCM of 10 and 15 = 30

= (3 × 3 + 7 × 2) / 30 = (14 + 9) / 30

= 23/30

(c) 4/9 + 2/7

LCM of 9 and 7 = 63

= (4 × 7 + 2 × 9) / 63 = (28 + 18) / 63

= 46/63

(d) 5/7 + 1/3

LCM of 7 and 3 = 21

= (5 × 3 + 1 × 7) / 21 = (15 + 7) / 21

= 22/21

(e) 2/5 + 1/6

LCM of 5 and 6 = 30

= (2 × 6 + 1 × 5) / 30 = (12 + 5) / 30

= 17/30

(f) 4/5 + 2/3

LCM of 5 and 3 = 15

= (4 × 3 + 5 × 2) / 15 = (12 + 10) / 15

= 22/15

(g) 3/4 - 1/3

LCM of 4 and 3 = 12

= (3 × 3 + 1 × 4) / 12 = (9-4) / 12

= 5/12

(h) 5/6 - 1/3

LCM of 6 and 3 = 6

= (1 × 5 - 1 × 2) / 6 = (5 - 2) / 6

= 3/6

= 1/2

(i) 2/3 + 3/4 + 1/2

LCM of 3,4 and 2 = 12

= (2 × 4 + 3 × 3 + 1 × 6) /12 = (8 + 9 + 6) / 12

= 23 / 12

(j) 1/2 + 1/3 + 1/6

LCM of 2,3 and 6 = 6

= (1 × 3 + 1 × 2 + 1 × 1) / = (3 + 2 + 1) / 6

= 6 / 6

= 1

(k) 113 + 323

= 1 + 1/3 + 3 + 2/3 = 4 + 1/3 + 2/3

= 4 + 1/3 + 2/3 = 4 + 3/3

= 4 + 1 = 5

(l) 423 + 314

= 4 + 2/3 + 3 + 1/4 = 7 + 2/3 + 1/4

= 7 + (2 × 4 + 1 × 3) / 12

= 7 + 11/12

= 95 / 12

(m) 16/5 - 7/5

= 16 × 1 - 7 × 1 = (16 - 7) / 5

= 9 / 5

(n) 4/3 - 1/2

= (4 × 2 - 1 × 3) / 6

= (8 - 3) / 6

= 5 / 6

You can also use the Fraction Calculator to check your answer.

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Answer:

     <u>First figure:</u>            954cm^3

     <u>Second figure:</u>      1,508yd^3

     <u>Third figure:</u>

  •          Height= q
  •           Side length = r

     <u>Fourth figure: </u>        726cm^3

Explanation:

<u></u>

<u>A. First figure:</u>

<u>1. Formula:</u>

            \text{Volume of a cylinder}=\pi \times radius^2\times length

<u>2. Data:</u>

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<u>3. Substitute in the formula and compute:</u>

          Volume=\pi \times (4.5cm)^2\times (15cm)\approx 954cm^3\approx 954cm^3

<u>B. Second figure</u>

<u>1. Formula: </u>

       \text{Volume of a leaned cylinder}=\pi \times radius^2\times height

<u>2. Data:</u>

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<u>3. Substitute and compute:</u>

      Volume=\pi \times (12yd)^2\times (40yd)\approx 1,507.96yd^3\approx 1,508yd^3

<u></u>

<u>C) Third figure</u>

a) The<em> height </em>is the segment that goes vertically upward from the center of the <em>base</em> to the apex of the pyramid, i.e.<u>  </u><u>q  </u>.

The apex is the point where the three leaned edges intersect each other.

b) The side length is the measure of the edge of the base, i.e.<u>  r </u><u> </u>.

When the base of the pyramid is a square the four edges of the base have the same side length.

<u>D) Fourth figure</u>

<u>1. Formula</u>

The volume of a square pyramide is one third the product of the area of the base (B) and the height H).

          Volume=(1/3)B\times H

<u>2. Data: </u>

  • height: H = 18cm
  • side length of the base: 11 cm

<u>3. Calculations</u>

a) <u>Calculate the area of the base</u>.

The base is a square of side length equal to 11 cm:

          \text{Area of the base}=B=(11cm)^2=121cm^2

b) <u>Volume of the pyramid</u>:

         Volume=(1/3)B\times H=(1/3)\times 121cm^2\times 18cm=726cm^3

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