Can I get the steps of solving the fractions ?
1 answer:
Step-by-step explanation:
In adding fractions, first you have to make the denominators the same. To do this, you need to find the GCF (greatest common factor).
3/4 + 4/8
The GCF on this would be 8, since both 4 and 8 can go into it. Next, you need to change both the denominators to the GCF, but you have to make sure the fractions are still equal to the original one. To do this, you have to multiply the numerator by the amount the original denominator is multiplied to get to the GCF.
4(2) = 8
3(2) = 6
So now you have 6/8 + 4/8. Next, you just add up the numbers normally, leaving the denominators the same.
6/8 + 4/8 = 10/8
If necessary, you simplify the fraction. To do this, you need to find the smallest number that goes into both of them, besides one. In this case, it would be 2. Then, you divide both the numerator and denominator by that number.
10/2 = 5
8/2 = 4
Then, to find the most simplified version, you need to divide the numorator by the denominator.
5/4 = 1 with a remainder of 1.
You put your answer as the whole number, and your remainder as the numorator. Leave the denominator the same.
1
Hope this helped with adding fractions!
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Answer:
Formula of Trapezoid:
A = (a + b) × h / 2
The formula can be derived in different ways. for now, we have discussed two ways:
1. By using the formula of a triangle
2. By dividing into different sections
Step-by-step explanation:
1. By using the formula of a triangle
One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.
Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.
The image is attached below.
Connect vertices P and R with a diagonal.
Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).
Its area is
S1=
Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).
Its area is
S2=
Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.
They both are equal to the altitude of the trapezoid h.
Therefore, we can represent areas of our two triangles as
S1=
S2=
Adding them together, we get the area of the whole trapezoid:
S=S1+S2=
which is usually represented in words as "half-sum of the bases times the altitude".
2. By dividing into different sections
Trapezoid PQRS is shown below, with PQ parallel to RS.
Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)
We are going to derive the area of a trapezoid by dividing it into different sections.
If we drop another line from Q, then we will have two altitudes namely PT and QU.
Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)
From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that
=>
Simplifying, we have
=>
Factoring we have,
=>
But, is equal to
, the longer base of our trapezoid.
Hence,
We have discussed two ways by which we can derive area of a trapezoid.
Read to know more about Trapezoid
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Answer:
2x^2+6x+3
Step-by-step explanation:
answer : 2x^2+6x+3
