Assignment about Rewriting Mixed Fraction

1 Question 1.
1.1
Rewriting Mixed Fraction 22
3 as 11
3 we get
( 2
5 )
1
3 ( 3
4 − 1
4 ) + ( 11
3 )
11
9
Combining 3
4 − 1
4 we get2
4 and factoring out 2 we get1
2 , and we get
= 2
5
1
3 ( 1
2 ) + 11
3
11
9
Removing Parantheses we get
= 2
5
1
3 · 1
2
+ 11
3
11
9
Apply the fraction rule :b
c
a = b
c · a and Divide fractions : a
b
c
d
= a· d
b· c we get
= 2
5· 1
3 · 1
2
+ 11· 9
3· 11
Multiply fractions : a · b
c · d
e = a · b · d
c · e , 2
5
6
+ 3
Apply the fraction rule :a
b
c
= a· c
b we get
= 2· 6
5 + 3
= 12
5 + 3
Convert element to fraction :3 = 3· 5
5
= 3· 5
5 + 12
5
= 3· 5+12
5
= 27
5
1.2
Number of shares left after selling it to her brother and cousin = 1 −1
5 − 4
11 =
24
55
Number of shares sold to Emily =1
2 · 24
55 = 12
55.
1.3
Hence number of shares left =24
55 − 12
55 or 12
55.
1.4
Considering Number of shares was x,12
55x = 72 or x = 330.
1

2 Question 2.
2.1
Rewrite1
4 in power − base form :1
4 = 1
2
2 we get log1
2
1
2
2
and then loga xb = b · loga (x) we get log1
2
1
2
2 = 2 log1
2
1
2
Apply log rule : loga (a) = 1 we get log1
2
1
4 = 2
Similarly we get log3 (27) = 3
Now Apply radical rulen
√ an = a, assuming a ≥ 0
log4
q
(10 + 6)
2 = log4 (16) = 2
log3 (27) − log1
2
1
4 + log4
q
(10 + 6)2 = 3 − 2 + 2 = 3.
2.2
Using 2x = 2x−1+1, 2x+1 = 2x−1+2 and ab+c = abac and Factor out common term 2x−1
we get
2x−1 21 + 22 − 1 = 40
2x−1 = 8
2x−1 = 23
x = 4.
3 Question 3.
3.1
(ab + d)
2 + (a + d) (b − d) = a2b2 + 2abd + d2 + ab − ad + bd − d2
= −ad + 2abd + bd + a2b2 + ab.
3.2
9 a y − 4 d x − 6 d y + 6 a x = 3a(3y + 2x) − 2d(3y + 2x)
= (3a − 2d)(3y + 2x)
3.3
l=20+w
3.4
Area=l x w
Area= w(20+w)
Area= w2 + 20w.
2

3.5
w2 + 20w = 4800
w2 + 20w − 4800 = 0
For a quadratic equation of the form ax2 + bx + c = 0 the solutions are x1, 2 =
−b±√ b2 −4ac
2a
w = −20+√ 202 −4· 1·(−4800)
2· 1
w = −80 or 60
But since Width is positive width=60 and length=80.
4 Question 4.
Let number of boys be x.Then number of girls is 10+4x.Hence x+10+4x=100
5x+10-10=100-10
x = 90
5
x=18.
Hence number of girls is 10+4*18=82.
4.1
2s+5m=41
3s+10m=74.5
Multiplying Equation with -2 we get -4s-10m=-82,
Adding this to equation 2 we get
-s=74.5-82
s = 7.5
Substituting this in equation 1 we get 2*7.5 + 5m = 41
5m=41-15
5m = 26
m=5.20
4.2
8x2 − 2x − 15 = 0
4.3
x2 − 1
4 x − 15
8 = 0
(x − 3
2) ( x = +5
4 ) = 0
Hence x =3
2 , x = −5
4
3

4.4
8x2 − 2x − 15 = 0
x1,2 = −(−2)+
√ (−2) 2 −4· 8(−15)
2· 8
x = 3
2 , x = −5
4
4