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Answers
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1. 5−39 and 54−6
Let numerator p=5−39=−34
Denominator q=54−6=48
Hence, rational number,
q
p
=
48
−34
2. The greatest common divisor of 33 and 44 is 11. Therefore, the standard form of -33/44 is -3/4.
3. Evaluate \dfrac32y-3+\dfrac53z
2
3
y−3+
3
5
zstart fraction, 3, divided by, 2, end fraction, y, minus, 3, plus, start fraction, 5, divided by, 3, end fraction, z when y=4y=4y, equals, 4 and z=3z=3z, equals, 3.
4. −13−(5)
=−13−5
=
−18
5. Reduce 24/24 to lowest terms
The simplest form of 2424 is 11.
6. Simplify : [3]
4
×[(3)
2
]
4
= 3
12
7. x+7y=10; ------------(I)
3x−2y=7 -----------(II)
multiplying (I) with 3
3x+21y=30; ---------(III)
3x−2y=7 ---------------(IV)
Subtracting (IV) from (III) we get
3x+21y−3x+2y=30−7
23y=23
⇒1
Putting the value of y in (IV) we get
3x−2(1)=7
⇒3x=7+2=9
⇒3x=9
⇒x=3
Thus, (x,y)=(3,1)
8. 0.000035 = 3.5 x 10 raised to power -5. 2) 4050000 = 4.05 x 10 raised to power 6
9. dU=dQ−dW=(8×10
5
−6.5×10
5
)=1.5×10
5
J
dW=dQ−dU=10
5
−1.5×10
5
=−0.5×10
5
J
- ve sign indicates that work done on the gas is 0.5×10
5
J
10. The given surds can be simplified as follows:
(6
2
−7
3
)(6
2
−7
3
)
=6
2
(6
2
−7
3
)−7
3
(6
2
−7
3
)
=(6×6
2×2
)−(6×7
3×2
)−(7×6
3×2
)+(7×7
3×3
)
=(36×2)−42
6
−42
6
+(49×3)
=72−84
6
+147=219−84
6
.
Hence, (6
2
−7
3
)(6
2
−7
3
)=219−84
6
.