3.01 Simplifying expressions
Simplify the following:
\left( 5 u - 2 u\right) \times 3
\left( 13 a + 15 a\right) \div 7
9 p \div \left( 6 p - 3 p\right)
80 m n \div \left( 4 m\right) \div \left( 5 n\right).
\left( - 7 n \right) \times 4 - \left( 2 n + 5 n\right)
\left( 6 u \times 12 v w\right) \div \left( 6 v \times 32 u\right)
\left( 19 v - 5 v\right) \div 2 \times 3.
30 r \div \left( 3 r + 2 r\right) + 5 r.
5 v - 5 \left( 6 v - 2 v\right)
6 v + \left( 15 v - \left( 9 v - 2 v\right)\right).
- 8 t - \left( 8 t - 6 t \div 2\right)
\left( \left( - 8 r \right) \times 16 s t\right) \div \left( 24 s \times \left( - 9 r \right)\right)
\left( 7 m - 5 m\right) \times 4 m
\left(-4n\right)\times 8-\left(7n+4n\right)
Simplify the following:
\dfrac{16 x}{3 x + 5 x}
\dfrac{20 s}{4 s} \times 6 t
\dfrac{21 m}{3} + \dfrac{10 m}{2}
9 v \times 2 - \dfrac{25 v}{5}
15 m + \dfrac{51 m - m}{5 m}.
\dfrac{58 r + 5 r}{7 r \times 3}
\dfrac{7 r + 5 r}{7 r - 5 r}
\dfrac{7 r s + 23 r s}{5 r \times 3 s}
5 n^{2} + \dfrac{20 n^{2}}{5}
3 m - \dfrac{12 m^{2}}{3 m}.
5 n \times 4 n - \dfrac{8 n^{2}}{4}
\dfrac{7st+53st}{4s\times 5t}
Simplify the following:
2 t + 4 \times 8 t
2 c + 7 c \times 3 + 4 c
61 a - 6 \times 9 a - 2 a
8 \times 3 a + 6 \times 2 a
3 n^{2} + 8 n^{2} - 3 n^{2}
9 n^{2} + 3 n \times 6 n
5 n^{2} + 5 n^{2} \times 2 + 7 n^{2}
5 m n \times 3 n - 2 m n^{2}
20 w - 10 w \div 2 - 3 w
6 p \times 8 q \div 2
60 n^{2} \div 5 n \div 3
8 j k \times 15 k \div 10 j
20 p q \div 5 q \times 2 p
12 s - 8 s \div 4
12 u \div 3 - 2 u
8jk\times 15k\div 20j
Consider \dfrac{w}{3} + \dfrac{w}{9}.
Find the lowest common denominator of \dfrac{w}{3} and \dfrac{w}{9}.
Hence, write \dfrac{w}{3} + \dfrac{w}{9} as a single fraction.
Consider \dfrac{m}{4} - \dfrac{m}{12}.
Find the lowest common denominator of \dfrac{m}{4} and \dfrac{m}{12}.
Hence, write \dfrac{m}{4} - \dfrac{m}{12} as a single fraction in simplest form.
Simplify the following expressions:
Write an algebraic expression for the perimeter of the following shapes:
Write an algebraic expression for the area of the following shapes:
Consider the following rectangular prism:
Write an expression for its volume.
Write an expression for its surface area.
Dylan, Jimmy and Valentina are travelling from Adelaide to Sydney at x, y and z km/h respectively.
Let S_1 represent the average speed of Dylan and Jimmy's vehicles, and S_2 represent the average speed of Dylan and Valentina's vehicles.
Write a simplified expression for S_1 + S_2 in terms of x, y and z.
Frank wants to determine the profit he makes on each eraser he sells. Frank can sell 3 erasers for x dollars, and it costs y dollars to make 9 erasers.
Determine a simplified expression for the profit Frank makes on each eraser. Leave your answer as a single fraction.
Frank realised he could sell 3 erasers for \$3 more than they previously were, and reduce the cost of production of 9 erasers by \$2. Find the new profit per eraser.
Glen lived in a rectangular bedroom. His mother asked him to find out the area of his room, and since Glen did not have a measuring tape or ruler, he counted how many of his steps each wall was.
If Glen's foot length is x cm, and two adjacent walls were 12 and 10 footsteps long, write an expression for the area of his room.