1.02 Multiplying and dividing terms
Simplify the following:
10 \times 6 u
7 \times (-3 u)
5x \times 2
11 \times 3y
(-8x) \times 9
(-12) \times (-2u)
\left( - 3 w \right) \times 2
10 \times \left( - 3 y \right)
Simplify the following:
Simplify the following:
9 \times m \times n \times 8
w \times 4 \times z \times 6
10 \times \left( - r \right) \times s \times \left( - 5 \right)
9 r \times 6 s
6 u^{2} \times 7 v^{8}
16 p^{3} \times 14 q^{3}
\left( - 2 a \right) \times \left( - 4b \right)
3 w \times \left( - 7 z \right)
\left( - 5 r \right) \times \left( - 4 s \right)
\left( - 10 r^{8} \right) \times 6 s^{7}
4 p^{5} \times \left( - 3 q^{5} \right)
Simplify the following:
6 r \times 2 \times 8 s
7 w \times 9 x \times 10 y
\left( - 2 w \right) \times \left( - 4 x \right) \times \left( - 10 y \right)
\left( - 8 h \right) \times 5 k \times \left( - 3 r \right) \times \left( - 4 s \right)
5x \times 2y \times (-9)
4a \times (-2a) \times 10a
\left( - 5 x \right) \times \left( - 2 x \right) \times \left( -3 y \right)\times (-3)
\left( -2 h \right) \times 4 k \times \left( - j \right) \times \left( - 5i \right)
Simplify the following:
\dfrac{2 x}{2}
\dfrac{15 v}{5}
\dfrac{5 m}{20}
\dfrac{n}{4 n}
\dfrac{12 x y}{12}
\dfrac{63 p q}{9 p}
\dfrac{12 m n}{15 m}
\dfrac{6 r}{r w}
\dfrac{p r}{p q r}
\dfrac{10 u^{6} v^{4}}{u^{6}}
\dfrac{- 24 a}{4}
\dfrac{- 11 y}{y}
\dfrac{y}{- 11 y}
\dfrac{- 12 u}{3 u}
\dfrac{- 4 m}{- 9 m}
\dfrac{- a b c}{b}
\dfrac{k}{- j k}
\dfrac{- 6 j}{j k}
\dfrac{- a c}{a b c}
\dfrac{- 2 b^{3}}{3 b^{3}}
\dfrac{- 3 r^{3} w^{5}}{r^{3}}
\dfrac{12 n}{n}
Simplify the following:
5 m \div 40
20 w z \div 4 w z
10 r^{6} \div 5 r^{6}
\left( - 24 r^{4} \right) \div 6 r^{4}
\left( - 44 r s \right) \div 4 r
\left( - 36 u v\right) \div \left( - 6 u v\right)
10mn \div 5m
18xy \div 6y
27 r^{2} \div 9 r
\left( - 20 x^{4} \right) \div 10 x^{4}
\left( -22 x^2 y \right) \div -2 xy
\left(-50abc\right) \div \left(-5ab\right)
Simplify the following:
While Judy is packing rectangular boxes into crates, she notices that each crate is 12 times wider than the width of one box, and 11 times longer than the length of one box. Judy wants to know the greatest number of boxes she can pack into each crate.
Let the length of one box be L \text{ cm}, and the width of one box be W\,\text{cm}.
Find an expression for the volume of one box with a height of 44 \text{ cm}.
Find an expression for the volume of a crate of height H \text{ cm}.
Find an expression for the number of identical boxes that Judy can fit into each crate.
If the crate is 88 \text{ cm} high, calculate how many boxes can Judy fit into each crate.
Aaron have books to be placed on a shelf which is 6 times wider than the width of the book and 8 times longer than the length of the book. Aaron wants to know the greatest number of books he can place into the shelf.
Let the length of one book be x cm, and the width of one book be y cm.
Find an expression for the volume of one book with a height of 6 \text{ cm}.
Find an expression for the volume of the shelf of thickness z \text{ cm}.
Find an expression for the number of books that Aaron can fit into the shelf.
If the shelf is 15 cm thick, how many books can Aaron fit into the shelf?