135r. Review Multiplying and Dividing Terms

Learning Intentions

Know that a pronumeral can represent a number
Understand that multiplication can be written without the $\times$ sign, for example $3 x$
Know that repeated multiplication can be written using powers
Recall that coefficients are the numerical parts of terms
Be able to simplify basic numerical multiplication and division
Know that a fraction bar can represent division

State the meaning of each expression:
a) $x^{2}$
b) $x^{3}$
c) $2 x^{2}$

Multiply the terms and simplify:
a) $3 x \times 4$
b) $2 a \times 5 b$
c) $x \times x$

Multiply the terms and simplify:
a) $4 m \times 3 m$
b) $2 p \times p \times 5$
c) $3 x^{2} \times 2 x$

Divide the terms and simplify:
a) $12 x \div 3$
b) $10 a b \div 5$
c) $x^{2} \div x$

Divide the terms and simplify:
a) $20 m^{2} \div 4 m$
b) $18 p^{3} \div 3 p$
c) $24 x^{2} y \div 6 x$

Simplify each expression:
a) $\frac{15 x^{2}}{5 x}$
b) $\frac{12 a b}{3 a}$
c) $2 x \times 3 x^{2} \div 6 x$

State the meaning of each expression:
a) $y^{2}$
b) $y^{3}$
c) $5 y^{2}$

Multiply the terms and simplify:
a) $4 x \times 2$
b) $3 a \times 2 b$
c) $m \times m$

Multiply the terms and simplify:
a) $5 n \times 2 n$
b) $3 q \times q \times 4$
c) $2 x^{2} \times 3 x$

Divide the terms and simplify:
a) $15 x \div 5$
b) $14 c d \div 7$
c) $a^{2} \div a$

Divide the terms and simplify:
a) $24 m^{2} \div 6 m$
b) $16 r^{3} \div 4 r$
c) $30 x^{2} y \div 5 x$

Simplify each expression:
a) $\frac{18 x^{2}}{6 x}$
b) $\frac{20 a b}{4 a}$
c) $4 x \times 2 x^{2} \div 8 x$

State the meaning of each expression:
a) $x^{2}$
b) $x^{3}$
c) $a^{2}$
d) $b^{3}$
Write each repeated multiplication using powers:
a) $x \times x$
b) $x \times x \times x$
c) $m \times m$
d) $p \times p \times p$
Multiply the terms and simplify:
a) $2 x \times 3$
b) $4 a \times 5 b$
c) $x \times x$
d) $3 m \times 2 m$
Multiply the terms and simplify:
a) $5 p \times p$
b) $2 x^{2} \times 4 x$
c) $3 a b \times 2 a$
d) $6 y \times y \times 2$
Divide the terms and simplify:
a) $12 x \div 4$
b) $18 a b \div 6$
c) $x^{2} \div x$
d) $20 m^{2} \div 5 m$
Divide the terms and simplify:
a) $24 p^{3} \div 6 p$
b) $30 x^{2} y \div 10 x$
c) $14 a^{2} b \div 7 a$
d) $36 m^{2} \div 9 m$
Simplify each expression:
a) $\frac{10 x^{2}}{2 x}$
b) $\frac{21 a b}{7 a}$
c) $3 x \times 2 x$
d) $4 m \times 3 m^{2}$
Simplify each expression:
a) $2 x \times 5 x^{2} \div 10 x$
b) $6 a \times 2 a b \div 3 a$
c) $8 p^{2} \div 4 p$
d) $9 x y \div 3 x$

A square has side length $x$ cm. Write an expression for its area.
A cube has side length $x$ cm. Write an expression for its volume.
A rectangle has side lengths $3 x$ cm and $4 x$ cm. Write a simplified expression for its area.
A packet contains $5 x$ marbles and this amount is shared equally among $5$ students. Write a simplified expression for the number of marbles each student gets.
A strip has length $6 x^{2}$ cm and is cut into pieces of length $3 x$ cm. Write a simplified expression for the number of pieces.
A garden has length $2 x$ m and width $5 x$ m. Write a simplified expression for its area.