Multiplication algorithm with integers

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

old question, way too many things in one question! I have made better questions out of each part now.

Students seem to miss the fact that division is actually multiplication by the reciprocal or the inverse of multiplication. This question attempts to address that.

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

Multiplication algorithm with integers

Multiplication algorithm with integers

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

6 Exercises from HELM Book 1.4 Part 2: Multiplication and Division of Algebraic Fractions.

Multiply two numbers, at least one of which is negative.

Multiplication of $2 \times 2$ matrices.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Multiplication and adding matrices.

Gradient of $f(x,y,z)$.

Should warn that multiplied terms need * to denote multiplication.

Multiplication of $2 \times 2$ matrices.

This question is to practice order of precedence in mathematical expressions. 

Please use * for multiplication and / for division. 

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are asked to find a fraction of a fraction. There are 9 different versions of this question.

Multiplication and addition of complex numbers. Four parts.

Elementary examples of multiplication and addition of complex numbers. Four parts.

Calculate: $ a_1 \times a_2 \times a_3 \times a_4 $ and $ \frac{b_1 \times b_2 \times b_3 \times b_4}{b_5 \times b_6} $

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Multiplication of $2 \times 2$ matrices.

Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.

Multiplication of  matrices of different sizes.

Exercises in multiplying matrices. 

Multiplication of $2 \times 2$ matrices.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.