Multiplicative relationships between terms | Maths | Quizalize & Oak National Academy

Starter quiz

In the multiplication 7 × 8 = 56, you call 56 the __________ of 7 and 8.

factor

multiplicand

multiplier

product ✓
Which other related facts make up the fact family for 7 × 8 = 56?

56 ÷ 7 = 8 ✓

8 ÷ 56 = 7

56 ÷ 8 = 7 ✓

7 ÷ 56 = 8

8 × 7 = 56 ✓
132 × 17 = 2244, so 132 is a __________ of 2244.

factor ✓

multiple

prime factor

product
Which of these is equivalent to the division $20\div5$ ?

$5\div20$

$20\over5$ ✓

$5\over20$

$5\times20$
Match each expression to its simplified form.

$b\times{h}$

⇔

$bh$ ✓

$l\times{w}\times{h}$

⇔

$lwh$ ✓

$2\times{\pi}\times{r}$

⇔

$2\pi{r}$ ✓

$\pi\times{r}\times{r}$

⇔

${\pi}r^2$ ✓

$2\times{b} +2\times{h}$

⇔

$2b +2h$ ✓

$\pi\times{d}$

⇔

$\pi{d}$ ✓
Which of these expressions is the reciprocal of $3\over{xy^2}$ ?

$3x\over{y^2}$

$3y^2\over{x}$

$3\times{xy^2}$

$xy^2\over{3}$ ✓

$3xy^2$

Exit quiz

In algebra, the product is the result of two or more __________ multiplied together.

equations

solutions

terms ✓

unknowns
Which of these equations are valid rearrangements of the generalisation $a\times{b}=c$ ?

$b\times{a}=c$ ✓

$c\times{a}=b$

$b\div{c}=a$

$c\div{b}=a$ ✓

$c\div{a}=b$ ✓
The area of a parallelogram can be found using the formula $A=b\times{h}.$ Which of these are correct rearrangements of the formula?

$b=A\times{h}$

$A=h\times{b}$ ✓

${A\over{b}}=h$ ✓

${h\over{A}}=b$

${b\over{h}}=A$
The circumference of a circle can be found using the formula $C=2{\pi}r.$ Which of these are correct rearrangements of the formula?

${C\over{\pi}}=2r$ ✓

${C\over{r}}=2\pi$ ✓

${C\over{2r}}=\pi$ ✓

$2C={\pi}r$

${2r\over{C}}=\pi$
Sofia wants to rearrange the equation ${y\over{3x}}=z$ into the form $y=\square$ . Which first step would be most efficient for Sofia to apply to both sides of the equation?

$\div{3x}$

$\times{3x}$ ✓

$\times{x}$

$\times{3}$

$\times{y}$
Which of these equations is an arrangement of ${2c\over7de}=5d^2$ ?

$2c=35d^3e$ ✓

$2c=35d^2e$

$2c=35de^3$

$2c=35d^2e^2$

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Lesson Details

Key learning points

When multiplying terms, there are not the same restrictions.
The result of multiplication is called the product.
ab = c also means that a = c/b
a = c/b can also be written as a = c x 1/b

Common misconception

Rather than learning to rearrange multiplicative relationships pupils can just learn the rearrangements or use a trick.

There are many situations in school and out where this skill is valuable and understanding how to manipulate these relationships will help pupils to understand the mathematics rather than just learn a set of procedures or lots of formulae.

Keywords

Product - A product in algebra is the result of two or more terms multiplied together.