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      Multiplicative relationships between terms

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      Lesson details

      Learning outcome

      I can appreciate that a multiplicative relationship between variables can be written in a number of different ways.

      Key learning points

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

      Keywords

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

      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.

      Teacher tip

      Rearranging even simple multiplicative relationships correctly will be really valuable to pupils and will be used in many other topic areas. It is worth spending the time embedding this key skill.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
       except where otherwise stated. See Oak's terms & conditions
       (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      Download starter quiz questions (PDF)

      6 Questions

      Q1.
      In the multiplication 7 × 8 = 56, you call 56 the __________ of 7 and 8.

      factor
      multiplicand
      multiplier
      Correct answer: product

      Q2.
      Which other related facts make up the fact family for 7 × 8 = 56?

      Correct answer: 56 ÷ 7 = 8
      8 ÷ 56 = 7
      Correct answer: 56 ÷ 8 = 7
      7 ÷ 56 = 8
      Correct answer: 8 × 7 = 56

      Q3.
      132 × 17 = 2244, so 132 is a __________ of 2244.

      Correct answer: factor
      multiple
      prime factor
      product

      Q4.
      Which of these is equivalent to the division $$20\div5$$?

      $$5\div20$$
      Correct answer: $$20\over5$$
      $$5\over20$$
      $$5\times20$$

      Q5.
      Match each expression to its simplified form.

      Correct Answer:$$b\times{h}$$,$$bh$$

      $$bh$$

      Correct Answer:$$l\times{w}\times{h}$$,$$lwh$$

      $$lwh$$

      Correct Answer:$$2\times{\pi}\times{r}$$,$$2\pi{r}$$

      $$2\pi{r}$$

      Correct Answer:$$\pi\times{r}\times{r}$$,$${\pi}r^2$$

      $${\pi}r^2$$

      Correct Answer:$$2\times{b} +2\times{h}$$,$$2b +2h$$

      $$2b +2h$$

      Correct Answer:$$\pi\times{d}$$,$$\pi{d}$$

      $$\pi{d}$$

      Q6.
      Which of these expressions is the reciprocal of $$3\over{xy^2}$$?

      $$3x\over{y^2}$$
      $$3y^2\over{x}$$
      $$3\times{xy^2}$$
      Correct answer: $$xy^2\over{3}$$
      $$3xy^2$$

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      In algebra, the product is the result of two or more __________ multiplied together.

      equations
      solutions
      Correct answer: terms
      unknowns

      Q2.
      Which of these equations are valid rearrangements of the generalisation $$a\times{b}=c$$ ?

      Correct answer: $$b\times{a}=c$$
      $$c\times{a}=b$$
      $$b\div{c}=a$$
      Correct answer: $$c\div{b}=a$$
      Correct answer: $$c\div{a}=b$$

      Q3.
      The area of a parallelogram can be found using the formula $$A=b\times{h}.$$ Which of these are correct rearrangements of the formula?

      $$b=A\times{h}$$
      Correct answer: $$A=h\times{b}$$
      Correct answer: $${A\over{b}}=h$$
      $${h\over{A}}=b$$
      $${b\over{h}}=A$$

      Q4.
      The circumference of a circle can be found using the formula $$C=2{\pi}r.$$ Which of these are correct rearrangements of the formula?

      Correct answer: $${C\over{\pi}}=2r$$
      Correct answer: $${C\over{r}}=2\pi$$
      Correct answer: $${C\over{2r}}=\pi$$
      $$2C={\pi}r$$
      $${2r\over{C}}=\pi$$

      Q5.
      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?

      $$\div{3x}$$
      Correct answer: $$\times{3x}$$
      $$\times{x}$$
      $$\times{3}$$
      $$\times{y}$$

      Q6.
      Which of these equations is an arrangement of $${2c\over7de}=5d^2$$ ?

      Correct answer: $$2c=35d^3e$$
      $$2c=35d^2e$$
      $$2c=35de^3$$
      $$2c=35d^2e^2$$

      To help you plan your 9 maths lesson on: Multiplicative relationships between terms, download all teaching resources for free and adapt to suit your pupils' needs...