Algebraic ratios | Maths | Quizalize & Oak National Academy

Starter quiz

A numerical coefficient is a constant ______ of the variables in a term.

addition

subtraction

multiplier ✓
What is the equation of $y$ in terms of $x$ ?

$y=3x$ ✓

$y={1\over4}x$

$y={1\over3}x$

$y=4x$
What is the equation of $y$ in terms of $x$ ?

$y=5x$

$y={1\over6}x$ ✓

$y={1\over5}x$

$y=6x$
Match each ratio of $x$ : $y$ to the correct equation of $y$ in terms of $x$ .

3 : 1

⇔

$y={1\over3}x$ ✓

1 : 3

⇔

$y=3x$ ✓

4 : 5

⇔

$y=1.25x$ ✓

5 : 4

⇔

$y=0.8x$ ✓

4 : 3

⇔

$y=0.75x$ ✓
The ratio of adults to children at a running club is 8 : 5. Which of the following are correct equations linking adults and children?

$c={5\over8}a$ ✓

$c={8\over5}a$

$a={5\over8}c$

$a={8\over5}c$ ✓
$4x-6y = 3x-2y$ . What is the ratio of $x:y$ ?

'4 : 1' ✓

Exit quiz

To factorise is to express a term as the ______ of its factors.

'product' ✓
Which of these are equivalent ratios to the ratio 3 : 5

4 : 6

5 : 3

13 : 15

30 : 50 ✓

27 : 45 ✓
Given that $2x-7$ : $6-3x$ is equivalent to 3 : 5 which of the following equations are also true.

$\frac{2x-7}{6-3x}=\frac{3}{5}$ ✓

$\frac{6-3x}{2x-7}=\frac{5}{3}$ ✓

$\frac{2x-7}{3}=\frac{5}{6-3x}$

$\frac{2x-7}{3}=\frac{6-3x}{5}$ ✓

$\frac{2x-7}{6-3x}=\frac{5}{3}$
Work out the value of $x$ given that $7 : 10 + x = 2 : x$

'4' ✓
Given that $x>0$ Work out the value of $x$ given that $3x+1 : x+3 = 2x+4 : x+2$

'5' ✓
Given that $x>0$ Work out the value of $x$ given that $x : 2x+7= 2x+5 : 10x+13$ Give your answer as a decimal.

'3.5' ✓

Worksheet

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Lesson Details

Key learning points

Equivalent ratios have a scalar multiplier.
Two equations can be written which are simultaneous.
This can be set equal to each other and then solved.

Common misconception

When $x : y$ are in the ratio 1 : 2 pupils write the equation as $x = 2y$

Show that the equation $x = 2y$ in a ratio table would mean the multiplier from $y$ to $x$ would be times by 2, this would mean when $y=1 x=2$ which is 2 : 1 not 1 : 2

Keywords

Proportionality - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.
Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
Factorise - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.