Free Ratio and Proportion 01 Practice Test - 6th grade 

A ratio is a method by which two similar quantities are compared by using division.

Two or more quantities can be compared only when they have same unit. If they are not, they must be converted into the same units.

Example: Weight in gram cannot be compared to length in metre and weight in grams and kilograms can be compared only when kilograms is converted into grams or grams into kilograms so that both will be in same unit.

Ratio is a method of comparing two quantities having the same unit,

2 m = 200 cm

Hence, the ratio of the length of the snake to crocodile would be
$\frac{10}{200}=\frac{1}{20}=1:20$

There are 30 days in the month of April. So, the ratio of holidays to the number of days in April would be
$\frac{6}{30}=\frac{1}{5}=1:5$

A ratio obtained by multiplying or dividing the numerator and the denominator of a given ratio by the same number is called an equivalent ratio.

Hence, when the numerator and the denominator of the given ratio 3 : 2 are multiplied by 4, we get

$\frac{3\times 4}{2\times 4}$ = $\frac{12}{8}=12:8$

$\therefore$ 3 : 2 and 12 : 8 are equivalent ratios.

Partnership is directly proportional to the amount invested. As amount invested increases patnership(profit) increases. Hence they are directly proportional.

Two ratios are said to be in proportion if they are equivalent or equal.
Consider 3:5 :: 12:20
$12:20=\frac{12}{20}=\frac{3}{5}=3:5$
Hence, they are in proportion

Consider 1:2::3:6
$3:6=\frac{3}{6}=\frac{1}{2}=1:2$
Hence, they are in proportion.
Note that 2: 3 and 4: 9 are not in proportion as the product of extremes (2 $\times$ 9 = 18) is not equal to product of means (3  $\times$ 4 = 12).
Similarly, 1:2 and 4:5 are not in proportion as the product of extremes (1 $\times$ 5 = 5) is not equal to product of means (2  $\times$ 4 = 8).

Ratios are in proportion if they are equal or equivalent. This can be verified by using the product of means and product of extremes.

In a: b :: c: d; 'b' and 'c' are means and 'a' and 'd' are extremes.

For 4 kg : 20 kg :: ₹ 50 : ₹ 250

Product of means = 20 $\times$ 50 = 1000
Product of extremes = 4 $\times$ 250 = 1000
So, this is in proportion.

For 2 dozens : 3 dozens :: ₹ 40 : ₹ 80

Product of means = 3 $\times$ 40 = 120
Product of extremes = 2 $\times$ 80 = 160

So, this is not in proportion.

For  8 liters : 15 liters :: ₹ 25 : ₹ 50
Product of means = 15 $\times$ 25 = 375
Product of extremes = 8 $\times$ 50 = 400

So, this is also not in in proportion.

For  2 km : 3 km :: 1 m : 2m
Product of means = 3 $\times$ 1 = 3
Product of extremes = 2 $\times$ 2 = 4

So, this is also not in in proportion.

Weight of 80 identical books = 400 kg
Weight of 1 such book
$=\frac{400}{80}=\frac{10\times 40}{10\times 8}=\frac{40}{8}=5kg$

To decrease a quantity in the given ratio a : b, we multiply the given
$\text{quantity by}\frac{b}{a}$, 
where b < a.

Hence, new quantity
= $1551\times \frac{7}{11}$
= $141\times 7$
= $987$