Ratio, Proportion, and Unitary Method Practice Flashcards

Fill-in-the-blank practice flashcards covering definitions, core properties, worked examples, and mental ability problems on ratios, proportions, direct/inverse variations, and the unitary method.

The comparison of two quantities by division is called __________.

ratio

The ratio of two non-zero numbers $x$ and $y$ is written as $x:y$, where $x$ is the first term and $y$ is the __________.

second term

The quantities to be compared in a ratio should always be in the __________ unit.

same

A ratio has no __________ because it is a comparison between two quantities.

unit

The ratio $x:y$ is in its lowest term if the HCF of $x$ and $y$ is __________.

$$1$$

To convert a given ratio $x:y$ into its simplest form, each term should be divided by the __________ of $x$ and $y$.

HCF

When we multiply or divide each term of a ratio by the same non-zero number, we get an __________ ratio.

equivalent

In a ratio, reversing the antecedent and the consequent produces a __________ ratio.

different

When two ratios are equal, they are said to be in __________.

proportion

In the proportion $a:b::c:d$, the 2nd and 3rd terms ($b$ and $c$) are called __________.

means

In the proportion $a:b::c:d$, the 1st and 4th terms ($a$ and $d$) are called __________.

extremes

Four numbers $a$, $b$, $c$, and $d$ are in proportion if the product of means equals the product of __________.

extremes

In the proportion $a:b::c:d$, the term $d$ is called the __________ proportion.

fourth

Three numbers $a$, $b$, and $c$ are said to be in a continued proportion if $a:b::b:c$, where $b$ is called the __________ proportional between $a$ and $c$.

mean

In a continued proportion $a:b::b:c$, the relationship between the three terms is expressed by the formula __________.

$$b^2 = ac$$

The method in which we find the value of a unit and then the value of the required number of units is called the __________ method.

unitary

In __________ variation, an increase in one quantity results in a corresponding increase in the other quantity.

direct

In __________ variation, an increase in one quantity causes a corresponding decrease in the other quantity.

inverse

The ratio of $30\,cm$ to $3\,m$ expressed in simplest form is __________.

$$1:10$$

The ratio of the length of copper wire ($8\,m$) to the length of steel wire ($1.6\,cm$) in simplest form is __________.

$$500:1$$

If the cost of $6$ pencils is ₹$24$, then the cost of $12$ pencils is ₹__________.

$$48$$

The ratio of $18$ erasers to $15$ erasers in simplest form is expressed as __________.

$$6:5$$

The ratio of $9$ paise to $18$ rupees is __________.

$$1:200$$

In Example 4, the ratio of the unshaded portion ($18$ squares) to the shaded portion ($12$ squares) is __________.

$$3:2$$

If Amita purchased $15$ garlands for ₹$315$, the cost of $25$ such garlands is ₹__________.

$$525$$

If $12\,m$ of copper wire costs ₹$180$, the cost of $52\,m$ of copper wire is ₹__________.

$$780$$

If a worker gets ₹$4716$ for $9$ days, he should work for __________ days to get ₹$7860$.

$$15$$

If a train covers $390\,km$ in $6$ hours, it will cover a distance of __________ $km$ in $3\frac{1}{2}$ hours at the same speed.

$$227.5$$

If $44$ men can do a piece of work in $30$ days, then $24$ men will take __________ days to do it.

$$55$$

If $42$ workers can complete a work in $72$ days, __________ workers will be needed to complete the same work in $36$ days.

$$84$$

In Test Yourself, the ratio of $4\,mm$ to $12\,cm$ in simplest form is __________.

$$1:30$$