Conversion between yards, feet and inches examples with solutions are presented including more More questions with solutions .
Table of Conversion and Factor of Conversion
The relationships between \( \text{ yards (yd)} \) , \( \text{ feet (ft)} \) and \( \text{ inches (in)} \) are given by
\( 1 \text{ yard (yd)} = 3 \text{ feet (ft)} \)
\( 1 \text{ foot (ft)} = 12 \text{ inches (in)} \)
\( 1 \text{ yard (yd)} = 36 \text{ inches (in) } \)
Examples of Conversion with Solutions
Example 1
Convert \( 7 \text{ ft} \) to \( \text{ in} \).
Solution to Example 1
Since \( 1 \text{ ft} = 12 \text{ in} \) (given in table of conversion above), substitute \( \text{ft} \) by \( 12 \text{ in} \) the given "\( 7 \text{ ft} \)" and multiply as follows
\( 7 \text{ ft} = 7 \times 12 \text{ in} \)
Evaluate
\( 7 \text{ ft} = ( 7 \times 12) \text{ in} = 84 \text{ in} \)
Example 2
\( 5 \text{ yd} \) to \( \text{ ft} \).
Solution to Example 2
Since \( 1 \text{ yd} = 3 \text{ ft} \) (given in table of conversion above), substitute \( \text{ yd} \) by \( 3 \text{ ft} \) in the given "\( 5 \text{ yd} \)" and multiply
\( 5 \text{ yd} = 5 \times 3 \text{ ft} \)
Evaluate
\( 5 \text{ yd} = (5 \times 3) \text{ ft} = 15 \text{ ft} \)
Example 3
\( 12 \text{ ft} \) to \( \text{ yd} \).
Solution to Example 3
from the table of conversion above, \( 1 \text{ yd} = 3 \text{ ft} \). Write \( 12 \text{ ft} \) as a multiple of \( 3 \text{ ft} \) as follows
\( 12 \text{ ft} = 4 \times (3 \text{ ft}) \)
Substitute \( 3 \text{ ft} \) by \( \text{ yd} \) and write
\( 12 \text{ ft} = 4 \text{ yd} \)
Example 4
Convert \( 36 \text{ in} \) to \( \text{ ft} \).
Solution to Example 4
Since \( 1 \text{ ft} = 12 \text{ in} \) (from the table of conversion above), write \( 36 \text{ in} \) as a multiple of \( 12 \text{ in} \).
\( 36 \text{ in} = 3 \times ( 12 \text{ in} ) \)
Substitute \( 12 \text{ in} \) by \( \text{ ft} \)
\( 36 \text{ in} = 3 \text{ ft} \)
Example 5
Convert \( 17 \text{ ft} \) to \( \text{ yd} \) and \( \text{ ft} \).
Solution to Example 5
From table of conversion above, \( 1 \text{ yard (yd)} = 3 \text{ feet (ft)} \), we therefore need to write \( 17 \text{ ft} \) as a multiple of \( 3 \text{ ft}\) if possible using division.
The division of \( 17 \) by \( 3 \) gives \( 5 \) and a remainder equal to \( 2 \). Hence
\( 17 = 5 \times 3 + 2 \)
which may be used to write
\( 17 \text{ ft} = 5 × (3 \text{ ft}) + 2 \text{ ft} \)
Substitute \( 3 \text{ ft} \) by \( \text{ yd} \) and write
\( 17 \text{ ft} = 5 \text{ yd} + 2 \text{ ft} \)
which may also be written as
\( 17 \text{ ft} = 5 \text{ yd} \; \; 2 \text{ ft} \)
Example 6
Convert \( 21.4 \text{ ft} \) to decimal \( \text{ yd} \) and round the answer to two decimal places.
Solution to Example 6
From table of conversion \( 1 \text{ yd} = 3 \text{ ft} \).
The number of \( \text{ yd} \) in \( 21.4 \text{ ft} \) is found by division as follows
\( 21.4 \text{ ft} = ( 21.4 \div 3 ) \text{ yd} \)
Evaluate the division
\( 21.4 \text{ ft} = 7.13333333333 \text{ yd} \)
Round to two decimal places
\( 21.4 \text{ ft} = 7.13 \text{ yd} \)
Questions
Convert the following
\( 9 \text{ yd} \) to \( \text{ ft} \)
\( 5 \text{ ft} \) to \( \text{ in} \)
\( 21 \text{ ft} \) to \( \text{ yd} \)
\( 36 \text{ in} \) to \( \text{ ft} \)
\( 3 \text{ yd} \) to \( \text{ in} \)
\( 32 \text{ in} \) to \( \text{ ft} \) and \( \text{ in} \)
\( 41 \text{ in} \) to decimal \( \text{ yd} \) and round the answer to two decimal places.
Solutions to the Above Questions
Convert \( 9 \text{ yd} \) to \( \text{ ft} \)
From the table of conversion, we have \( \; 1 \text{ yd} = 3 \text{ ft} \), hence substitute \( \text{ yd} \) by \( 3 \text{ ft} \) in the given "\( 9 \text{ yd} \)".
\( 9 \text{ yd} = 9 \times ( 3 \text{ ft}) \)
Evaluate
\( 9 \text{ yd} = ( 9 \times 3 ) \text{ ft} = 27 \text{ ft} \)
Convert \( 5 \text{ ft} \) to \( \text{ in} \)
It is known from the table of conversion that \( 1 \text{ ft} = 12 \text{ in} \), hence substitute \( \text{ ft} \) by \( 12 \text{ in} \) in the given "\( 5 \text{ ft} \)".
\( 5 \text{ ft} = 5 \times ( 12 \text{ in}) \)
Evaluate
\( 5 \text{ ft} = (5 \times 12) \text{ in} = 60 \text{ in} \)
Convert \( 21 \text{ ft} \) to \( \text{ yd} \)
Using the table of conversion, we have \( 1 \text{ yd} = 3 \text{ ft} \)
To find how many \( \text{ yd} \) are in \( 21 \text{ ft} \) , divide \( 21 \) by \( 3 \) to obtain \( 7 \), hence
\( 21 \text{ ft} = 7 \times (3 \text{ ft}) \)
Substitute \( 3 \text{ ft} \) by \( \text{ yd} \)
\( 21 \text{ ft} = 7 \text{ yd} \)
Convert \( 36 \text{ in} \) to \( \text{ ft} \)
From the table of conversion, we \( 1 \text{ ft} = 12 \text{ in} \)
Divide \( 36 \) by \( 12 \) to obtain \( 3 \), and hence write
\( 36 \text{ in} = 3 \times (12 \text{ in}) \)
Substitute \( 12 \text{ in} \) by \( \text{ ft} \)
\( 36 \text{ in} = 3 \text{ ft} \)
Convert \( 3 \text{ yd} \) to \( \text{ in} \)
It is known from the table of conversion that \( 1 \text{ yd} = 36 \text{ in} \)
Substitute \( \text{ yd} \) by \( 36 \text{ in} \) in the given "\( 3 \text{ yd} \)"
\( 3 \text{ yd} = 3 \times 36 \text{ in} \)
Evaluate
\( 3 \text{ yd} = (3 \times 36) \text{ in} = 108 \text{ in} \)
Convert \( 32 \text{ in} \) to \( \text{ ft} \) and \( \text{ in} \)
It is known from the table of conversion above, that \( 1 \text{ ft} = 12 \text{ in} \)
Divide \( 32 \) by \( 12 \) to obtain \( 2 \) and remainder equal to \( 8 \), hence
\( 32 = 2 \times 12 + 8 \)
and use the above to write
\( 32 \text{ in} = 2 \times 12 \text{ in} + 8 \text{ in} \)
Substitute \( 12 \text{ in} \) by \( \text{ ft} \)
\( 32 \text{ in} = 2 \text{ ft} + 8 \text{ in} \)
which may also be written as
\( 32 \text{ in} = 2 \text{ ft} \; 8 \text{ in} \)
\( 41 \text{ in} \) to decimal \( \text{ yd} \) and round the answer to two decimal places.
From the table of conversion, \( 1 \text{ yd} = 36 \text{ in} \), hence to find how many yards in \( 41 \text{ in} \) we use division as follows
\( 41 \text{ in} = ( 41 \div 36 ) \text{ yd} = 1.13888888889 \text{ yd} \)
Round to two decimal places
\( 41 \text{ in} = 1.14 \text{ yd} \)
