Table of Conversion and Factor of Conversion
The relationships between \( \text{yards (yd)} \), \( \text{feet (ft)} \), and \( \text{inches (in)} \) are given by:
Examples of Conversion with Solutions
Example 1
Convert \( 7 \text{ ft} \) to \( \text{in} \).
View Solution
Since \( 1 \text{ ft} = 12 \text{ in} \) (given in the table of conversion above), substitute \( \text{ft} \) by \( 12 \text{ in} \) in the given "\( 7 \text{ ft} \)" and multiply as follows:
\[ 7 \text{ ft} = 7 \times 12 \text{ in} \]Evaluate:
Example 2
Convert \( 5 \text{ yd} \) to \( \text{ft} \).
View Solution
Since \( 1 \text{ yd} = 3 \text{ ft} \) (given in the 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:
Example 3
Convert \( 12 \text{ ft} \) to \( \text{yd} \).
View Solution
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 \( \text{yd} \):
Example 4
Convert \( 36 \text{ in} \) to \( \text{ft} \).
View Solution
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 \( \text{ft} \):
Example 5
Convert \( 17 \text{ ft} \) to \( \text{yd} \) and \( \text{ft} \).
View Solution
From the 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:
\[ 17 \text{ ft} = 5 \times (3 \text{ ft}) + 2 \text{ ft} \]Substitute \( 3 \text{ ft} \) by \( \text{yd} \):
Example 6
Convert \( 21.4 \text{ ft} \) to decimal \( \text{yd} \) and round the answer to two decimal places.
View Solution
From the 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 and round to two decimal places:
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 \( 1 \text{ yd} = 3 \text{ ft} \). Substitute \( \text{yd} \) by \( 3 \text{ ft} \) in \( 9 \text{ yd} \):
\[ 9 \text{ yd} = 9 \times (3 \text{ ft}) \]Multiply and evaluate:
\[ 9 \text{ yd} = (9 \times 3) \text{ ft} \]\[ 9 \text{ yd} = 27 \text{ ft} \] -
Convert \( 5 \text{ ft} \) to \( \text{in} \)
It is known from the table of conversion that \( 1 \text{ ft} = 12 \text{ in} \). Substitute \( \text{ft} \) by \( 12 \text{ in} \) in \( 5 \text{ ft} \):
\[ 5 \text{ ft} = 5 \times (12 \text{ in}) \]Multiply and evaluate:
\[ 5 \text{ ft} = (5 \times 12) \text{ in} \]\[ 5 \text{ ft} = 60 \text{ in} \] -
Convert \( 21 \text{ ft} \) to \( \text{yd} \)
Using the table of conversion, we have \( 1 \text{ yd} = 3 \text{ ft} \). Divide \( 21 \) by \( 3 \) to obtain \( 7 \):
\[ 21 \text{ ft} = 7 \times (3 \text{ ft}) \]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, \( 1 \text{ ft} = 12 \text{ in} \). Divide \( 36 \) by \( 12 \) to obtain \( 3 \):
\[ 36 \text{ in} = 3 \times (12 \text{ in}) \]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 \( 36 \text{ in} \):
\[ 3 \text{ yd} = 3 \times 36 \text{ in} \]Multiply and evaluate:
\[ 3 \text{ yd} = (3 \times 36) \text{ in} \]\[ 3 \text{ yd} = 108 \text{ in} \] -
Convert \( 32 \text{ in} \) to \( \text{ft} \) and \( \text{in} \)
Since \( 1 \text{ ft} = 12 \text{ in} \), divide \( 32 \) by \( 12 \) to obtain \( 2 \) with a remainder of \( 8 \):
\[ 32 = 2 \times 12 + 8 \]Write as units:
\[ 32 \text{ in} = 2 \times 12 \text{ in} + 8 \text{ in} = 2 \text{ ft} + 8 \text{ in} \]\[ 32 \text{ in} = 2 \text{ ft } 8 \text{ in} \] -
Convert \( 41 \text{ in} \) to decimal \( \text{yd} \)
From the table of conversion, \( 1 \text{ yd} = 36 \text{ in} \). Divide \( 41 \) by \( 36 \):
\[ 41 \text{ in} = (41 \div 36) \text{ yd} \approx 1.13888888889 \text{ yd} \]Round to two decimal places:
\[ 41 \text{ in} = 1.14 \text{ yd} \]