Question

How many pieces of tape $3\dfrac{4}{7}cm$ long can be cut from a tape, which is 1 metre 75 cm?

Answer 1

Hint: This question can be solved by simply dividing the length of one piece of tape which measures $3\dfrac{4}{7}cm$ long from the total length of the tape which is 1 metre 75 cm. This gives us the number of pieces of tape, each of length $3\dfrac{4}{7}cm.$

Complete step by step solution:
The length of the total tape is given as 1 metre 75 cm. Let us convert this to centimetres. We know the relation between centimetre and metre can be given as,
$\Rightarrow 1\text{ metre = 100 centimetres}$
Therefore, 1 metre and 75 centimetres can be converted to centimetres by multiplying the factor of 100 to the metres and adding with the 75 centimetres.
$\Rightarrow 1\text{ metre 75 centimetres = 100}\times \text{1+75 centimetres}$
Adding the two,
$\Rightarrow 1\text{ metre 75 centimetres = 175 centimetres}$
Now, the length of the piece of tape is given as $3\dfrac{4}{7}cm.$ In order to calculate the number of pieces of tape each of length $3\dfrac{4}{7}cm$ , we need to divide this by the total length of the tape.
Before dividing, we convert this to an improper fraction in order to simplify our calculations. We convert this mixed fraction to improper fraction as follows,
$\Rightarrow 3\dfrac{4}{7}=\dfrac{3\times 7+4}{7}$
Multiplying and adding,
$\Rightarrow 3\dfrac{4}{7}=\dfrac{25}{7}cm$
We now divide the two to calculate the number of pieces.
$\Rightarrow \dfrac{175}{\dfrac{25}{7}}$
Converting this division to multiplication by taking reciprocal of the denominator,
$\Rightarrow 175\times \dfrac{7}{25}$
Dividing 175 by 25, we get 7.
$\Rightarrow 7\times 7$
Multiplying the two,
$\Rightarrow 49$

Hence, the number of pieces of tape $3\dfrac{4}{7}cm$ long cut from a tape, which is 1 metre 75 cm is 49.

Note: We can also solve this question by adding up the length of each piece of tape $3\dfrac{4}{7}cm$ long till it is equal to the required length of tape which is 1 metre 75 cm. This is a simple method but it takes time. Hence, we can use either of the methods to solve this question.