Question

How many 1 3/4 foot pieces of ribbon can be cut from a piece of ribbon that is 36 feet long?

Answer 1

about 20 complete pieces can be cut

Explanation:

Answer 2

Approximately 20 complete pieces of 1 3/4 foot of ribbon can be obtained.

Explanation:

You have a piece of ribbon 36 feet long that should be divided into pieces of 1
`(3)/(4)` feet. In order to know the quantity of pieces of said measurement, the total length of the ribbon (36 feet) must then be divided by the desired measurement of each of the pieces (1 3/4 feet):

`amount of pieces of ribbon=(36)/(1 (3)/(4) )`

1
`(3)/(4)` is a mixed number. A mixed number or mixed fraction consists of a whole part (natural number) and a fractional part. All fractions greater than unity can be expressed as a mixed number.

To be able to make the division stated previously, it is convenient to pass the mixed number to an improper fraction (An improper fraction is a fraction in which the numerator is greater than or equal to the denominator). For this you multiply the denominator by the whole number. To the result, you must add the numerator. Then that number is placed over the original denominator. Expressed in general is:

`a (b)/(c) =(a*c+b)/(c)`

In this case:

`1 (3)/(4) =(4*1+3)/(4)=(7)/(4)`

Then the previously stated division is expressed as:

`(36)/((7)/(4) )`

One way to perform this division is to reverse the SECOND FRACTION, that is, change the denominator to the numerator and change the numerator to the denominator. Then, both numbers are multiplied.

`(36)/((7)/(4) ) =36*(4)/(7)`

Given that 36 can be expressed as 36/1, the multiplication is done "online." That is, the numerator of the first fraction by the numerator of the second and the denominator of the first fraction by the denominator of the second.

`(36)/(1) *(4)/(7) =(36*4)/(1*7) =(144)/(7)`

Now it will be passed from fraction to mixed number. For that, the numerator is divided by the denominator. The quotient of the division becomes the integer of the mixed number. The rest of the division is the numerator of the fraction. The denominator is the same as that of the fraction, being the divisor of the division.

When dividing 144 by 7 the quotient is 20, the remainder is 4 and the divisor is 7. Then the mixed number formed is
`20 (4)/(7)`

This indicates that approximately 20 complete pieces of 1 3/4 foot of ribbon can be obtained.