Video: Solving Word Problems by Dividing a Decimal Number by Another

A wood plank of length 4.5 feet was cut into 0.25 foot pieces. Determine how many pieces of wood there are.

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Video Transcript

A wood plank of length 4.5 feet was cut into 0.25-foot pieces. Determine how many pieces of wood there are.

The total length of the wooden plank is 4.5 feet, and the lengths of the individual pieces is 0.25 foot. In order to work out how many pieces of wood there are, we need to work out how many times 0.25 goes into 4.5. So we have the calculation 4.5 divided by 0.25. We’re, therefore, being asked to divide one decimal number by another. Let’s think about how to approach this.

First, we can express this division as a fraction: 4.5 divided by 0.25 is equivalent to the fraction 4.5 over 0.25. The difficulty of the form in this division comes from the fact that we’re currently being asked to divide by a decimal. We’d much prefer to divide by an integer. What we’re going to do is find an equivalent fraction where the denominator is an integer and therefore much easier to divide by.

To convert the decimal 0.25 to an integer, we need to multiply by 100, giving the integer 25. To ensure that the fraction remains equivalent, we need to do the same thing to the numerator. So we also need to multiply 4.5 by 100, giving 450. The equivalent fraction is therefore 450 over 25. And we’re now dividing an integer by an integer.

Now there are different ways that you could perform this division, but I’m first going to cancel down by a factor of five as I know that both 25 and 450 are multiples of five. 25 divided by five is five, and 450 divided by five is 90.

So we now have the division 90 divided by five. Now you could run through your five times table to work this out, or you could perform a short division. Five goes into nine one time with a remainder of four. Five goes into 40 eight times with no remainder. So 90 divided by five is equal to 18.

As the two fractions are equivalent, the answer to this division is the answer to the original question. There are 18 pieces of wood.

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