Question Video: Simplifying Ratios between Two Quantities Involving Area Unit Conversions Mathematics

Area a is 2/5 m². Area b is 415 dm². Express the ratio of areas a : b in its simplest form.

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Video Transcript

Area a is two-fifths square metres. Area b is 415 square decimetres. Express the ratio of areas a to b in its simplest form.

Let’s start by noticing that the areas are given in different units. The area of a is given in square metres. And the area of b is given in square decimetres. We will need to convert these into the same unit. But let’s start by looking at area a. It will be good if we could write the fractional value of two-fifths as a decimal. We can recall that one-fifth is equal to 0.2. So two-fifths must be equivalent to double that, which is 0.4. So two-fifths of a square metre is equal to 0.4 square metres. Area b is given as 415 square decimetres. So we will need to use a conversion between square metres and square decimetres. And that is that one square metre is equal to 100 square decimetres.

So let’s change our area a in square metres into square decimetres. To do this, we take our value of 0.4. And we multiply it by 100, giving us 40. So now, we can say that area a is equivalent to 40 square decimetres. The question then asks us to express these areas as a ratio, with a first and then b. So we write our values of 40 to 415. And we don’t worry about units in a ratio. Now, we need to see if we can write this ratio in a simpler form. We can notice that since 40 ends in zero and 415 ends in five, then both of these numbers must be divisible by five. So dividing both sides of our ratio by five will give us eight to 83. Since we can’t simplify this any further, this will be our final answer.

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