Video: KS2-M19 • Paper 2 • Question 20

Tick the fractions that are equal to 20%. [A] 1/20 [B] 20/40 [C] 1/5 [D] 3/15 [E] 2/100

05:27

Video Transcript

Tick the fractions that are equal to 20 percent. One twentieth, twenty fortieths, one-fifth, three fifteenths, or two one hundredths.

Here, we have five different fractions. And we’re asked to identify and tick the fractions that are equal to 20 percent. Percentages are a way of showing an amount or a part out of 100. So 20 percent is the same as 20 out of 100. And the most obvious way of writing this as a fraction is as twenty hundredths, 20 out of a possible 100. Now, two of our possible fractions have got the number 20 in them. And one of them shows a denominator of 100. But none of them actually show twenty hundredths. This doesn’t mean that none of them can be equal to twenty hundredths. It just means we need to think about them. So let’s go through each fraction in turn and to try to work out what percentage each fraction is equal to.

Our first fraction is one twentieth. Ideally, we like to turn the twentieth into hundredth so that we can see a fraction out of 100. Because 20 is a factor of 100, we can multiply it by five and it will make 100. To keep the value of the fraction equal, we need to do the same to the numerator. One times five equals five. And so, one twentieth is the same as five hundredths, five out of 100. And five out of a possible 100 is the same as five percent, not 20 percent. So we don’t need to tick the first fraction.

Onto the second, in a way, this is one of the clearest ones to work out. We know that 20 percent is the same as twenty hundredths, 20 out of a possible 100. Well, this fractions shows 20 as a numerator. But it’s only out of a possible 40. That’s not the same as 20 out of 100. So we know we don’t need to tick the second fraction. Just to prove this, let’s look at what percentage twenty fortieths is worth. Twenty fortieths is the same as a half. 20 is half of 40. And we know that a half can be represented as a percentage as 50 percent.

What about one-fifth? Is that equivalent to 20 percent? Like the first fraction, we can convert this fraction into hundredths because five is a factor of 100. There are five 20s in 100. So if we multiply five by 20, we get 100. Again, we need to remember to do the same to the numerator. One multiplied by 20 equals 20. So one-fifth is the same as twenty hundredths or 20 out of 100. And we know that this is the value we’re looking for. 20 out of a possible 100 is the same as 20 percent. So let’s tick that box.

Now at this point, we need to continue going through the fractions. We look at the question. We’re asked to tick the fractions — that’s plural — that are equal to 20 percent. We’re looking for more than one. Is three fifteenths equal to 20 percent? Unfortunately, we can’t convert this fraction directly into hundredths. 15 is not a factor of 100. So we can’t multiply it by a whole number to give 100. We’re gonna have to do something else to help us find the answer. What if we try simplifying the fraction?

Both three and 15 can be divided by three. Let’s see how the fraction changes when we simplify it. Three divided by three equals one and 15 divided by three equals five. Three fifteenths is the same as one-fifth. How does this help us? Well, look back at the previous fraction. We’ve already found out that one-fifth is the same as twenty hundredths which is equal to 20 percent. So if three fifteenths is equal to one-fifth, we know that’s equal to 20 percent too. So we can tick the box for three fifteenths.

Finally, we have quite a straightforward one to end with, two one hundredths. We know that 20 percent would be written as 20 out of 100 or twenty hundredths. Well, this fraction shows two one hundredths. So it only has a value of two percent, two out of 100. So we don’t need to tick the final fraction.

We found the fractions that were equal to 20 percent by looking for equivalent fractions that were equal to those fractions that we were given. If we could convert them into hundredths, we would. And if not, we’d use reasoning to help. We didn’t just tick the fractions that had a 20 in them. We actually thought about what each fraction was worth.

So the only two ticks that we should’ve made are the two fractions that are equal to 20 percent: one-fifth and three fifteenths.

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