These diagrams show three equivalent fractions. Write the missing values. Three-quarters equals nine over what equals what twenty-fourths.
The first part of the question tells us that the three diagrams show equivalent fractions. Each large rectangle may be divided into different numbers of pieces. But the shaded areas are all the same the fractions have the same value. They are equivalent. That’s why there are equal signs in between them. And the three fractions underneath refer to the three diagrams above. But two of the numbers are missing and we’re asked to write the missing values.
The first fraction shows three-quarters. Let’s see where we get this from. Each row of the first rectangle contains one piece: one, two, three, four, four parts altogether. This is where the denominator or the bottom number in the fraction comes from. It’s the total number of equal parts. But how many parts have been shaded?
In the first diagram, the shading comes as far as here. So we can see that there are three parts shaded. And this is where we get the numerator or the top number in our fraction from, the number of shaded parts. Three shaded parts out of a possible four equals three-quarters. Our second fraction is equivalent to three-quarters.
How many parts has a rectangle been divided into? Three, six, nine, 12. The rectangle has been split into twelfths. So the missing value in our fraction, the denominator, equals 12, the total number of equal parts. We can see that nine out of 12 parts have been coloured in. So nine twelfths is the same as three-quarters.
Let’s look at our final fraction. This time, the numerator is missing. This is the number of shaded parts. The denominator 24 tells us that the shape has been split into 24 equal parts: six, 12, 18 — 24 altogether. But how many out of those 24 parts have been shaded? We can see that three rows is the same as 18 parts. So eighteen twenty-fourths is the same as nine twelfths, which is also the same as three-quarters.
We found the two missing values by thinking carefully about what the numerator and the denominator stand for in a fraction. We counted the total number of the equal parts and the number of the shaded parts. And we used these to find the missing values.
Three-quarters equals nine twelfths equals eighteen twenty-fourths.