03 Solving Percent Problems Numerically : Finding Whole and Amount

Finding whole and amount #

Let’s try to find the value of percentages numerically as well, since making tape diagrams for bigger numbers is not feasible.

Going back to our previous question, we have - “What is 30% of 50?”

We can write it as 30% of 50 = ?

50 is the whole here and 30% is the part of this whole or a fraction of this whole.

This means we can write 30% of 50 as 30% x 50. Think of how we used to do the same for fractional multiplication like ⅓ of 5 is ⅓ x 5. In this case, what do we do with the 30% value? Do we simply multiply? This will give us 1500%. What does this mean? We do not need an answer in percent form, but actual numbers. Let;s convert the 30% into what it actually means, 30 parts per 100 parts. This is given by the ratio 30 : 100, but we cannot calculate using this form. Remember when we learnt that ratios can be written as fractions as well? This helps us calculate the above case. 30:100 can be written as 30/100.

We have, 30% x 50 = 30/100 x 50 = 15

This tells us that taking a percent of a whole is simply multiplication. And that P% of a whole can be solved by writing it as P/100 of whole.

In the second example from before, we have - “if 140% of some weight is 28 kg, what is 100% of the same weight?”

We can write it as 140% of total weight = 28

140% is the percent of the whole, whose value is equal to 28. We do not have the value ofr the whole here.

This is similar to the previous case but the missing value this time is different.

Let’s compare once to clarify:

30% of 50 = ? 140% of ? = 28

In the first case, we needed to find the value that corresponded with a percent of the whole. In the second case, we need to find the whole based on the value of percent given.

With the equation formed, we solve the second question in a similar manner.

140% of total weight = 28 140% x total weight = 28 140/100 x total weight = 28 Total weight = 28x100/140 = 20

Easy right?

These are two types of percent problems you might face. Finding the value of the percent of some whole. Finding the whole based on the value of percent.

There is one final type of percent problem that we will learn about later.

Questions like: What percentage is 5 out of 20?