Show how to use a percent table and either the method of going through 1% or the method of going through 1 to solve the following problems: a. 690 is 23% of what number? b: What percent of 40 is 32 C. 210 is 14% of what number? n S f d. What percent of 800 is 282'
The Correct Answer and Explanation is:
To solve percent problems, percent tables and the methods of going through 1% or going through 1 are both useful tools. Let’s solve each question using a percent table and the most appropriate method. Then, a full explanation follows.
a. 690 is 23% of what number?
Using the percent table and going through 1%:
| Percent | Value |
|---|---|
| 23% | 690 |
| 1% | 690 ÷ 23 = 30 |
| 100% | 30 × 100 = 3,000 |
Answer: 690 is 23% of 3,000
b. What percent of 40 is 32?
Using the percent table and going through 1 (whole):
| Value | Percent |
|---|---|
| 40 | 100% |
| 1 | 100 ÷ 40 = 2.5% |
| 32 | 32 × 2.5 = 80% |
Answer: 32 is 80% of 40
c. 210 is 14% of what number?
Using the percent table and going through 1%:
| Percent | Value |
|---|---|
| 14% | 210 |
| 1% | 210 ÷ 14 = 15 |
| 100% | 15 × 100 = 1,500 |
Answer: 210 is 14% of 1,500
d. What percent of 800 is 282?
Using the percent table and going through 1 (whole):
| Value | Percent |
|---|---|
| 800 | 100% |
| 1 | 100 ÷ 800 = 0.125% |
| 282 | 282 × 0.125 = 35.25% |
Answer: 282 is 35.25% of 800
📘 Explanation
Percent tables help break down percent problems by organizing information clearly. Each row in the table shows either a percent or a part of the whole value. Depending on the question, we choose either the 1% method (if a percent is known) or the going through 1 (whole) method (if the whole is known).
In problems like a and c, we are told a certain percent of a number equals a value. The 1% method is best here. For example, in (a), if 23% = 690, then 1% = 690 ÷ 23 = 30. Since 1% of a number is 30, the full (100%) number is 30 × 100 = 3,000.
In problems like b and d, we are given the whole and part, and we need to find the percent. The easiest approach is the going through 1 method. In (b), 40 is 100%, so 1 unit = 2.5%. If 1 = 2.5%, then 32 = 32 × 2.5 = 80%.
These methods are powerful because they break complex percent problems into basic multiplication and division steps. They also visually show the relationships between part, whole, and percent, making it easier for students to avoid confusion and check their work. Using a percent table ensures all information is logically aligned, which is especially helpful in word problems.
