Lesson 5: Determine the Whole Given the Part and Percent6.AT.4

I can…

I can determine the whole when I know a part and the percent that part represents.

Key words

• Determine the Whole Given the Part and Percent — Working backwards from a part and its percent to find the whole amount it came from.
• Part — The amount you already know — the piece of the whole that the percent describes.
• Whole — The full amount the percent is measured against. The whole is always 100%.
• Double number line — Two lines lined up — dollars on one, percents on the other — so matching marks show the same amount two ways.
• Equation — A math sentence with an equal sign. Here it says percent × whole = part, with the whole unknown.
• Percent — A ratio comparing a number to 100. To compute with it, write it in decimal form: 60% = 0.6.
• Inverse operation — The operation that undoes another operation.

Steps

1. Akela paid $42 for a sweater on sale, and that was 60% of the original price. The $42 is the part; the original price is the whole, which is 100%.
2. On a double number line, I put $42 under 60%. To find a smaller step, I use 10%: if 60% is $42, then 10% is 42 ÷ 6 = $7.
3. Now I count up to the whole: 100% is ten of those 10% steps, so 10 × $7 = $70.
4. The equation says the same thing in one move: 0.6 × v = 42, so v = 42 ÷ 0.6 = 70. The original price was $70 — larger than the sale price, which is exactly what a discount should mean.

Try it

A bike's sale price is $36, which is 40% of the original price. What was the original price?

Check your answer

$90, because 36 ÷ 0.4 = 90

Percent × whole = part, so 0.4 × v = 36. Dividing both sides by 0.4 gives v = $90 — larger than the sale price, as a discount requires.

Sentence starter

I know ___ because ___.

Goal: I can explain how I found the whole using the words part, whole, percent, and equation.