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

I can…

I can use equivalent ratio tables to determine the whole when I know a part and the percent it represents.

Key words

• Determine the Whole Given the Part and Percent — Use a part and its percent to find the whole.
• Part — A piece of the whole.
• Whole — The full amount. It is always 100%.
• Double number line — Two number lines side by side. Marks that line up go together.
• Equation — A math sentence with an equal sign.
• Percent — A number out of 100, shown with the % sign.
• Inverse operation — Two actions that undo each other, like × and ÷.

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. I put the matching values in a ratio table: 60% pairs with $42. I want a friendly 10% row, so I divide both values by 6: 10% pairs with $7.
3. To reach the whole, I multiply both values in the 10% row by 10: 100% pairs with $70. The original price is $70, which is larger than the sale price.
4. I can check the table with an equation: 0.6 × v = 42, so v = 42 ÷ 0.6 = 70. The equation describes the same part-to-whole relationship.

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 an equivalent ratio table helps me scale a known part and percent to 100%.