Finding the Whole by Dividing by the Percent Fraction
Finding the Whole by Dividing by the Percent Fraction is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 5: Ratios and Rates. When the part and percent are known, find the whole by dividing: Whole = Part ÷ (Percent/100) = Part × (100/Percent). Example: '15 is 75% of what number?' → 75% = 3/4 → Whole = 15 ÷ (3/4) = 15 × (4/3) = 20. Dividing by a fraction is equivalent to multiplying by its reciprocal, making this a natural extension of fraction division skills.
Key Concepts
To find the whole when the part and percent are known, you can divide the part by the percent expressed as a fraction. This is equivalent to multiplying the part by the reciprocal of the percent fraction. $$ \text{Whole} = \frac{\text{Part}}{\text{Percent (as a fraction)}} = \text{Part} \times \text{Reciprocal of Percent Fraction} $$.
Common Questions
How do you find the whole when you know the part and percent?
Divide the part by the percent written as a fraction (or multiply by the reciprocal). Formula: Whole = Part ÷ (Percent/100). Example: 15 is 75% of what? 75% = 3/4, so Whole = 15 ÷ 3/4 = 15 × 4/3 = 20.
What does it mean to divide by a fraction?
Dividing by a fraction is the same as multiplying by its reciprocal (flip the fraction). So 30 ÷ (1/5) = 30 × 5 = 150. This is the 'keep, change, flip' rule: keep the first number, change division to multiplication, flip the second fraction.
When would you need to find the whole from a percent?
Real-world examples: '20 students is 40% of the class — how many students total?' Whole = 20 ÷ 0.40 = 50. 'You saved $15, which is 25% of the item's price — what was the price?' Whole = 15 ÷ 0.25 = $60.
What is a worked example of finding the whole?
30 is 20% of what number? 20% = 1/5. Whole = 30 ÷ (1/5) = 30 × 5 = 150. Check: 20% of 150 = (1/5) × 150 = 30. Correct.
When do Grade 6 students learn to find the whole from a percent?
This skill is in Big Ideas Math, Course 1, Chapter 5: Ratios and Rates, complementing the skills of finding the part and finding the percent as part of the complete Grade 6 percent triangle.
What are the three types of percent problems?
The three types are: (1) Find the part: Part = % × Whole. (2) Find the percent: % = Part/Whole × 100. (3) Find the whole: Whole = Part ÷ %. This problem teaches type 3.