🔢 MathGrade 6Lesson 13
← Back🔒 PDF with full access

Find Percent of a Quantity

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

Learning Objectives

  • 1Find a percent of a whole number by converting the percent to a decimal and multiplying
  • 2Find a percent of a whole number by writing the percent as a fraction over 100 and multiplying
  • 3Use 10% as a benchmark to find 20%, 30%, 50%, and other friendly percents mentally
  • 4Solve real-world problems involving discounts, tips, and savings as percent of a quantity
📘

Mini Lesson

Finding a percent OF a quantity means asking: how big is that share of the whole? "25% of 80" asks for 25 out of every 100 of the 80 marbles, or the dollars in a sale, or the seats in a theater. The percent tells you what fraction of the whole to take, and the quantity tells you the size of the whole. Once you can convert a percent into a decimal or a fraction, finding the part is just a multiplication.

Method 1 — Decimal Method

  • Step 1 — Convert the percent to a decimal: divide by 100, which shifts the point two places left. 25% becomes 0.25; 7% becomes 0.07.
  • Step 2 — Multiply the decimal by the whole quantity. 0.25 x 80 = 20, so 25% of 80 = 20.
  • Example: 30% of 50 = 0.30 x 50 = 15.
  • Example: 8% of 200 = 0.08 x 200 = 16.
  • This method works for ANY percent, including awkward ones like 7% or 12.5%.

Method 2 — Fraction Method

  • Step 1 — Write the percent as a fraction with denominator 100. 25% = 25/100; 40% = 40/100.
  • Step 2 — Multiply the fraction by the whole quantity, then simplify. (25/100) x 80 = 2000/100 = 20.
  • You can simplify the fraction first to make the numbers easier: 25/100 = 1/4, so 25% of 80 = (1/4) x 80 = 20.
  • Useful equivalents to memorize: 50% = 1/2, 25% = 1/4, 75% = 3/4, 10% = 1/10, 20% = 1/5.
  • The fraction method is great when the percent is a friendly fraction like 1/2, 1/4, or 1/5.

Method 3 — Mental Math with 10%

  • To find 10% of any number, divide by 10 (shift the decimal point one place left). 10% of 80 = 8; 10% of 250 = 25.
  • Once you know 10%, double it for 20%, halve it for 5%, multiply by 3 for 30%, and so on.
  • Example: 30% of 80 = 3 x (10% of 80) = 3 x 8 = 24.
  • Example: 15% of 80 = 10% + 5% = 8 + 4 = 12.
  • Use 10% as a stepping stone whenever you can do the math in your head.

Real-World Percent — Discounts, Tips, and Savings

  • Discount: a 20% discount on a 50 dollar shirt saves you 20% of 50 = 10 dollars; you pay 50 - 10 = 40 dollars.
  • Tip: a 15% tip on a 40 dollar bill is 15% of 40 = 6 dollars added to the bill.
  • Savings: putting 5% of a 200 dollar paycheque into savings is 5% of 200 = 10 dollars per check.
  • Always read the question carefully: do you need the percent itself, or the new total after adding/subtracting it?
25% of 80 = 20 (bar model)A bar split into four equal quarters of 20 each, with the first quarter shaded to show 25 percent equals 20.25% of 80 = 20Whole = 80 (100%)2020202025%50%75%100%25% = 20Method: 0.25 x 80 = 20Convert percent to a decimal, then multiply.25% of 80 = (25/100) x 80 = 20.
A bar split into quarters shows 25% as one of four equal parts.
Percent of 60Three rows using dot strips to show 10 percent, 20 percent and 50 percent of 60 with results 6, 12 and 30.Percent of 6010% of 60620% of 601250% of 6030Each dot stands for 10% of 60 = 6.20% = 2 dots = 12. 50% = 5 dots = 30.Use 10% as a stepping stone for other percents.
Find 10% first, then multiply to reach any percent you need.
💡

Tip: when a percent ends in 0 or 5, the 10% method is usually fastest. When the percent is awkward, multiply by the decimal. Always estimate first — 49% of 80 should be a little less than half of 80, so close to 40.

Vocabulary
percent of a quantity
The part of a whole that the percent names; found by multiplying the whole by the percent expressed as a decimal or fraction.
decimal method
A way to find a percent of a number by converting the percent to a decimal and multiplying.
fraction method
A way to find a percent of a number by writing the percent as a fraction over 100 and multiplying.
benchmark percent
An easy percent like 10%, 25%, or 50% that you use as a stepping stone to find other percents.
discount
An amount taken off the original price; often given as a percent of the price.
Free · 7 days · No credit card

Unlock the full HSEA system for 7 days.

Add your first kid profile and your 7 days start: every lesson in every grade, saved progress for each child. Nothing to set up, no card required, nothing to cancel.

  • ✓ All 1,680 lessons, Grades 1–6, every subject
  • ✓ Profiles + saved progress for every kid
  • ✓ Printable lessons with answer key
Start your 7-day free trial →
Already convinced? See full membership plans →
← Lesson 12: Percent as Rate per HundredLesson 14: Percent Increase and Decrease →