See It 1: Percent as a bar of ten blocks
In this module every question becomes a picture first. One bar = the whole = 100%. In the bars below each block is 5% of the whole, so ten blocks make 50% and twenty blocks make the full 100%.
See the basics first
Every picture in this module starts from one idea: 100 equal squares make the whole.
1. What is a percent? "Per cent" means per hundred. 35% means 35 out of every 100. Think of ₹100 as 100 coins of ₹1. If you spend 35 of the coins, you spent 35 out of 100, which is 35% of your money. On a 100-square grid each square is 1%, so 35% is 35 shaded squares:
███████████████████████████████████·································································
Text version: 35 of the 100 squares are shaded (35%); 65 are not (65%).
2. What does "of" mean? "Of" tells you which thing the percent is taken from. "35% of ₹200" means: cut ₹200 into 100 equal pieces (each piece is ₹200 ÷ 100 = ₹2) and take 35 pieces: 35 × ₹2 = ₹70.
3. Whole and part. The number after "of" is the whole: all of it, 100%. A part is a piece of the whole. The rest is what is left: whole − part, which is (100 − percent)%. In the example: whole ₹200, part ₹70 (35%), rest ₹130 (65%).
4. The one tool you will use in every question: find 1% first. 1% of anything = that thing ÷ 100. From 1% you can build any percent (multiply by the percent) or get back to the whole (multiply by 100). Try it now: 1% of ₹300 = 300 ÷ 100 = ₹3, so 35% of ₹300 = 35 × 3 = ₹105.
Words to know
- Percent (%)
- out of every 100 35% = 35 out of 100
- Whole
- the number after 'of' = 100% ₹200 in '35% of ₹200'
- Part
- a piece of the whole ₹70 = 35% of ₹200
- Rest
- whole − part ₹130 = 65% of ₹200
- 1%
- whole ÷ 100 1% of ₹200 = ₹2
Think of a thali with 100 small portions.
The full thali Whole (base)
Always 100%, whatever its rupee value.
The portions you eat Part
A number of rupees, grams or people.
Portions out of 100 Percent
How many hundredths of the thali you ate.
Picture: 35% of 180
| Bar | Picture (each █ = 5% of 180) | Value |
|---|---|---|
| Whole | ████████████████████ | 180 |
| 35% | ███████░░░░░░░░░░░░░ | 63 |
Text version: The whole bar is 180, so each 5% block is 180 ÷ 20 = 9. Seven blocks (35%) are 7 × 9 = 63.
Question
What is 35% of 180?
Solution
- What is the question asking?
- 180 students is the whole: all of it, 100%.
- We need 35% of it: a smaller part of 180 students.
- Make it a story
- A school has 180 students. 35% of them come by school bus. How many students is that?
- We know / We need
- We know: 100% of all the students = 180 students
- We need: 35% of all the students = ?
- Step 1: find 1%
- 100% means 100 equal pieces. One piece is 1%.
- 1% of all the students = 180 ÷ 100 = 1.8 students
- Step 2: find 35%
- 35% is 35 pieces of 1%.
- 35% of all the students = 35 × 1.8 = 63 students
- See it on a bar
███████░░░░░░░░░░░░░each block = 5% of all the students = 9 students- █ 35% = 63 students (come by bus)
- ░ 65% = 117 students (come another way)
- Whole bar = 100% = 180 students
- Shortcut (only after you understand)
- Part = Percent × Whole ÷ 100 = 35 × 180 ÷ 100 = 63
- Faster way (optional): With the bar: one 5% block = 180 ÷ 20 = 9 students, and 35% = 7 blocks = 7 × 9 = 63.
- Quick check
- Part + rest = 63 + 117 = 180 ✓
- 35% is less than half, so the part must be less than half of 180 students ✓
Answer: 63 students
Watch out: Most important concept: The whole is the number that comes after 'of' (180 students). Always find 1% of the whole first. The answer 63 students is a part, so it must be smaller than 180 students.
Try it
The bar shows 240 split into ten equal blocks. Seven blocks are shaded. What is the shaded amount?
Show answer
Correct answer: C
Ten blocks of 24; seven shaded = 168 = 70% of 240.
Option A: Answered the remainder: 72 is the three unshaded blocks.
Option B: Decimal slip: 16.8 is only 7% of 240, a decimal slip.
Option D: Guessed: 170 is a rounded guess; 7 × 24 is exactly 168.
Hint: Find one block first.
Picture: the whole from a part
Question
36 students walk to school. That is 20% of all the students. How many students are there?
Solution
- What is the question asking?
- 36 students is only a part. It is 20% of a bigger number.
- We must find that bigger number: the whole, which is 100%.
- Make it a story
- In another school, the 36 students who walk are 20% of all the students.
- We know / We need
- We know: 20% of all the students = 36 students
- We need: 100% of all the students = ?
- Step 1: find 1%
- 20% of all the students = 36 students
- 20% means 20 equal pieces of 1%. Share 36 students equally among 20 pieces.
- 1% of all the students = 36 ÷ 20 = 1.8 students
- Step 2: find 100%
- 1% of all the students = 1.8 students
- 100% is 100 such pieces: 100% of all the students = 1.8 × 100 = 180 students
- See it on a bar
████░░░░░░░░░░░░░░░░each block = 5% of all the students- █ 20% = 36 students (walk)
- ░ 80% = 144 students (come another way)
- Whole bar = 100% = 36 students + 144 students = 180 students
- Shortcut (only after you understand)
- Whole = Part × 100 ÷ Percent = 36 × 100 ÷ 20 = 180
- Faster way (optional): With the bar: 20% = 4 blocks of 5% = 36, so one block = 9 and the whole bar (20 blocks) = 180.
- Quick check
- 20% of 180 students = 180 × 20 ÷ 100 = 36 students ✓
- Part + rest = 36 + 144 = 180 ✓
Answer: 180 students
Watch out: Most important concept: 36 students is only a PART of all the students. Work backward from the part to the whole (100%). Do not calculate 20% of 36: that gives 7.2, which is even smaller than the part.
| Bar | Picture (each █ = 5% of the whole) | Value |
|---|---|---|
| Shaded 30% | ██████░░░░░░░░░░░░░░ | 54 |
| Whole ? | ████████████████████ | ? |
Text version: Six shaded 5%-blocks hold 54. The whole bar has 20 blocks.
On a bar, 30% is shaded and the shaded part is 54. What is the whole bar?
Show answer
Correct answer: A
Shaded 3 blocks = 54 → 1 block = 18 → whole = 180.
Option B: Took percent of the part: 16.2 is 30% of 54.
Option C: Answered the remainder: 126 is the unshaded 70% of a 180 bar, not the whole.
Option D: Percent read as units: 84 adds 30 to 54.
Hint: How many 10%-blocks are shaded?
Test your understanding: on a bar, 40% is shaded and the shaded part is ₹26. What is the whole bar?
Show answer
Correct answer: D
We know: 40% of the bar = ₹26. Step 1: 1% = 26 ÷ 40 = ₹0.65 (or 10% = 26 ÷ 4 = ₹6.50). Step 2: 100% = 0.65 × 100 = ₹65. Bar: 40% = ₹26 shaded, 60% = ₹39 unshaded, total ₹65 ✓.
Option A: Took percent of the part: ₹10.40 is 40% of ₹26. But ₹26 is the shaded piece, not the whole bar.
Option B: Added the percent: ₹66 = 26 + 40 adds a percent to rupees.
Option C: Wrong block count: ₹104 = 4 × 26 counts 4 blocks of 10% as the whole. The whole bar is 10 blocks of 10%.
Hint: Shaded 4 blocks of 10% = ₹26. Find one block.
Shading the wrong bar. The number after of is the full bar; the other number is a piece of it. If you are given the piece, the full bar is bigger.
Five questions are attached below. Sketch a bar on rough paper for each one.
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