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Reveal Math · Unit 4 · Supplemental

Decimals & Percents

Extra support and enrichment for decimal operations, long division, fraction-decimal-percent conversions, and finding the percent of a number. Standards 6.NS.B.2, 6.NS.B.3, 6.RP.A.3c.

🖨️ Differentiated Practice Worksheets

Ready-to-print practice at three levels — pick the right fit for each student.

Level 0 · Extra Support Scaffolded steps, worked examples, extra space. Level 1 · Support Guided practice on the core skills. Level 2 · Enrichment Stretch problems and deeper reasoning.

Visual Vocabulary

3.75 decimal point
Decimal
Decimal
A number with a dot (decimal point) that shows parts smaller than 1. The digits after the dot are tenths, hundredths, etc.
ones . tenths 5 . 3
Place Value
Valor posicional
Each spot in a number has a value. After the decimal: tenths (0.1), hundredths (0.01), thousandths (0.001).
75 out of 100 75%
Percent
Porcentaje
A number out of 100. The symbol % means "per hundred." 75% means 75 out of every 100.
3/4 = 0.75 = 75%
Equivalent Forms
Formas equivalentes
The same amount written as a fraction, decimal, or percent. 3/4 = 0.75 = 75%.
dividend divisor 845 5
Long Division
Division larga
A step-by-step method to divide large numbers. Steps: Divide, Multiply, Subtract, Bring down. Repeat!
multiply 2.5 x 0.3 0.75
Decimal Multiplication
Multiplicacion decimal
Multiply without the decimals first, then count total decimal places in both numbers and put the decimal point in the answer.
25% of 80 = 20
Percent of a Number
Porcentaje de un numero
To find a percent of a number, change the percent to a decimal and multiply. 25% of 80 = 0.25 x 80 = 20.
~ estimate: about 25%
Estimate Percent
Estimar porcentaje
Use friendly percents (10%, 25%, 50%) to make quick guesses. 10% = divide by 10. 50% = divide by 2.

Sentence Frames

The decimal   is the same as the fraction   and the percent  .
To change a fraction to a decimal, I   the numerator by the  .
To change a decimal to a percent, I move the decimal point   places to the  .
  percent of   is   because   x   =  .
When I multiply decimals, the answer has   decimal places because   +   =  .
I can estimate  % of   by finding  % first, then  .

Step-by-Step Visual Guides

How to Convert Between Fractions, Decimals, and Percents

Fraction Decimal Percent divide top by bottom make denominator 100 x 100 and add % / 100 to go back
1 Fraction → Decimal: Divide the numerator by the denominator. Example: 3/8 = 3 / 8 = 0.375
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2 Decimal → Percent: Multiply by 100 (move decimal 2 places right) and add %. Example: 0.375 = 37.5%
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3 Percent → Decimal: Divide by 100 (move decimal 2 places left). Example: 37.5% = 0.375

How to Find the Percent of a Number

Find 30% of 60.

1 Change the percent to a decimal: 30% = 0.30
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2 Multiply: 0.30 x 60 = 18
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3 Check: 30% is a bit less than one-third. One-third of 60 is 20. Is 18 close to 20? Yes!
30%
01860

How to Do Long Division (DMSB: Divide, Multiply, Subtract, Bring down)

Solve: 846 / 6

D Divide: How many times does 6 go into 8? 1 time. Write 1 above the 8.
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M Multiply: 1 x 6 = 6. Write 6 under the 8.
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S Subtract: 8 - 6 = 2.
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B Bring down the next digit (4) to make 24. Now repeat: 24 / 6 = 4. Continue until done. Answer: 141.

Simplified Practice

  1. Write 0.6 as a fraction and a percent.
    0.6 means 6 tenths. As a fraction: 6/10 (simplify!). For percent: move the decimal 2 places right.
    Fraction: 6/10 = 3/5. Percent: 60%.
  2. Write 45% as a decimal and a fraction.
    Decimal: divide by 100 (move decimal 2 places left). Fraction: 45/100, then simplify.
    Decimal: 0.45. Fraction: 45/100 = 9/20.
  3. Write 3/4 as a decimal and a percent.
    Divide 3 by 4 to get the decimal. Then multiply by 100 for the percent.
    Decimal: 3 / 4 = 0.75. Percent: 75%.
  4. Find 50% of 84.
    50% means half. Divide 84 by 2.
    84 / 2 = 42.
  5. Find 10% of 250.
    10% means divide by 10. Just move the decimal point one place left.
    250 / 10 = 25.
  6. Find 25% of 120.
    25% means one quarter. Divide 120 by 4. Or: change 25% to 0.25 and multiply.
    0.25 x 120 = 30. (Or 120 / 4 = 30.)
  7. Solve: 4.5 + 2.38
    Line up the decimal points. Write 4.5 as 4.50 so both have 2 decimal places. Add normally.
    4.50 + 2.38 = 6.88.
  8. Solve: 0.6 x 0.4
    Multiply 6 x 4 = 24. Count decimal places: 1 + 1 = 2 decimal places in the answer.
    0.24 (6 x 4 = 24, then place the decimal to make 2 decimal places).
  9. Solve: 156 / 12 using long division.
    12 goes into 15 one time (12). Subtract: 15-12=3. Bring down 6 to make 36. 12 goes into 36 exactly 3 times.
    13. (12 goes into 15 once with remainder 3, bring down 6 to get 36, 36/12 = 3.)
  10. Estimate 19% of 50. (Use a friendly percent.)
    19% is close to 20%. Find 20% of 50 (which is 10% doubled).
    20% of 50 = 10. So 19% of 50 is about 10. (Exact: 9.5.)

Real-World Connections

SALE 20% OFF

Shopping Discounts

A shirt costs $40 and is 20% off. Find 20% of $40: 0.20 x 40 = $8 discount. Sale price: $40 - $8 = $32. Percents help you find real sale prices!

85 / 100

Test Scores

You got 85 out of 100 on a test. That is 85%. Your friend got 17 out of 20. As a percent: 17/20 = 0.85 = 85%. You scored the same! Percents help compare different totals.

TIP 15%

Restaurant Tips

A meal costs $24. You want to leave a 15% tip. Find 10%: $2.40. Find 5% (half of 10%): $1.20. Add: $2.40 + $1.20 = $3.60 tip. Estimating percents saves time!

75%

Phone Battery

Your phone is at 75%. If the full battery is 4,000 mAh, you have 0.75 x 4,000 = 3,000 mAh left. Percents tell you what fraction of a full amount you have.

Challenge Problems

  1. A store marks up items by 40%, then offers a 25% discount. If the original price is $50, what is the final price? Is the final price equal to the original price plus 15%? Medium
    First apply the 40% markup to $50. Then take 25% off that new price. Compare to $50 + 15%.
    Markup: $50 x 1.40 = $70. Discount: $70 x 0.75 = $52.50. Compare: $50 x 1.15 = $57.50. No! $52.50 is not equal to $57.50. A 40% increase followed by a 25% decrease is not the same as a 15% increase.
  2. Calculate: 3.14 x 2.5 without a calculator. Show your work. Medium
    Multiply 314 x 25 first (ignoring decimals), then place the decimal. Total decimal places: 2 + 1 = 3.
    314 x 25 = 314 x 20 + 314 x 5 = 6,280 + 1,570 = 7,850. Place decimal (3 places): 7.850. Answer: 7.85.
  3. A population of 8,000 grows by 5% each year. What is the population after 1 year? After 2 years? Hard
    After 1 year: multiply by 1.05. After 2 years: multiply the year-1 population by 1.05 again.
    Year 1: 8,000 x 1.05 = 8,400. Year 2: 8,400 x 1.05 = 8,820.
  4. You scored 72% on a test with 25 questions. How many questions did you get right? How many more would you have needed for 80%? Medium
    72% of 25 = 0.72 x 25. For 80%: 0.80 x 25. Find the difference.
    Correct: 0.72 x 25 = 18 questions. For 80%: 0.80 x 25 = 20 questions. Needed 2 more correct answers.
  5. A coat originally costs $120. It goes on sale for 30% off. Then you have a coupon for 10% off the sale price. Sales tax is 8%. What is the total you pay? Hard
    Apply discounts one at a time: 30% off first, then 10% off that result. Then add 8% tax to the final discounted price.
    After 30% off: $120 x 0.70 = $84. After 10% coupon: $84 x 0.90 = $75.60. With 8% tax: $75.60 x 1.08 = $81.648 = $81.65.
  6. Divide 7 by 11. Write the answer as a decimal. What do you notice about the pattern? Medium
    Use long division. Keep going past the decimal point for several places.
    7 / 11 = 0.636363... The digits 63 repeat forever. This is a repeating decimal, written as 0.63 with a bar over the 63.
  7. A basketball player makes 7 out of 20 free throws in the first half and 9 out of 15 in the second half. What is her overall free throw percentage? Hard
    Add total makes and total attempts. Do NOT average the two percentages — that would be wrong because the sample sizes differ.
    Total makes: 7 + 9 = 16. Total attempts: 20 + 15 = 35. Percentage: 16/35 = 0.4571... = about 45.7%.
  8. A recipe calls for 2.75 cups of flour per batch. You have 10 cups. How many full batches can you make, and how much flour is left over? Medium
    Divide 10 by 2.75. The whole number part is the number of batches. The remainder in cups is the leftover.
    10 / 2.75 = 3.636... So 3 full batches. Flour used: 3 x 2.75 = 8.25 cups. Leftover: 10 - 8.25 = 1.75 cups.
  9. What is 0.1% of 5,000? What is 150% of 40? Hard
    0.1% = 0.001. 150% = 1.5. Percents can be less than 1 or greater than 100!
    0.1% of 5,000 = 0.001 x 5,000 = 5. 150% of 40 = 1.5 x 40 = 60. (Yes, a percent greater than 100% gives an answer bigger than the original!)
  10. In a school of 600 students, 55% are girls. 40% of the girls play a sport, and 60% of the boys play a sport. How many total students play a sport? Expert
    Find the number of girls and boys first. Then find the percent of each group that plays sports.
    Girls: 0.55 x 600 = 330. Boys: 600 - 330 = 270. Girls who play sports: 0.40 x 330 = 132. Boys who play sports: 0.60 x 270 = 162. Total: 132 + 162 = 294 students.

Real-World Investigations

Smart Shopper Challenge

Investigate which sales are truly the best deals by comparing different discount strategies.

  1. Find 3 items you would like to buy (use real prices from ads or websites)
  2. Calculate the final price for each with: 30% off, buy-one-get-one-50%-off, and $10 off $50
  3. Which discount saves the most money for each item?
  4. Does the "best" discount depend on the original price? Explain with evidence
  5. Create a "shopper's guide" explaining when each type of discount is the best value

Nutrition Label Detective

Analyze the percent daily values on food nutrition labels.

  1. Collect 5 nutrition labels from different foods
  2. Record the % Daily Value for sodium, sugar, fiber, and protein
  3. If you ate 3 servings (not 1), recalculate each percentage
  4. Create a "daily total" if these were your only foods — what % of each nutrient did you consume?
  5. Write recommendations: which foods are healthy choices based on the percents?

Savings Account Simulator

Model how money grows with interest using decimals and percents.

  1. You start with $500 in a savings account earning 3% interest per year
  2. Calculate your balance at the end of each year for 5 years (add 3% of the current balance each year)
  3. Create a table: Year, Starting Balance, Interest Earned, Ending Balance
  4. How much total interest did you earn over 5 years?
  5. Compare: What if the interest rate were 5% instead? How much more would you earn?

Brain Teasers

The Shrinking Price

A price increases by 20%, then decreases by 20%. Is the final price the same as the original? Prove it with a $100 example.

Start: $100. After 20% increase: $100 x 1.20 = $120. After 20% decrease: $120 x 0.80 = $96. The final price is $96, NOT $100. You lose $4! This happens because the 20% decrease is applied to a larger number ($120).

The Decimal Detective

I am a decimal between 0 and 1. When you multiply me by myself, I get smaller. When you divide 1 by me, you get a number greater than 1. My digits add up to 9, and I have exactly 2 decimal places. What am I?

A decimal between 0 and 1 with 2 decimal places: 0.__ __. The digits after the decimal add to 9. Possibilities: 0.18, 0.27, 0.36, 0.45, 0.54, 0.63, 0.72, 0.81, 0.90. All satisfy the multiplication property (any number between 0 and 1 gets smaller when squared). Multiple answers work! Some examples: 0.45 x 0.45 = 0.2025 (smaller). 0.72 x 0.72 = 0.5184 (smaller).

The 99.9% Trap

A factory claims 99.9% of its products pass quality control. They produce 10,000 items per day. How many defective items are made each day? Each week (5 days)?

Defective rate = 100% - 99.9% = 0.1% = 0.001. Daily defects: 0.001 x 10,000 = 10 items. Weekly: 10 x 5 = 50 defective items. Even 99.9% is not perfect when the numbers are large!

The Tip Trick

To calculate a 15% tip mentally, you find 10% and then add half of that. A meal costs $73.40. Without a calculator, estimate a 15% tip to the nearest dollar.

10% of $73.40 = $7.34. Half of $7.34 = $3.67. Total 15% tip: $7.34 + $3.67 = $11.01. Rounded to the nearest dollar: about $11.

Extension Topics

Where This Leads: Percent Change (7th Grade)

In 7th grade, you will learn to calculate percent increase and percent decrease using the formula: percent change = (amount of change / original) x 100. You already know how to find the percent of a number — this is the reverse: finding WHAT percent a change represents.

Where This Leads: Proportional Relationships & Equations

Finding "25% of 80" is the same as solving 0.25 x 80 = n. In algebra, you will solve problems like: "What percent of 80 is 20?" This becomes n/100 x 80 = 20, and you solve for n. Percent problems are really proportion problems in disguise.

Where This Leads: Compound Interest & Exponential Growth

When a savings account earns 5% interest each year, the money grows by multiplying by 1.05 each year. Over many years, this creates exponential growth — the amount increases faster and faster. This is a key concept in high school math and personal finance.

Self-Assessment

Rate your confidence: 1 = Need help, 2 = Getting there, 3 = Got it, 4 = Can teach it

  • I can add and subtract decimals by lining up the decimal point
  • I can multiply decimals and correctly place the decimal point
  • I can perform long division with multi-digit numbers
  • I can convert between fractions, decimals, and percents
  • I can find the percent of a number (e.g., 25% of 80)
  • I can estimate percents using benchmarks (10%, 25%, 50%)
  • I can solve real-world percent problems (discounts, tips, tax)
  • I understand that percent increase then decrease does not cancel out