No-Prep Independent Work Packet
Page 1

Sub Plans Math Packet Grade 6

Ratios, Percentages, and Order of Operations for Independent Practice
Name
Date
Teacher Note

This packet is designed for fully independent student work. Students should complete the pages in order, show their work clearly, and check each section before moving on.

Student Directions

Read each page carefully before you begin.

Complete every question using pencil only.

Show all work for percent and order of operations problems.

When a page is finished, go back and check your answers.

Keep your work neat and easy to read.

What Is Included
  1. Ratios review and practice
  2. Percent of a number review and practice
  3. Order of operations review and practice
  4. Mixed review, challenge problems, and answer key
Grade 5–6 Black & White PDF Ready A4 Portrait
Use this packet from beginning to end. Show your work whenever space is provided. Work carefully and independently.
Welcome / About This Book
Page 2

How to Complete This Packet

Follow the steps below so your work is complete, neat, and easy to check.
Directions
  • Read the directions at the top of each page before answering the questions.
  • Write every answer clearly on the line, in the box, or in the table provided.
  • For multi-step problems, solve carefully and keep your work in order.
  • If you finish a page early, reread the questions and check your work.
  • Complete all pages in order unless your teacher gives a different instruction.
If You Finish Early
  • Check all arithmetic again.
  • Rewrite any messy answers neatly.
  • Make sure all ratio tables are complete.
  • Look for missing steps in PEMDAS problems.
  • Review the challenge page when directed.
Show Your Work Reminder

You must show your work for percent and order of operations problems. Clear work helps you catch mistakes and earn full credit.

Check each direction as you complete it. Initial each step after you read it.
Skill Reference / Standards Page
Page 3

Math Skills in This Packet

Use this page as a quick reference before you begin the practice pages.
Ratios
  • Write a ratio to compare two quantities.
  • Simplify a ratio to lowest terms.
  • Complete ratio tables using equivalent ratios.
  • Use ratios in short word problems.
Example: If there are 4 red pencils and 6 blue pencils, the ratio of red to blue is 4:6, which simplifies to 2:3.
Percents
  • Understand percent as “out of 100.”
  • Match percents, fractions, and decimals.
  • Find a percent of a whole number.
  • Use percents in real-life situations.
Example: 25% of 40 means 25 out of every 100 parts. One fourth of 40 is 10.
Order of Operations
  • Solve expressions using parentheses first.
  • Evaluate exponents before multiplication and division.
  • Work left to right for multiplication/division, then addition/subtraction.
  • Show steps in a clear order.
Example: 6 + 2 × 5 = 6 + 10 = 16
Packet Flow
  1. Ratio review and practice
  2. Percent review and practice
  3. Order of operations review and practice
  4. Mixed review and challenge
  5. Answer key
Practice Review Independent Work
Keep this reference page nearby while you work. Use it to review vocabulary and examples.
Ratios Section
Page 4

Ratio Basics Practice

Write each ratio in simplest form using a colon ( : ).
Examples
1. 4 red marbles and 6 blue marbles → red to blue = 4:6 = 2:3
2. 10 boys and 15 girls → boys to girls = 10:15 = 2:3
1.There are 5 apples and 10 oranges. Write the ratio of apples to oranges.
2.A class has 8 pencils and 12 pens. Write the ratio of pencils to pens.
3.There are 6 red beads and 9 blue beads. Write the ratio of red to blue beads.
4.A recipe uses 3 cups of flour and 5 cups of sugar. Write the ratio of flour to sugar.
5.In a park there are 12 dogs and 4 cats. Write the ratio of dogs to cats.
6.A box has 20 green marbles and 30 yellow marbles. Write the ratio of green to yellow.
7.There are 14 boys and 21 girls in a group. Write the ratio of boys to girls.
8.A store sold 16 red shirts and 24 blue shirts. Write the ratio of red to blue shirts.
9.A jar has 18 chocolate cookies and 27 vanilla cookies. Write the ratio of chocolate to vanilla.
10.There are 25 small balls and 15 large balls. Write the ratio of small to large balls.
11.A bag contains 36 white candies and 48 black candies. Write the ratio of white to black.
12.A classroom has 40 students and 5 teachers. Write the ratio of students to teachers.
Write ratios in simplest form. Use a colon ( : ) between the numbers.
Ratios Section
Page 5

Simplify Each Ratio

Reduce each ratio to simplest form.
Example
12:18 → divide both by 6 → 2:3
Original→Simplified
4:6→
10:15→
8:12→
6:9→
14:21→
15:25→
18:24→
20:30→
Divide both numbers by their greatest common factor.
Ratios Section
Page 6

Equivalent Ratios Table

Fill in the missing values to make each table of equivalent ratios.
ABCD
123
248
XYZW
239
4912
PQRS
346
61216
MNOT
51520
124
JKLV
2515
41020
R1R2R3R4
3520
61015
FGHI
4812
31218
S1S2S3S4
4618
81216
Multiply or divide by the same number to find equivalents.
Ratios Section
Page 7

Ratio Word Problems

Read each problem carefully. Write your answer in simplest form.
1. In a class, there are 12 boys and 18 girls. What is the ratio of boys to girls in simplest form?
2. A recipe uses 3 cups of flour and 4 cups of sugar. What is the ratio of flour to sugar?
3. A bag has 20 red marbles and 30 blue marbles. What is the ratio of red to blue marbles?
4. There are 15 pencils and 25 pens in a box. Write the ratio of pencils to pens in simplest form.
5. A store sold 24 apples and 16 oranges. What is the ratio of apples to oranges?
6. A library has 40 fiction books and 60 non-fiction books. What is the ratio of fiction to non-fiction?
7. In a park, there are 9 dogs and 15 cats. What is the ratio of dogs to cats in simplest form?
8. A jar contains 35 chocolate cookies and 25 vanilla cookies. What is the ratio of chocolate to vanilla?
Write ratios in simplest form.
Ratios Section
Page 8

Find and Fix the Ratio Mistake

Each student work has a mistake. Explain what is wrong and write the correct ratio.
Student Work
Problem: 12 red marbles and 18 blue marbles
Student answer: 12:18 = 6:9
What is wrong?
Correct answer:
Student Work
Problem: 20 pencils and 30 pens
Student answer: 20:30 = 4:6
What is wrong?
Correct answer:
Student Work
Problem: 25 apples and 15 oranges
Student answer: 25:15 = 5:2
What is wrong?
Correct answer:
Student Work
Problem: 16 red beads and 24 blue beads
Student answer: 16:24 = 8:12
What is wrong?
Correct answer:
Student Work
Problem: 30 boys and 20 girls
Student answer: 30:20 = 3:1
What is wrong?
Correct answer:
Student Work
Problem: 18 chocolate and 27 vanilla cookies
Student answer: 18:27 = 6:9
What is wrong?
Correct answer:
Check if both numbers can be divided by a larger common factor.
Ratios Section
Page 9

Ratios Quick Check

Show what you know about writing, simplifying, and extending ratios.
1.Write the ratio 8:12 in simplest form.
2.Write the ratio 15:25 in simplest form.
3.Write an equivalent ratio for 2:3 by multiplying both numbers by 4.
4.Fill in the blank: 3:5 = 9:
5.There are 10 red marbles and 15 blue marbles. Write the ratio of red to blue.
6.Simplify 24:36.
7. A recipe uses 4 cups of flour and 6 cups of sugar. What is the ratio of flour to sugar in simplest form?
8. In a class there are 16 boys and 24 girls. What is the ratio of boys to girls?
9. A bag has 30 green marbles and 20 yellow marbles. Write the ratio of green to yellow in simplest form.
10. A store sold 18 apples and 12 oranges. What is the ratio of apples to oranges?
Check all your work before finishing.
Percents Section
Page 10

Percent Means Out of 100

Complete the table by matching percents, fractions, and decimals.
Reference
25% = 25 out of 100 = 25/100 = 0.25
50% = 50 out of 100 = 50/100 = 0.50 = 0.5
PercentFractionDecimal
10%
20%
½0.5
25%
30%
¾0.75
40%
50%
60%
75%
80%
100%
Remember: percent means "out of 100."
Percents Section
Page 11

Find the Percent of a Number

Calculate each percent of the whole number. Show your work.
Example
25% of 40 = (0.25 × 40) = 10
1.10% of 50
2.20% of 60
3.25% of 80
4.50% of 40
5.30% of 90
6.40% of 50
7.75% of 40
8.60% of 30
9.15% of 100
10.80% of 25
11.35% of 40
12.90% of 50
13.45% of 60
14.70% of 30
15.55% of 20
Convert percent to decimal first, then multiply.
Percents Section
Page 12

Percent in Real Life

Solve each real-life problem. Show your work and write the final answer.
1. A shirt costs $40 and is on sale for 25% off. How much is the discount?
2. A class has 40 students and 30% of them bring lunch from home. How many students bring lunch?
3. A $60 jacket is marked 20% off. What is the discount amount?
4. In a survey of 100 people, 45% said they like spicy food. How many people like spicy food?
5. A store has 50 items and 15% of them are on sale. How many items are on sale?
6. A test has 80 points and you scored 90%. How many points did you earn?
Show your work for each problem.
Percents Section
Page 13

Percent Table Practice

Complete the table by finding the missing part, whole, or percent.
PartWholePercentMissing Value
1040%—
5020%Part
1530%Whole
25100%—
8040%Part
1260%Whole
3060%—
10075%Part
4590%Whole
520%—
4050%Part
1845%Whole
Part = Whole × Percent (as decimal)Whole = Part ÷ Percent (as decimal)Percent = Part ÷ Whole
Percents Section
Page 14

Find the Percent Error

Each student work has a mistake. Explain what is wrong and write the correct answer.
Student Work
Problem: Find 30% of 60
Student work: 30% = 0.30, so 0.30 × 60 = 180
Mistake:
Correct Answer:
Student Work
Problem: Find 25% of 80
Student work: 25% = 0.25, so 0.25 × 80 = 200
Mistake:
Correct Answer:
Student Work
Problem: Find 50% of 90
Student work: 50% = 0.50, so 0.50 × 90 = 45
Mistake:
Correct Answer:
Student Work
Problem: Find 40% of 50
Student work: 40% = 0.40, so 0.40 × 50 = 160
Mistake:
Correct Answer:
Student Work
Problem: Find 60% of 40
Student work: 60% = 0.60, so 0.60 × 40 = 24
Mistake:
Correct Answer:
Check your decimal multiplication carefully.
Percents Section
Page 15

Percents Review Check

Show what you know about percents, fractions, decimals, and percent of a number.
1.Write 40% as a decimal.
2.Write 0.75 as a percent.
3.Write 60% as a fraction in simplest form.
4.Find 25% of 60.
5.Find 50% of 80.
6.Find 75% of 20.
7.10% of what number is 8?
8.What percent of 50 is 10?
9. A $70 pair of shoes is on sale for 30% off. How much is the discount?
10. A class has 40 students and 40% bring lunch from home. How many students bring lunch?
11. A test has 60 points and you scored 80%. How many points did you earn?
12. In a survey of 80 people, 25% said they like tea. How many people like tea?
Check all your work before finishing.
Order of Operations Section
Page 16

PEMDAS Review

Solve each expression using the order of operations.
PEMDAS Rules
1. Parentheses first
2. Exponents next
3. Multiply and divide from left to right
4. Add and subtract from left to right
1.8 + 4 × 2
2.12 − 3 + 5
3.6 × 3 + 2
4.20 ÷ 4 + 3
5.15 − 6 ÷ 2
6.7 + 9 − 4
7.(8 + 2) × 3
8.(15 − 5) ÷ 2
9.4 × (6 + 2)
10.30 ÷ (5 + 5)
11.12 + (8 − 3)
12.(20 − 4) ÷ 4
13.5 + (12 ÷ 3)
14.(9 + 3) × 2
15.16 − (10 − 4)
16.(7 + 5) ÷ 3
Work inside parentheses first.
Order of Operations Section
Page 17

Order of Operations with Exponents

Solve each expression. Evaluate exponents before multiplying or dividing.
Example
6 + 2³ = 6 + 8 = 14
1.5 + 2²
2.10 − 3²
3.4 × 2³
4.18 ÷ 3²
5.7 + 4²
6.(5 + 3)²
7.12 + 2³
8.20 − 5²
9.3 × 3²
10.(6 + 2)² ÷ 4
11.8 + (4 − 2)²
12.15 − (3 + 2)²
Evaluate exponents before multiplying or dividing.
Order of Operations Section
Page 18

Solve the Expression Step by Step

Show each step as you solve. Write your work clearly.
1. 8 + (6 − 2) × 3
Step 1: (Work inside parentheses)
Step 2: (Multiply)
Final Answer:
2. (15 − 5) ÷ 2 + 4
Step 1: (Work inside parentheses)
Step 2: (Divide)
Final Answer:
3. 6 × (4 + 2) − 10
Step 1: (Work inside parentheses)
Step 2: (Multiply)
Final Answer:
4. 20 ÷ (5 − 3) + 6
Step 1: (Work inside parentheses)
Step 2: (Divide)
Final Answer:
5. 3² + (8 − 4)
Step 1: (Evaluate exponent)
Step 2: (Add)
Final Answer:
6. (10 + 2) ÷ 3 × 2
Step 1: (Work inside parentheses)
Step 2: (Divide and multiply from left to right)
Final Answer:
7. 5 + 2³ − 3
Step 1: (Evaluate exponent)
Step 2: (Add and subtract from left to right)
Final Answer:
8. (12 + 4) ÷ (8 − 4)
Step 1: (Work inside both parentheses)
Step 2: (Divide)
Final Answer:
Show each step clearly.
Order of Operations Section
Page 19

Order of Operations Mistakes

Each student work has a mistake. Explain what step was wrong and write the correct answer.
Student Work
Problem: 8 + 4 × 2
Student work: 8 + 4 = 12, then 12 × 2 = 24
What step was wrong?
Correct Answer:
Student Work
Problem: 15 − 6 ÷ 2
Student work: 15 − 6 = 9, then 9 ÷ 2 = 4.5
What step was wrong?
Correct Answer:
Student Work
Problem: (8 + 2) × 3
Student work: 8 + 2 = 10, then 10 × 3 = 30
What step was wrong?
Correct Answer:
Student Work
Problem: 6 + 2³
Student work: 6 + 2 = 8, then 8³ = 512
What step was wrong?
Correct Answer:
Student Work
Problem: 20 ÷ 4 + 3
Student work: 4 + 3 = 7, then 20 ÷ 7 ≈ 2.86
What step was wrong?
Correct Answer:
Student Work
Problem: 5 + (12 ÷ 3)
Student work: 5 + 12 = 17, then 17 ÷ 3 ≈ 5.67
What step was wrong?
Correct Answer:
Remember PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract.
Order of Operations Section
Page 20

PEMDAS Quick Check

Show what you know about order of operations.
1.10 + 5 × 2
2.20 − 8 ÷ 4
3.(9 + 3) × 2
4.15 ÷ (5 − 2)
5.4² + 3
6.12 − 2³
7.(6 + 4) ÷ 2
8.3 × (8 − 5)
9. Solve: 10 + (12 ÷ 4) × 2. Explain which operation you do first.
10. Why do we evaluate exponents before multiplication? Explain in one sentence.
Check all your work before finishing.
Mixed Review Section
Page 21

Mixed Review 1

Review ratios, percents, and order of operations together.
Ratios
1.Simplify 12:18.
2.There are 10 boys and 15 girls. Write the ratio of boys to girls.
3.Fill in the blank: 2:3 = 6:
4.Simplify 20:30.
5.A recipe uses 3 cups flour and 4 cups sugar. Ratio of flour to sugar?
Percents
6.Write 75% as a decimal.
7.Find 25% of 80.
8.Find 50% of 60.
9.Write 0.4 as a percent.
10.What percent of 100 is 35?
Order of Operations
11.12 + 4 × 3
12.(10 + 2) ÷ 3
13.20 − 6 ÷ 2
14.5² + 3
15.(8 − 3) × 4
Check all sections before finishing.
Mixed Review Section
Page 22

Mixed Review 2: Word Problems

Apply ratios, percents, and order of operations to real-world situations.
1. A class has 30 students and 40% bring lunch from home. How many students bring lunch? Show your work.
2. A shirt costs $50 and is on sale for 20% off. How much is the discount? Show your work.
3. There are 18 red marbles and 24 blue marbles. What is the ratio of red to blue marbles in simplest form?
4. Solve: 10 + (12 ÷ 4) × 2. Show your steps.
5. A store sold 60 apples and 40 oranges. What is the ratio of apples to oranges in simplest form?
6. A test has 80 points and you scored 75%. How many points did you earn? Show your work.
Show your work for each problem.
Challenge / Enrichment
Page 23

Challenge Problems

These problems require multi-step reasoning. Show your work and explain your thinking.
1. A recipe uses flour and sugar in a ratio of 3:2. If you use 12 cups of flour, how many cups of sugar do you need? Explain your reasoning.
Explain:
2. A store has a 30% discount on a $80 jacket, then an additional 10% off the discounted price. What is the final price? Show all steps.
Final price:
3. Solve: (15 − 3²) × (8 ÷ 4) + 5. Show your work in order.
Answer:
4. In a class, the ratio of boys to girls is 4:5. If there are 36 students total, how many boys and how many girls are there? Explain.
Explain:
5. A $100 item is discounted 25%, then the discounted price is increased by 25%. What is the final price? Is it $100? Explain why or why not.
Explain:
These problems are harder than the rest.Take your time and show your thinking.
Answer Key
Page 24

Answer Key: Pages 3–12

Ratios and Percents Answer Reference
Page 3 — Skill Reference

This page contains examples and references only. No answers to check.

Page 4 — Ratio Basics Practice
  1. 5:10 = 1:2
  2. 8:12 = 2:3
  3. 6:9 = 2:3
  4. 3:5
  5. 12:4 = 3:1
  6. 20:30 = 2:3
  7. 14:21 = 2:3
  8. 16:24 = 2:3
  9. 18:27 = 2:3
  10. 25:15 = 5:3
  11. 36:48 = 3:4
  12. 40:5 = 8:1
Page 5 — Simplify Each Ratio
  1. 4:6 = 2:3
  2. 10:15 = 2:3
  3. 8:12 = 2:3
  4. 6:9 = 2:3
  5. 14:21 = 2:3
  6. 15:25 = 3:5
  7. 18:24 = 3:4
  8. 20:30 = 2:3
Page 6 — Equivalent Ratios Table

Row 1: 1:2:3:4 → D = 4

Row 2: 2:4:6:8 → Z = 6

Row 3: 2:3:6:9 → Z = 6

Row 4: 4:6:9:12 → Y = 6

Row 5: 3:4:6:8 → S = 8

Row 6: 6:8:12:16 → Y = 8

Row 7: 5:10:15:20 → N = 10

Row 8: 1:2:3:4 → Z = 3

Page 7 — Ratio Word Problems
  1. 12:18 = 2:3
  2. 3:4
  3. 20:30 = 2:3
  4. 15:25 = 3:5
  5. 24:16 = 3:2
  6. 40:60 = 2:3
  7. 9:15 = 3:5
  8. 35:25 = 7:5
Page 8 — Find and Fix the Ratio Mistake
  1. Mistake: 6:9 is not simplified (divide by 3 again). Correct: 12:18 = 2:3
  2. Mistake: 4:6 is not simplified (divide by 2 again). Correct: 20:30 = 2:3
  3. Mistake: 25:15 = 5:3, not 5:2. Correct: 5:3
  4. Mistake: 8:12 is not simplified (divide by 4). Correct: 16:24 = 2:3
  5. Mistake: 30:20 = 3:2, not 3:1. Correct: 3:2
  6. Mistake: 6:9 is not simplified (divide by 3 again). Correct: 18:27 = 2:3
Page 9 — Ratios Quick Check
  1. 8:12 = 2:3
  2. 15:25 = 3:5
  3. 8:12
  4. 15
  5. 10:15 = 2:3
  6. 24:36 = 2:3
  7. 4:6 = 2:3
  8. 16:24 = 2:3
  9. 30:20 = 3:2
  10. 18:12 = 3:2
Page 10 — Percent Means Out of 100

10% = 10/100 = 1/10 = 0.10

20% = 20/100 = 1/5 = 0.20

50% = 1/2 = 0.5

25% = 25/100 = 1/4 = 0.25

30% = 30/100 = 3/10 = 0.30

75% = 3/4 = 0.75

40% = 40/100 = 2/5 = 0.40

50% = 50/100 = 1/2 = 0.50

60% = 60/100 = 3/5 = 0.60

75% = 75/100 = 3/4 = 0.75

80% = 80/100 = 4/5 = 0.80

100% = 100/100 = 1 = 1.00

Page 11 — Find the Percent of a Number
  1. 10% of 50 = 5
  2. 20% of 60 = 12
  3. 25% of 80 = 20
  4. 50% of 40 = 20
  5. 30% of 90 = 27
  6. 40% of 50 = 20
  7. 75% of 40 = 30
  8. 60% of 30 = 18
  9. 15% of 100 = 15
  10. 80% of 25 = 20
  11. 35% of 40 = 14
  12. 90% of 50 = 45
  13. 45% of 60 = 27
  14. 70% of 30 = 21
  15. 55% of 20 = 11
Page 12 — Percent in Real Life
  1. 25% of $40 = $10 discount
  2. 30% of 40 = 12 students
  3. 20% of $60 = $12 discount
  4. 45% of 100 = 45 people
  5. 15% of 50 = 7.5 ≈ 8 items (or 7 if rounding down)
  6. 90% of 80 = 72 points
Answers are for teacher reference only.
Answer Key
Page 25

Answer Key: Pages 13–20

Percents Review, Order of Operations, and Mixed Review Answers
Page 13 — Percent Table Practice
  1. 10 out of 40 = 25%
  2. 20% of 50 = 10
  3. 15 is 30% of 50 → Whole = 50
  4. 25 out of 100 = 25%
  5. 40% of 80 = 32
  6. 12 is 60% of 20 → Whole = 20
  7. 30 out of 60 = 50%
  8. 75% of 100 = 75
  9. 45 is 90% of 50 → Whole = 50
  10. 5 out of 20 = 25%
  11. 50% of 40 = 20
  12. 18 is 45% of 40 → Whole = 40
Page 14 — Find the Percent Error
  1. Mistake: 0.30 × 60 = 18, not 180. Correct: 18
  2. Mistake: 0.25 × 80 = 20, not 200. Correct: 20
  3. Student work is correct: 50% of 90 = 45
  4. Mistake: 0.40 × 50 = 20, not 160. Correct: 20
  5. Student work is correct: 60% of 40 = 24
Page 15 — Percents Review Check
  1. 40% = 0.40
  2. 0.75 = 75%
  3. 60% = 60/100 = 3/5
  4. 25% of 60 = 15
  5. 50% of 80 = 40
  6. 75% of 20 = 15
  7. 10% of 80 = 8 → number is 80
  8. 10 out of 50 = 20%
  9. 30% of $70 = $21 discount
  10. 40% of 40 = 16 students
  11. 80% of 60 = 48 points
  12. 25% of 80 = 20 people
Page 16 — PEMDAS Review
  1. 8 + 4 × 2 = 8 + 8 = 16
  2. 12 − 3 + 5 = 9 + 5 = 14
  3. 6 × 3 + 2 = 18 + 2 = 20
  4. 20 ÷ 4 + 3 = 5 + 3 = 8
  5. 15 − 6 ÷ 2 = 15 − 3 = 12
  6. 7 + 9 − 4 = 16 − 4 = 12
  7. (8 + 2) × 3 = 10 × 3 = 30
  8. (15 − 5) ÷ 2 = 10 ÷ 2 = 5
  9. 4 × (6 + 2) = 4 × 8 = 32
  10. 30 ÷ (5 + 5) = 30 ÷ 10 = 3
  11. 12 + (8 − 3) = 12 + 5 = 17
  12. (20 − 4) ÷ 4 = 16 ÷ 4 = 4
  13. 5 + (12 ÷ 3) = 5 + 4 = 9
  14. (9 + 3) × 2 = 12 × 2 = 24
  15. 16 − (10 − 4) = 16 − 6 = 10
  16. (7 + 5) ÷ 3 = 12 ÷ 3 = 4
Page 17 — Order of Operations with Exponents
  1. 5 + 2² = 5 + 4 = 9
  2. 10 − 3² = 10 − 9 = 1
  3. 4 × 2³ = 4 × 8 = 32
  4. 18 ÷ 3² = 18 ÷ 9 = 2
  5. 7 + 4² = 7 + 16 = 23
  6. (5 + 3)² = 8² = 64
  7. 12 + 2³ = 12 + 8 = 20
  8. 20 − 5² = 20 − 25 = −5
  9. 3 × 3² = 3 × 9 = 27
  10. (6 + 2)² ÷ 4 = 64 ÷ 4 = 16
  11. 8 + (4 − 2)² = 8 + 4 = 12
  12. 15 − (3 + 2)² = 15 − 25 = −10
Page 18 — Solve the Expression Step by Step
  1. 8 + (6 − 2) × 3 = 8 + 4 × 3 = 8 + 12 = 20
  2. (15 − 5) ÷ 2 + 4 = 10 ÷ 2 + 4 = 5 + 4 = 9
  3. 6 × (4 + 2) − 10 = 6 × 6 − 10 = 36 − 10 = 26
  4. 20 ÷ (5 − 3) + 6 = 20 ÷ 2 + 6 = 10 + 6 = 16
  5. 3² + (8 − 4) = 9 + 4 = 13
  6. (10 + 2) ÷ 3 × 2 = 12 ÷ 3 × 2 = 4 × 2 = 8
  7. 5 + 2³ − 3 = 5 + 8 − 3 = 13 − 3 = 10
  8. (12 + 4) ÷ (8 − 4) = 16 ÷ 4 = 4
Page 19 — Order of Operations Mistakes
  1. Mistake: Did multiplication before addition. Correct: 8 + 4 × 2 = 8 + 8 = 16
  2. Mistake: Did subtraction before division. Correct: 15 − 6 ÷ 2 = 15 − 3 = 12
  3. Student work is correct: (8 + 2) × 3 = 10 × 3 = 30
  4. Mistake: Did addition before exponent. Correct: 6 + 2³ = 6 + 8 = 14
  5. Mistake: Did addition before division. Correct: 20 ÷ 4 + 3 = 5 + 3 = 8
  6. Mistake: Did addition before parentheses. Correct: 5 + (12 ÷ 3) = 5 + 4 = 9
Page 20 — PEMDAS Quick Check
  1. 10 + 5 × 2 = 10 + 10 = 20
  2. 20 − 8 ÷ 4 = 20 − 2 = 18
  3. (9 + 3) × 2 = 12 × 2 = 24
  4. 15 ÷ (5 − 2) = 15 ÷ 3 = 5
  5. 4² + 3 = 16 + 3 = 19
  6. 12 − 2³ = 12 − 8 = 4
  7. (6 + 4) ÷ 2 = 10 ÷ 2 = 5
  8. 3 × (8 − 5) = 3 × 3 = 9
  9. 10 + (12 ÷ 4) × 2 = 10 + 3 × 2 = 10 + 6 = 16. First operation: 12 ÷ 4
  10. Exponents come before multiplication in PEMDAS order.
Answers are for teacher reference only.
Answer Key
Page 26

Answer Key: Mixed Review & Challenge

Pages 21–23 Answer Reference
Page 21 — Mixed Review 1
Ratios
  1. 12:18 = 2:3
  2. 10:15 = 2:3
  3. 9
  4. 20:30 = 2:3
  5. 3:4
Percents
  1. 75% = 0.75
  2. 25% of 80 = 20
  3. 50% of 60 = 30
  4. 0.4 = 40%
  5. 35%
Order of Operations
  1. 12 + 4 × 3 = 12 + 12 = 24
  2. (10 + 2) ÷ 3 = 12 ÷ 3 = 4
  3. 20 − 6 ÷ 2 = 20 − 3 = 17
  4. 5² + 3 = 25 + 3 = 28
  5. (8 − 3) × 4 = 5 × 4 = 20
Page 22 — Mixed Review 2: Word Problems
  1. 40% of 30 = 12 students
  2. 20% of $50 = $10 discount
  3. 18:24 = 3:4
  4. 10 + (12 ÷ 4) × 2 = 10 + 3 × 2 = 10 + 6 = 16
  5. 60:40 = 3:2
  6. 75% of 80 = 60 points
Page 23 — Challenge Problems
  1. Ratio 3:2 means 3 flour for every 2 sugar. If 12 flour = 4 × 3, then sugar = 4 × 2 = 8 cups.
  2. First discount: 30% of $80 = $24, price = $56. Second discount: 10% of $56 = $5.60, final = $56 − $5.60 = $50.40
  3. (15 − 3²) × (8 ÷ 4) + 5 = (15 − 9) × 2 + 5 = 6 × 2 + 5 = 12 + 5 = 17
  4. Ratio 4:5 means 4+5 = 9 parts. 36 ÷ 9 = 4 per part. Boys = 4 × 4 = 16, girls = 5 × 4 = 20.
  5. First: 25% of $100 = $25, price = $75. Second: 25% of $75 = $18.75, final = $75 + $18.75 = $93.75. Not $100 because the 25% increase is on the discounted price ($75), not the original ($100).
Challenge answers include sample solutions.Students may show work differently.
Certificate of Completion
Page 27

CERTIFICATE

OF COMPLETION

This certificate is awarded to

for successfully completing the

Sub Plans Math Packet Grade 6

Ratios • Percents • Order of Operations

Date

Teacher

Keep this certificate as proof of your math practice.
Congratulations on completing this packet!

Thank You!

You have completed the Sub Plans Math Packet Grade 6.

Skills practiced:

  • Writing and simplifying ratios
  • Finding percents of numbers
  • Using order of operations (PEMDAS)
  • Solving mixed word problems

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