Home / Mathematics / Grade 7 / Fractions, Decimals and Percentages in Problem Solving
GRADE 7 · MATHEMATICS

Fractions, Decimals and Percentages in Problem Solving

Fractions, decimals and percentages are three ways to represent parts of a whole. Learn to move between them, compare values and choose an efficient method for real-life problems such as discounts, increases and proportions.

Learning time: approximately 30–40 minutes · Curriculum-neutral learning support

What You Will Learn

1. 1. Three Ways to Represent a Part

A fraction compares a part with a whole, a decimal uses place value, and a percentage means “out of 100”. These forms can represent the same amount.

Equivalent forms: 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%.

To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100 and add the percent sign. To convert a percentage to a decimal, divide by 100.

2. 2. Convert Between Forms

Example: Convert 3/5 to a percentage. 3 ÷ 5 = 0.6; 0.6 × 100 = 60%.
Example: Convert 35% to a fraction. 35/100 simplifies by dividing top and bottom by 5 to give 7/20.
Example: Convert 0.125 to a fraction. 0.125 = 125/1000 = 1/8.

3. 3. Compare and Order Values

Convert values to the same form before comparing them. Decimals are often convenient.

Example: Compare 2/3, 0.65 and 70%. Convert to decimals: 2/3 ≈ 0.667, 0.65 = 0.65 and 70% = 0.70. Therefore: 0.65 < 2/3 < 70%.

Keep enough decimal places when an exact comparison matters. A repeating decimal may need a fraction comparison or a stated approximation.

4. 4. Find a Fraction or Percentage of an Amount

To find a fraction of an amount, divide by the denominator and multiply by the numerator. To find a percentage of an amount, convert the percentage to a decimal and multiply.

Percentage of amount = percentage as a decimal × amount
Example: Find 3/4 of 28. First 28 ÷ 4 = 7; then 7 × 3 = 21.
Example: Find 15% of 80. 0.15 × 80 = 12.

5. 5. Discounts and Percentage Decrease

A discount reduces an original price. Find the discount amount, then subtract it from the original price.

Example: A jacket costs $60 and is reduced by 20%. Discount = 0.20 × 60 = $12. Sale price = $60 − $12 = $48.

An equivalent shortcut is to calculate the remaining percentage: after a 20% discount, 80% remains. So 0.80 × $60 = $48.

6. 6. Percentage Increase

An increase adds a percentage of the original amount. Calculate the increase, then add it to the original.

Example: A monthly fee of $40 increases by 10%. Increase = 0.10 × 40 = $4. New fee = $40 + $4 = $44.

Or multiply by 1.10 because 110% of the original remains after a 10% increase.

7. 7. Percentage Change

Percentage change compares the change with the original value, not the new value.

Percentage change = (change ÷ original value) × 100%
Example: A price rises from $50 to $60. Change = $10. Percentage increase = (10 ÷ 50) × 100% = 20%.

If a value falls, use the size of the decrease and describe the result as a percentage decrease.

8. 8. Reverse Percentages

Sometimes you know the final amount after an increase or decrease and need to find the original. Divide by the multiplier for the final percentage.

Example: After a 20% discount, a bag costs $64. The sale price is 80% of the original. Original price = 64 ÷ 0.80 = $80.
Common mistake: Do not add 20% to $64 to reverse a 20% discount. The 20% discount was calculated from the original price, not the sale price.

9. 9. Choose a Sensible Method and Check

Read the question carefully. Identify the original amount, the percentage and whether the value increases or decreases. Estimate first, calculate, then check that the result makes sense.

10. Practice Exercises

Try these questions before revealing the worked solutions.

  1. Convert 7/20 to a percentage.
  2. Convert 0.375 to a fraction in simplest form.
  3. Order 0.4, 35% and 3/8 from smallest to largest.
  4. Find 25% of 96.
  5. A $120 item has a 15% discount. Find the discount and sale price.
  6. A quantity of 80 increases by 12.5%. Find the new quantity.
  7. A price rises from $40 to $46. Find the percentage increase.
  8. After a 25% discount, a bicycle costs $150. Find its original price.
Show practice answers and explanations
  1. 7 ÷ 20 = 0.35 = 35%.
  2. 0.375 = 375/1000 = 3/8.
  3. 35% = 0.35; 3/8 = 0.375; 0.4 = 0.4. Order: 35%, 3/8, 0.4.
  4. 0.25 × 96 = 24.
  5. Discount = 0.15 × 120 = $18. Sale price = $120 − $18 = $102.
  6. 12.5% = 0.125. Increase = 0.125 × 80 = 10. New quantity = 90.
  7. Change = 6. (6 ÷ 40) × 100% = 15%.
  8. $150 is 75% of original. Original = 150 ÷ 0.75 = $200.

11. Check Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. What is 3/4 as a percentage?
2. What is 20% of 150?
3. A $50 item is discounted by 10%. What is its sale price?
4. A value rises from 80 to 100. What is the percentage increase?
5. A final price of $72 is after a 10% discount. What was the original price?

12. Printable Worksheet

Print this worksheet or choose Save as PDF in your browser's print options.

Learnora — Grade 7 Mathematics

Fractions, Decimals and Percentages in Problem Solving Worksheet

Name: __________________________ Date: ______________

  1. Convert 9/25 to a percentage.
  2. Convert 0.625 to a fraction in simplest form.
  3. Find 18% of 250.
  4. A $90 pair of shoes is discounted by 30%. Find the sale price.
  5. A quantity rises from 120 to 150. Find the percentage increase.

Show your working and check your answers.

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 9 ÷ 25 = 0.36 = 36%.
  2. 0.625 = 625/1000 = 5/8.
  3. 0.18 × 250 = 45.
  4. Discount = $27; sale price = $63.
  5. Increase = 30; (30 ÷ 120) × 100% = 25%.

Lesson Summary

Check your school's course sequence and teacher guidance. Examples are designed for learning and practice.

Return to the Grade 7 Maths Learning Path

Continue Learning