The best order to review fractions, decimals, and percents is not random. Start with fraction meaning, then decimal place value, then conversions, then percent meaning, and finally mixed word problems. Students who jump straight into percent equations often struggle because the earlier ideas are not secure.
This sequence works for parents, tutors, and teachers who need to repair gaps efficiently. It is especially useful for Grade 6 and Grade 7 students, test prep, summer review, and back-to-school diagnostics.
The Best Review Order
| Step | Skill | Why It Comes Here |
|---|---|---|
| 1 | Fraction meaning | Students must know what numerator and denominator mean before comparing or converting. |
| 2 | Equivalent fractions | Equivalent forms are the bridge to simplifying, common denominators, and decimals. |
| 3 | Decimal place value | Decimals are base-ten fractions, so students need tenths, hundredths, and thousandths. |
| 4 | Fraction-decimal conversions | This connects the two systems and makes percent conversions easier. |
| 5 | Percent meaning | Percent means “per 100,” so students should connect it to hundredths. |
| 6 | Percent applications | Discounts, tax, tips, increases, and decreases require flexible conversion. |
| 7 | Mixed word problems | Students practice choosing the right representation without being told the topic. |
Step 1: Rebuild Fraction Meaning
Before students calculate, ask what the fraction means. In 3/8, the denominator says the whole is split into 8 equal parts. The numerator says 3 of those parts are being counted. If students cannot explain this, they are likely to memorize procedures without understanding them.
Quick check: Which is larger, 1/4 or 1/6? A student should answer 1/4 and explain that fourths are larger pieces than sixths when the wholes are the same size.
Step 2: Practice Equivalent Fractions
Equivalent fractions are the engine behind comparing, adding, simplifying, and converting. Start with visuals, then move to multiplication and division.
Example: 3/5 = 6/10 because both numerator and denominator were multiplied by 2. Also, 12/16 = 3/4 because both numerator and denominator were divided by 4.
Students are ready to move on when they can generate three equivalents for a fraction and simplify a fraction without changing its value.
Step 3: Review Decimal Place Value
Decimals are easier when students read them as fractions. The decimal 0.47 means 47 hundredths, or 47/100. The decimal 2.305 means 2 and 305 thousandths. This language helps students compare decimals correctly.
Quick check: Which is greater, 0.7 or 0.68? Write 0.7 as 0.70. Since 70 hundredths is greater than 68 hundredths, 0.7 > 0.68.
Step 4: Convert Fractions and Decimals
Start with friendly denominators: halves, fourths, fifths, tenths, twentieths, and hundredths. Then move to division for less friendly fractions.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/10 | 0.1 | 10% |
Do not rush this table. Students who know these benchmark values solve percent and estimation problems much faster.
Step 5: Teach Percent as “Out of 100”
Percent should not be introduced as a trick with moving decimals. First, teach that 37% means 37 out of 100, or 37/100, or 0.37. Then teach efficient conversion.
Example: 65% = 65/100 = 0.65. Also, 0.08 = 8/100 = 8%.
Step 6: Move Into Percent Applications
Once students can convert, teach the three most common percent question types:
- Find the part: What is 30% of 80? Answer: 0.30 x 80 = 24.
- Find the percent: 18 is what percent of 60? Answer: 18/60 = 0.30 = 30%.
- Find the whole: 15 is 25% of what number? Answer: 15 divided by 0.25 = 60.
After that, add real-world contexts such as tax, tip, sale price, markup, and percent increase or decrease.
Step 7: Finish with Mixed Problems
Mixed practice is where you learn whether the student truly understands the relationship among fractions, decimals, and percents. Do not label each problem. Let the student decide whether to use a fraction, decimal, percent, picture, table, or equation.
Mini Practice Set
- Write 3/4 as a decimal and percent.
- Write 0.35 as a fraction and percent.
- Which is greater: 2/5 or 0.45?
- Find 15% of 60.
- A shirt costs $40 and is 25% off. What is the sale price?
- 12 out of 30 students ride the bus. What percent is that?
- A test score increases from 70 to 84. What is the percent increase?
- Write 0.125 as a percent.
Answers
1. 0.75 and 75%. 2. 35/100 = 7/20 and 35%. 3. 0.45 is greater because 2/5 = 0.4. 4. 9. 5. Discount = $10, sale price = $30. 6. 12/30 = 0.4 = 40%. 7. Increase = 14; 14/70 = 0.20 = 20%. 8. 12.5%.
One-Week Review Routine
Day 1: Fraction meaning and equivalent fractions. Day 2: Decimal place value and comparing decimals. Day 3: Fraction-decimal conversions. Day 4: Percent meaning and benchmark percents. Day 5: Percent applications. Day 6: Mixed word problems. Day 7: Error log and retest.
When to Slow Down
If the student cannot explain why 1/4 equals 25%, slow down and return to hundredths. If the student can convert but misses word problems, the problem is probably setup, not conversion. Ask, “What is the whole? What is the part? What is the percent?” before calculating.
Use ViewMath Grade 6 and Grade 7 resources when students need more practice with ratios, percents, rational numbers, and proportional reasoning. Start with a workbook for skill repair and move to practice tests once the student can convert and choose strategies independently.
