1
Fraction foundations
Simplify, compare, and identify equivalent fractions before dividing.
Worked examples + 20 practice questions
Grade 6 Fractions and Decimals Review
Strengthen the fraction and decimal skills that support Grade 6 problem solving, with special focus on dividing fractions and calculating accurately with multi-digit decimals.
Grade 6 standards emphasize dividing fractions by fractions and fluent multi-digit decimal computation. This guide also reviews earlier fraction foundations needed for those skills. View the official mathematics standards.
Review map
Six connected fraction and decimal skills
A secure Grade 6 learner can choose representations, compute accurately, and explain why the answer is reasonable.
2
Fraction division
Interpret how many groups fit and use reciprocal multiplication accurately.
3
Decimal place value
Read, compare, round, and align decimals by place value.
4
Decimal operations
Add, subtract, multiply, and divide multi-digit decimals fluently.
5
Conversions
Move between common fractions and decimals when useful.
6
Reasonableness
Estimate first and check whether the size and unit of the result make sense.
Foundation review
Equivalent fractions and simplification come first
Fraction division is easier when the student can simplify factors and recognize equivalent values.
Simplify by dividing numerator and denominator
The fraction 18/24 can be simplified because both numbers share a factor of 6.
1824=18 ÷ 624 ÷ 6=34
Important: Dividing the numerator and denominator by the same nonzero number does not change the fraction's value.
Compare
5/8 > 3/8
With equal denominators, compare numerators.
Rename
3/4 = 6/8
Multiply both numerator and denominator by 2.
Mixed to improper
2 1/3 = 7/3
Multiply 2 × 3, then add 1.
Grade 6 focus
Dividing fractions asks how many groups fit
The reciprocal rule is efficient, but a model and an estimate explain why the result makes sense.
Meaning model
How many 1/4-cup servings fit in 3/4 cup?
34÷14=3
Three one-fourth groups fit into three-fourths.
Reciprocal method
Keep the first fraction, change division to multiplication, and invert the divisor.
23÷45=23×54=1012=56
Estimate: dividing by 4/5, a number less than 1, should give an answer slightly larger than 2/3. The result 5/6 is reasonable.
Four-step fraction-division procedure
- Convert mixed numbers to improper fractions.
- Rewrite division as multiplication by the reciprocal.
- Cancel common factors before multiplying when possible.
- Simplify the final fraction and convert to a mixed number if useful.
Decimal foundations
Align values by place, not by the final digit
A decimal point fixes the location of ones, tenths, hundredths, and thousandths.
Place-value example: 47.306
Tens4
Ones7
Decimal.
Tenths3
Hundredths0
Thousandths6
Compare
4.07 < 4.7
Write 4.7 as 4.70. Seven tenths is greater than seven hundredths.
Round
8.376 → 8.38
To round to the nearest hundredth, inspect the thousandths digit.
Estimate
19.84 + 6.12 ≈ 26
Round to compatible values before calculating exactly.
Grade 6 computation
Use place value to calculate with multi-digit decimals
Estimate before calculating, then use the estimate to check the decimal point and size of the answer.
14.68 + 3.7
- Align decimal points.
- Rewrite 3.7 as 3.70.
- Add by place value.
Answer: 18.38
20.00 − 6.475
- Add placeholder zeros.
- Subtract from right to left.
- Regroup across place values.
Answer: 13.525
3.24 × 1.5
- Estimate: 3 × 1.5 ≈ 4.5.
- Multiply 324 × 15 = 4860.
- There are three decimal places in the factors.
Answer: 4.860 = 4.86
18.72 ÷ 2.4
- Move both decimal points one place right.
- Rewrite as 187.2 ÷ 24.
- Divide and check by multiplication.
Answer: 7.8
Decimal-point warning: Do not place the decimal point by counting digits in addition or subtraction. Align decimal points. Counting decimal places applies to multiplication.
Flexible number forms
Connect common fractions and decimals
Fractions and decimals are different notations for numbers. Choose the form that makes the reasoning clearer.
Fraction to decimal
Divide the numerator by the denominator.
38=3 ÷ 8=0.375
Some fractions terminate; others produce repeating decimals.
Decimal to fraction
Use the place value of the final digit, then simplify.
0.45=45100=920
Forty-five hundredths simplifies to nine twentieths.
| Fraction | Decimal | Useful interpretation |
|---|---|---|
| 1/2 | 0.5 | Half |
| 1/4 | 0.25 | One quarter |
| 3/4 | 0.75 | Three quarters |
| 1/5 | 0.2 | One fifth |
| 1/8 | 0.125 | One eighth |
| 3/8 | 0.375 | Three eighths |
Eight worked examples
Follow the reasoning, not only the rule
The examples include fraction division, decimal operations, conversions, and real-world applications.
Example 1: Fraction divided by a fraction
Compute 5/6 ÷ 2/3.
- Rewrite as 5/6 × 3/2.
- Cancel 3 with 6 to make 1 and 2.
- Multiply 5/2.
Answer: 5/2 = 2 1/2
Example 2: Mixed-number division
Compute 2 1/4 ÷ 3/5.
- Convert 2 1/4 to 9/4.
- Rewrite as 9/4 × 5/3.
- Cancel 9 and 3 to make 3 and 1.
- Multiply 15/4.
Answer: 15/4 = 3 3/4
Example 3: Fraction-division word problem
A 4 1/2-foot board is cut into pieces that are 3/4 foot long. How many pieces can be made?
- Convert 4 1/2 to 9/2.
- Compute 9/2 ÷ 3/4 = 9/2 × 4/3.
- Cancel and multiply.
Answer: 6 pieces
Example 4: Decimal addition
Compute 18.407 + 6.95.
- Rewrite 6.95 as 6.950.
- Align decimal points.
- Add each place.
Answer: 25.357
Example 5: Decimal subtraction
Compute 12 − 3.684.
- Rewrite 12 as 12.000.
- Regroup across the zeros.
- Subtract by place value.
Answer: 8.316
Example 6: Decimal multiplication
Compute 2.75 × 0.6.
- Estimate: 3 × 0.6 ≈ 1.8.
- Multiply 275 × 6 = 1650.
- Use three total decimal places.
Answer: 1.650 = 1.65
Example 7: Decimal division
Compute 45.36 ÷ 1.2.
- Move both decimal points one place right.
- Rewrite as 453.6 ÷ 12.
- Divide and verify by multiplication.
Answer: 37.8
Example 8: Convert decimal to fraction
Write 0.625 as a fraction in simplest form.
- Write 625/1000.
- Divide numerator and denominator by 125.
Answer: 5/8
Error prevention
Common fraction and decimal mistakes
Invert the wrong fraction
Only the divisor—the second fraction—is replaced by its reciprocal.
Skip mixed-number conversion
Convert mixed numbers to improper fractions before using the reciprocal method.
Expect every quotient to be smaller
Dividing by a number less than 1 can produce a larger answer.
Misalign decimal places
For addition and subtraction, line up decimal points and add placeholder zeros.
Count decimal places in division
For decimal division, shift both decimals equally until the divisor is a whole number.
Ignore estimation
An estimate can reveal a misplaced decimal point or an unreasonable fraction result.
Independent practice
20 Grade 6 fractions and decimals questions
Show the main steps. Simplify fractions and include units where needed.
A. Fraction foundations and division
- Simplify 21/28.
- Write 2 3/5 as an improper fraction.
- Compute 3/4 ÷ 1/2.
- Compute 5/8 ÷ 10/12.
- Compute 1 1/2 ÷ 3/8.
B. Fraction applications
- A 3 3/4-yard ribbon is cut into pieces that are 3/8 yard long. How many pieces are made?
- A recipe uses 2/3 cup of oats per batch. How many batches can be made with 4 cups?
- A tank is 5/6 full. Each bucket holds 1/12 of the tank's capacity. How many bucketfuls are represented by the water in the tank?
- A runner completed 7/10 of a mile in 1/4 hour. What was the rate in miles per hour?
- A 2 1/4-pound bag is divided equally into portions of 3/16 pound. How many portions are made?
C. Decimal operations
- Compute 47.308 + 6.92.
- Compute 30 − 8.746.
- Compute 4.82 × 1.7.
- Compute 0.064 × 2.5.
- Compute 63.84 ÷ 2.4.
D. Conversions and mixed applications
- Write 7/20 as a decimal.
- Write 0.875 as a fraction in simplest form.
- A store sells 3.5 pounds of apples at $1.68 per pound. Find the total cost.
- A 12.6-liter container is filled equally into 8 bottles. How many liters go into each bottle?
- A student used 0.45 of a 2.4-meter roll of paper. How many meters were used?
Complete all four sections before opening the answers.
Go to the Answer KeyCheck and diagnose
Practice answer key
Use each explanation to locate the exact step that needs review.
Question 13/4
Divide 21 and 28 by 7.
Question 213/5
2 × 5 + 3 = 13.
Question 33/2 = 1 1/2
3/4 × 2/1 = 6/4 = 3/2.
Question 43/4
5/8 × 12/10; simplify before multiplying.
Question 54
3/2 × 8/3 = 4.
Question 610 pieces
15/4 ÷ 3/8 = 15/4 × 8/3 = 10.
Question 76 batches
4 ÷ 2/3 = 4 × 3/2 = 6.
Question 810 bucketfuls
5/6 ÷ 1/12 = 5/6 × 12 = 10.
Question 92.8 miles per hour
7/10 ÷ 1/4 = 7/10 × 4 = 28/10 = 2.8.
Question 1012 portions
9/4 ÷ 3/16 = 9/4 × 16/3 = 12.
Question 1154.228
Align decimals: 47.308 + 6.920.
Question 1221.254
Rewrite 30 as 30.000 before subtracting.
Question 138.194
482 × 17 = 8194; use three decimal places.
Question 140.16
64 × 25 = 1600; use four decimal places: 0.1600.
Question 1526.6
Move both decimals one place: 638.4 ÷ 24.
Question 160.35
7 ÷ 20 = 0.35.
Question 177/8
0.875 = 875/1000; simplify by 125.
Question 18$5.88
3.5 × $1.68 = $5.88.
Question 191.575 liters
12.6 ÷ 8 = 1.575.
Question 201.08 meters
0.45 × 2.4 = 1.08.
Choose the correct follow-up
- Missed foundation questions: review simplification, equivalent fractions, and mixed-number conversion.
- Missed fraction division: model the meaning first, then practice reciprocal multiplication.
- Missed decimal addition or subtraction: align decimal points and use placeholder zeros.
- Missed decimal multiplication: estimate and check total decimal places.
- Missed decimal division: shift both decimals equally until the divisor is whole.
- Missed applications: identify the quantities, units, and operation before calculating.
Focused revision
A five-session fractions and decimals plan
Fraction foundations
Simplify, compare, and convert mixed and improper fractions.
Fraction division
Use models, reciprocal multiplication, and estimation.
Decimal place value
Compare, round, estimate, add, and subtract.
Decimal multiplication and division
Use standard algorithms and reasonableness checks.
Mixed applications
Choose the operation and representation in real-world problems.
Need a complete Grade 6 review?
Use the free diagnostic to identify gaps, then continue with all major Grade 6 math domains.
Frequently asked questions
Grade 6 fractions and decimals FAQ
What fraction skills are emphasized in Grade 6?
A major Grade 6 focus is extending multiplication and division understanding to divide fractions by fractions and solve related real-world problems. Earlier fraction concepts still matter as prerequisites.
What decimal skills should a Grade 6 student know?
Students should compute fluently with multi-digit decimals using addition, subtraction, multiplication, and division, while applying place-value understanding and standard algorithms.
Why does dividing by a fraction make the answer larger sometimes?
Dividing by a number less than 1 asks how many small groups fit into the original quantity. More than one small group may fit, so the quotient can be larger than the dividend.
How can a student check decimal multiplication?
Estimate first, count decimal places only after multiplying the whole-number digits, and compare the final answer with the estimate to confirm that the decimal point is reasonable.
Should fractions always be converted to decimals?
No. Fractions are often more exact and easier to simplify or divide. Decimals are useful for money, measurement, and place-value calculations. Choose the representation that best fits the problem.
What should a student practice after this review?
Practice mixed fraction division, multi-digit decimal operations, conversions between fractions and decimals, estimation, and real-world problems that require choosing the correct operation.
Standards reference and scope
The Grade 6 Number System standards emphasize applying and extending earlier multiplication and division understanding to divide fractions by fractions, and computing fluently with multi-digit decimals. This review also includes earlier fraction foundations because they are prerequisites for successful Grade 6 work. Read the official Common Core mathematics standards. GradeCove is an independent educational publisher and is not endorsed by the Common Core State Standards Initiative. State, district, school, and curriculum expectations may differ.