Evaluate 1/2 + 3/4 × 2/3.
Give me a hint
Multiply before adding.
Compare a worked response
1
3/4 × 2/3 = 1/2; then 1/2 + 1/2 = 1.
Order of operations with fractions
Fractions change the arithmetic, not the priority of the operations.
Your learning goal
Evaluate fraction expressions with brackets, powers and all four operations, checking each step.
Understand the idea
Read the structure before calculating
Evaluate brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Multiplication does not automatically come before division; the two share priority. The same is true of addition and subtraction.
Words worth knowing
- Expression
- A mathematical phrase with numbers and operations.
- Exponent
- A number telling how many equal factors to multiply.
- Operation priority
- The order in which parts of an expression are evaluated.
- Fraction bar
- A division symbol that also groups the entire numerator and denominator.
Make it visible
Move the brackets. Change the calculation.
Predict a result, change a value, and use the diagram to explain your reasoning.
Predict before changing a value. Every whole in a bar diagram uses the same size. The models use non-negative amounts up to two wholes per input.
Use fraction skills only where they apply
You need common denominators for addition and subtraction. You multiply numerators and denominators for multiplication. You use a reciprocal for division by a non-zero number. Identify the next operation before choosing a procedure.
A power belongs to its base
(2/3)² means (2/3) × (2/3) = 4/9. The brackets make the whole fraction the base. It does not mean doubling the numerator or denominator. Convert a mixed number inside a power to an improper fraction before evaluating.
Write one meaningful change per line
Keep every unchanged part of the expression as you work. When a fraction bar spans a numerator such as 1/2 + 1/4, finish that entire numerator before dividing by the denominator. An estimate and a second method can help check a complicated result.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Evaluate 1/3 + (2/5 × 1/4)
- Inside the brackets, multiply: 2/5 × 1/4 = 2/20 = 1/10.
- Now add 1/3 + 1/10. Use thirtieths: 10/30 + 3/30.
- The result is 13/30. It is greater than 1/3 but less than 1/2.
Evaluate (3/4)² ÷ 3/8 − 1/2
- First the power: (3/4)² = 9/16.
- Then divide: 9/16 × 8/3 = 3/2.
- Finally subtract: 3/2 − 1/2 = 1.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Evaluate 3/4 ÷ 1/2 × 1/3.
Give me a hint
Division and multiplication have the same priority. Work from left to right.
Compare a worked response
1/2
3/4 ÷ 1/2 = 3/2, then 3/2 × 1/3 = 1/2.
Independent practice
Build a strategy you can explain.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
What does the answer mean?
A recipe calculation may combine scaling and subtraction. Write brackets to make clear whether you scale the full amount or only the amount remaining.