Add 1/3 + 1/4.
Give me a hint
Use a common denominator of 12.
Compare a worked response
7/12
1/3 = 4/12 and 1/4 = 3/12; count seven twelfths.
Add fractions & mixed numbers
You can combine the counts once the parts have the same name.
Your learning goal
Add fractions and mixed numbers using equivalent fractions, then simplify and estimate.
Understand the idea
Add quantities expressed in the same units
Two fifths plus one fifth is three fifths: 2/5 + 1/5 = 3/5. The denominator stays 5 because the parts are still fifths. Adding the denominators would change the unit size.
Words worth knowing
- Sum
- The result of addition.
- Common multiple
- A number divisible by both denominators.
- Least common denominator
- The least positive common multiple of the denominators.
- Regroup
- Rename an amount without changing its value, such as 6/4 = 1 2/4.
Make it visible
Different names. Equal-sized units.
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.
Unlike denominators need equivalent names
For 1/2 + 1/3, rename both in sixths. The sum is 3/6 + 2/6 = 5/6. A common denominator must be a multiple of both original denominators; it does not have to be the smallest, but smaller numbers often save work.
Mixed numbers can be added in two reliable ways
You may add the whole parts and fractional parts separately, then regroup. Or convert each mixed number to an improper fraction and add with a common denominator. Explain the equal units in either method.
Khan AcademyWatch · pause · explain
Adding fractions with unlike denominators
Before each equivalent fraction is written, name the factor that changes both its numerator and denominator.
Open on YouTube →The player loads when you choose to watch. Captions and availability depend on the provider.Simplify and check the size
An answer greater than one is allowed. Since 3/4 and 2/3 are each greater than 1/2, their sum must exceed 1. An estimate catches errors that a remembered procedure can hide. Finish in simplest form unless another form is requested.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Add 3/4 + 2/3
- Use twelfths: 3/4 = 9/12 and 2/3 = 8/12.
- Add the numerators: 9/12 + 8/12 = 17/12.
- 17/12 = 1 5/12. The result is between 1 and 2, as expected.
Add 3 5/6 + 1 1/4
- Add whole parts: 3 + 1 = 4. Rename the fractional parts in twelfths.
- 5/6 + 1/4 = 10/12 + 3/12 = 13/12 = 1 1/12.
- 4 + 1 1/12 = 5 1/12. Using twenty-fourths, as in the class notes, gives the same value.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Add 1 3/4 + 2 2/3.
Give me a hint
The fraction parts sum to more than one whole.
Compare a worked response
4 5/12
Whole parts total 3. The fraction parts total 17/12 = 1 5/12, giving 4 5/12.
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?
Combining two measured amounts of flour uses addition. Keep the measurement unit and the reference whole consistent.