Year 5 Maths | Learn, see, try
Add fractions by counting the same-sized parts
A fraction describes equal parts of a whole. The denominator names the size of the parts and the numerator counts how many you have. This page focuses on adding and subtracting fractions that already have the same denominator.
What to notice
Check both the whole and the part size. Two sevenths and three sevenths can be counted together because every piece is one seventh of the same-sized whole. Halves and thirds would need a different preparation step.
What to do
Count the numerators together for addition, or find the difference for subtraction. Keep the denominator because the size of each piece has not changed. Finally ask whether the result makes a whole or can be named more simply.
Why it works
If you combine two apples and three apples, you have five apples. Combining two sevenths and three sevenths similarly gives five sevenths. Addition changes the count of the units, not what each unit is called.
Work through an example
A strip has 2/7 marked, then another 3/7 is marked without overlap. What fraction is marked?
- Both fractions count sevenths of the same strip. The coloured regions do not overlap.
- Count 2 + 3 = 5 seventh-sized pieces.
- The total is 5/7, leaving 2/7 uncoloured.
A common mistake
2/7 + 3/7 is not 5/14. Adding the denominators would rename the pieces as fourteenths even though no piece was cut in half. The original pieces are still sevenths.
A strategy to try
Sketch one bar and divide it into the denominator number of equal sections. Mark the two addends with different symbols, not colour alone, then count all marked parts. This also makes a result of one whole easy to see.
Try it now
Try three questions
No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.
For parents and carers
Ask your child to name the unit before calculating: “We are counting sixths.” If unlike denominators appear, return to equivalent fractions instead of encouraging a rule that only works for matching denominators.
Ready for more practice?
Continue in Adaptigo with Year 5 Maths selected. Choose a skill in the practice hub. Access to the full app follows its current guest and account options.
Continue practising in AdaptigoNeed offline practice instead? Browse printable Maths worksheets with worked answers.