The idea in brief. Parts can only be added or subtracted when they are the same size, so both fractions are renamed over one denominator, the smallest common multiple of the two, and then only the numerators are added or subtracted. A whole number gives up one whole as that many parts before a fraction comes off it. An answer is never left improper or unsimplified.
Lesson video, with the working
Adding and subtracting fractions
3 min 34 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
How can I help with adding and subtracting unlike fractions?
Unlike fractions need equal-sized parts before their numerators can be combined.
What your child learns here
Unlike fractions need equal-sized parts before their numerators can be combined. Your child learns to rename the fractions with a common denominator while preserving each value. The MOE Primary 4 outcome covers addition and subtraction with given denominators not exceeding 12 and no more than two different denominators. A common denominator found during the working may be larger than 12; the limit refers to the fractions given in the question.
Find a common multiple of the denominators so both fractions can be expressed using parts of the same size.
Multiply each numerator and denominator by the same whole number when renaming, so the fraction keeps its original value.
Add or subtract the renamed numerators while retaining the common denominator, which still names the size of each part.
Express a whole as the appropriate number of equal parts when subtracting a fraction from it, then simplify the result if possible.
Read a fraction story to decide whether the requested amount is a combined part, a difference or what remains of the whole.
Does the answer make sense?
For a subtraction of a smaller positive fraction from a larger one, the answer must be less than the starting fraction. Your child can add the subtracted fraction back to the answer, using equal-sized parts, to recover the starting value.
How to practise these questions
The Basic question adds two unlike fractions. Intermediate questions combine masses, find an amount left after use, or recover a ribbon's original length; some require a mixed number in simplest form. Challenge work includes a missing value in a fraction equation and a transfer of ribbon that leaves two people with equal lengths. Ask your child to identify the whole used by each fraction before finding a common denominator. In a story, name the total, the amount used or the amount left on each working line, then check the form requested for the answer. Members can consult the solution film after an attempt if the sequence of operations is unclear. The free addition card has written working that renames both fractions with a common denominator before adding their numerators.
Questions parents ask
Why can my child not add the denominators? The denominator describes how many equal parts make one whole, so changing it changes the size of the parts. Addition counts parts of a shared size. Once both fractions have been renamed with the same denominator, the numerators can be added while that denominator stays the same.
Must my child use the smallest common denominator? Any common denominator works when both fractions are renamed correctly. The smallest one usually keeps the arithmetic shorter and reduces later simplification. Your child can first list multiples to find a suitable shared number, then check that the new fractions still equal the original ones.
Do all Primary 4 fraction sums stay below one whole? Do not assume that from the topic name. The P4 addition and subtraction outcome does not state the P3 restriction of staying within one whole. Your child should judge the result from the given fractions and express it in the form requested, including a mixed number where appropriate.
