Mei Ling has 31/3 m of cloth. She uses 13/4 m of it to make a bag. How much cloth is left? Give your answer as a mixed number.
17/12 m of cloth are left.
Ans: 1{7|12}
How to solve it
Take the whole metre off first: 3 and one third becomes 2 and one third, and three quarters still has to come off.
Thirds and quarters are different sizes of part. 3 and 4 both go into 12, so write both fractions in twelfths.
One third is 4 twelfths, and three quarters is 9 twelfths. So 2 and 4 twelfths minus 9 twelfths is left to work out.
9 twelfths is more than 4 twelfths, so open one whole: 1 whole is 12 twelfths, and 12 and 4 make 16 twelfths.
2 and 4 twelfths is the same length as 1 and 16 twelfths. Now 16 twelfths minus 9 twelfths is 7 twelfths.
The 1 whole metre beside them was never touched, so 1 and 7 twelfths metres of cloth are left.
Take the wholes off first, then write both fractions in the same parts. When the fraction coming off is the bigger one, open one whole into those parts.
For parents
How do you add and subtract mixed numbers in P5?
This page teaches adding and subtracting mixed numbers whose fractions have different denominators, set in measurement word problems.
What your child learns here
This page teaches adding and subtracting mixed numbers whose fractions have different denominators, set in measurement word problems. It is the first outcome under Four Operations in the Primary 5 Fractions sub-strand.
Rename both fractions as equivalent fractions with a common denominator before adding or subtracting: thirds and quarters both become twelfths.
Wholes can be taken away first: 3 1/3 − 1 3/4 becomes 2 1/3 − 3/4.
When the fraction being subtracted is bigger, regroup one whole into equal parts: 2 4/12 = 1 16/12.
When adding, a fraction part of 12/12 or more makes another whole, so carry it into the whole number.
Write the answer as a mixed number in simplest form, with its unit, unless the question asks for another form.
Does the answer make sense?
The answer to a subtraction must be less than the starting mixed number, and an addition must give more than either part. Check the whole numbers roughly first: 3 1/3 m minus about 2 m leaves a little over 1 m, so 1 7/12 m is sensible.
How to practise these questions
Basic questions add two masses or two distances given as mixed numbers, take a shorter ribbon from a longer one, and put three fractions with different denominators in order. Intermediate questions find how much more flour is needed, or cut two pieces from one wire, so a whole has to be opened along the way. Challenge questions work back to an amount at the start, or take two cuts from one length of cloth and give the answer as a fraction in its simplest form. If renaming the fractions goes wrong, compare your child's common denominator with the one in the worked solution first.
Questions parents ask
Why do the fractions need the same denominator? Thirds and quarters are different sizes of part, so they cannot be counted together. Renaming both as twelfths makes the parts the same size.
What does regrouping mean in a mixed number subtraction? One whole is changed into equal parts and added to the fraction, so 2 4/12 is written as 1 16/12. The value stays the same.
Should my child change mixed numbers into improper fractions first? That method also works. The lesson keeps the wholes and fractions apart, which keeps the numbers small and makes each step easy to check.
