Discover Mathematics P5: Term 2, Unit 8, Lessons 5–8
GoalSubtract mixed numbers with unlike denominators, regrouping a whole when the fraction is too small, and subtract from a whole number.
New words
regroup · to borrow one whole and write it as a fraction, such as 1 = 12/12difference · the result of subtractingwhole number · a number without a fraction part, such as 6
Explanation
Rewrite both fractions with a common denominator first. If the fraction in the first number is smaller than the fraction you take away, regroup: take 1 from the whole part and add it to the fraction as denominator/denominator. 5 1/3 − 2 3/4 becomes 5 4/12 − 2 9/12. Since 4/12 is less than 9/12, write 5 4/12 as 4 16/12 (the extra 1 is 12/12, and 12/12 + 4/12 = 16/12). Then 4 16/12 − 2 9/12 = 2 7/12. To subtract from a whole number such as 6 − 2 3/5, write 6 as 5 5/5 and then subtract: 5 5/5 − 2 3/5 = 3 2/5. Check every answer by adding the difference back.
Borrow a whole. Use two sheets of paper as 2 wholes. Fold one into twelfths. Show 2 1/12 and take away 1 5/12: you need to cut one whole into twelfths first. Do it for 2 1/12 − 1 5/12 and write what you did as numbers. Repeat with 3 − 1 1/4.
