☰ خطة العام · الرياضيات (بالإنجليزية)

Mixed numbers: like denominators, common denominators and models

الأسبوع 18 · الأعداد الكسرية: المقامات المتحدة والمشتركة والنماذج · 3 دروس
2

Common denominators and estimates for mixed numbers

Discover Mathematics P5: Term 2, Unit 8, Lessons 1–4
GoalEstimate sums and differences of mixed numbers by rounding, then work them out with a common denominator.
New words
round · to replace a number by a nearby friendly numberestimate · a close answer found with rounded numberscommon denominator · a denominator shared by two fractions
Explanation

To estimate with mixed numbers, round each one to the nearest whole number. If the fraction part is less than 1/2, round down; if it is 1/2 or more, round up. 2 1/3 rounds to 2 and 1 3/4 rounds to 2, so 2 1/3 + 1 3/4 is about 4. To find the exact answer with unlike denominators, find the LCM, rewrite both fractions, then add or subtract as before: 2 1/3 + 1 3/4 = 2 4/12 + 1 9/12 = 3 13/12 = 4 1/12. The exact answer 4 1/12 is close to the estimate 4, so it is sensible.

Mixed numberFraction partRounds to
2 1/3less than 1/22
1 3/4more than 1/22
3 1/2exactly 1/24
Worked examples
Estimate and then add 2 1/3 + 1 3/4. Estimate: 2 + 2 = 4. Exact: 2 4/12 + 1 9/12 = 3 13/12 = 4 1/12.
Estimate and then subtract 5 7/8 − 2 1/6. Estimate: 6 − 2 = 4. Exact: 5 21/24 − 2 4/24 = 3 17/24, which is close to 4.
Add 3 1/2 + 2 2/5. Estimate: 4 + 2 = 6. Exact: 3 5/10 + 2 4/10 = 5 9/10, which is close to 6.
Class activity

Estimate race. The grown-up writes a mixed-number sum or difference on a card. The child must give an estimate within 10 seconds and say how each number was rounded. Then the child works out the exact answer and decides if it is close to the estimate. Do six cards.

Practice
1
Estimate 4 1/5 + 2 5/6, then find the exact answer.
2
Rewrite 2 1/4 and 3 1/6 with a common denominator.
3
Estimate 6 3/4 − 2 1/3, then find the exact answer.
4
Add 1 1/2 + 2 3/10 and compare with the estimate.
5
Is 3 2/3 + 1 1/4 closer to 4 or to 5?