☰ خطة العام · الرياضيات (بالإنجليزية)

Term 2 review

الأسبوع 30 · مراجعة الفصل الثاني · 3 دروس
1

Review: fractions, decimals, ratio and rate

Discover Mathematics P6: Term 2, Units 8–13, Review
GoalReview dividing fractions and decimals, ratios, unit rates and the best buy.
New words
reciprocal · a fraction turned upside down; dividing by a fraction means multiplying by its reciprocalratio · a comparison of two quantities, such as 3 : 5unit rate · the amount for one unit, such as LE per kg
Explanation

Dividing by a fraction asks “how many of these fit?”. 3/4 ÷ 1/8: 3/4 is 6/8, so 6 eighths fit; or multiply by the reciprocal, 3/4 × 8 = 6. A fraction divided by a whole number: 2/3 ÷ 4 = 2/3 × 1/4 = 1/6. For decimals, multiply both numbers by the same power of 10 to remove the decimal point: 3.6 ÷ 0.4 = 36 ÷ 4 = 9. A ratio such as 3 : 5 splits a total into 3 + 5 = 8 equal parts. A unit rate is found by dividing, and the best buy is the lowest price for one unit.

★Remember
Divide by a fraction: multiply by its reciprocal. Decimals: scale both numbers by 10, 100… Ratio: add the parts, find one part. Rate: divide to get one.
Worked examples
3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. And 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6.
Plants152540
A garden has roses and jasmine in the ratio 3 : 5 and 40 plants. There are 3 + 5 = 8 parts and each part is 40 ÷ 8 = 5 plants. Roses: 3 × 5 = 15. Jasmine: 5 × 5 = 25.
5 kg of oranges cost 85 LE: 85 ÷ 5 = 17 LE per kg. Shop A sells 5 pens for 35 LE (7 LE each) and shop B sells 8 pens for 52 LE (6.5 LE each). B is the better buy.
Class activity

Make a quiz. Write one question for each skill above (fraction division, decimal division, ratio, unit rate) using your own numbers. Swap with a friend and mark each other’s answers.

Practice
1
Calculate 5/6 ÷ 1/12.
2
Calculate 3/5 ÷ 6.
3
Calculate 4.2 ÷ 0.6.
4
Share 63 LE between two friends in the ratio 2 : 7. How much does each get?
5
A bag of 3 kg of rice costs 51 LE and a bag of 5 kg costs 80 LE. Which is the better buy?