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Dividing decimals by whole numbers and by decimals

الأسبوع 12 · قسمة الكسور العشرية على أعداد صحيحة وعلى كسور عشرية · 3 دروس
3

Challenging decimal stories with all four operations

Discover Mathematics P5: Term 1, Unit 5, Lessons 15–17
GoalSolve stories that need two or three steps with decimals, choosing the right operation each time.
New words
multistep problem · a problem that needs more than one calculationchange · the money you get back when you pay more than the pricereasonable answer · an answer that makes sense in the story
Explanation

For a long story, read it twice and ask: what do I need to find first? Write each step as a short number sentence and keep the unit (LE, kg, m). A bar picture helps you see which numbers go together. Typical steps are: multiply a price by a number of items, add the parts of a bill, subtract the total from the money paid, or divide a total to share it equally. After the last step, check that the answer makes sense: a price cannot be negative and a share cannot be bigger than the total. Estimate first to catch slips with the decimal point.

3 × 12.57.25?50
Worked examples
37.57.255.2550
Mina buys 3 notebooks at 12.5 LE each and a pen for 7.25 LE. She pays 50 LE. Notebooks: 3 × 12.5 = 37.5. Total: 37.5 + 7.25 = 44.75. Change: 50 − 44.75 = 5.25. She gets 5.25 LE back.
A fruit seller has 45.6 kg of oranges and sells 15.6 kg. The rest is packed into 6 equal boxes. 45.6 − 15.6 = 30. 30 ÷ 6 = 5, so each box holds 5 kg. If a box sells for 42.5 LE, the 6 boxes bring in 6 × 42.5 = 255 LE.
PartWorkResult
Distance cost12 × 2.530
Whole fare30 + 535
Each friend35 ÷ 48.75
A taxi charges 5 LE to start and 2.5 LE for each km. For 12 km: 12 × 2.5 = 30, and 30 + 5 = 35 LE. Four friends share the fare equally: 35 ÷ 4 = 8.75, so each pays 8.75 LE. Check: 4 × 8.75 = 35.
Class activity

Shop at home. Choose three food items from the kitchen and make up realistic prices per kg, such as 8 LE and 6.5 LE. Write a two-step story such as “2.5 kg of one and 3 kg of the other, paid with 100 LE: how much change?”, solve it, and swap stories with the grown-up.

Practice
1
Jana has 2.4 m of ribbon and buys 3.6 m more. Each bow needs 0.75 m. How many bows can she make?
2
A bus ticket costs 4.5 LE. Youssef buys 8 tickets and pays 50 LE. How much change does he get?
3
Farida runs 1.25 km a day for 6 days and then 0.75 km on the 7th day. How far does she run in all?
4
Seif has 100 LE. He buys 2.5 kg of tomatoes at 8 LE per kg and 3 kg of potatoes at 6.5 LE per kg. How much money is left?
5
A 7.2 kg bag of rice is repacked into bags of 0.9 kg, and each small bag is sold for 14.5 LE. How much money do all the small bags bring?