Dividing distances

A truck has covered 540 km in 6 hours, all at the same speed. How much did it cover in 1 hour? To find a "per-something" amount, we divide.

What is this?

Division is the reverse of multiplication. When we share a total equally, or when we want a rate "per unit", we divide.

$540 \text{ km} \div 6 \text{ hours} = 90 \text{ km per hour}$

We use the long-division method we learnt in Class 4. The number being divided (here 540) is the dividend. The number we divide by (6) is the divisor. The answer is the quotient, and anything left over is the remainder.

Step by step for 540 ÷ 6:

• 6 goes into 5? No. Take 54.
• 6 × 9 = 54. Write 9. Subtract: 54 − 54 = 0.
• Bring down 0. 6 goes into 0 zero times. Write 0.
• Remainder = 0.

So 540 ÷ 6 = 90.

Division is also how we share. If 4 friends share a 480 km road trip equally for the driving, each drives 120 km.

Sometimes the division leaves a remainder. 50 sweets shared among 6 children = 8 each, with 2 left over. The 2 sweets are the remainder. In word problems, you decide what to do with the remainder , sometimes you keep it, sometimes you give it away, sometimes you need one more group.

Worked examples

Example 1. A train covers 450 km in 5 hours, all at the same speed. Speed per hour?

• 450 ÷ 5 = 90 km/hour.

Example 2. A car uses 24 litres of petrol for a 360 km trip. How many km per litre?

• 360 ÷ 24 = ?
• 24 × 10 = 240. 360 − 240 = 120 left.
• 24 × 5 = 120.
• So 24 × 15 = 360. Answer: 15 km per litre.

Example 3. 285 mangoes are packed in boxes of 12 each. How many boxes? Any left over?

• 285 ÷ 12: 12 × 20 = 240. Remainder = 45. 12 × 3 = 36. Remainder 9.
• So 23 full boxes, with 9 mangoes left over.

Try it

1. 168 ÷ 8.
2. 525 ÷ 15.
3. A 720 km trip is shared by 6 drivers. How much each?
4. A box of 144 chocolates is shared among 12 kids. How many each?
5. 200 books to be packed in cartons of 18. How many full cartons? Remainder?

Hands-on

Sweet share. Take 60 small grapes or sweets. Share them equally between 5 family members. How many does each get? Now try 7 family members. How many each, and how many left over?

Mileage maths. Ask a family member how many km their bike or car runs per litre. If the tank holds 12 litres, what is the full range? (Multiply, since you have a rate.)