الرياضيات (بالإنجليزية) الصف الخامس الابتدائي، الأسبوع 12: Dividing a decimal by a decimal

Dividing decimals by whole numbers and by decimals

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

Dividing a decimal by a decimal

Discover Mathematics P5: Term 1, Unit 5, Lessons 15–17

GoalMake the divisor a whole number by multiplying both numbers by 10 or 100, then divide.

New words

equivalent division · a division with the same answer, found by multiplying both numbers by the same power of tendecimal divisor · a divisor that has digits after the decimal pointwhole-number divisor · a divisor with no decimal part

Explanation

It is easier to divide by a whole number than by a decimal. If you multiply both the dividend and the divisor by 10, the answer does not change: 6 ÷ 2 = 3 and 60 ÷ 20 = 3. So 4.8 ÷ 0.6 becomes 48 ÷ 6 = 8. Multiply by 10 when the divisor has one decimal place, by 100 when it has two. The point moves the same number of places in both numbers; write a 0 if you need to: 7.2 ÷ 0.09 = 720 ÷ 9 = 80. After the change, divide as in the last lesson. Check by multiplying: 8 × 0.6 = 4.8.

Original	Multiply both by	Whole-number division	Answer
4.8 ÷ 0.6	10	48 ÷ 6	8
7.2 ÷ 0.09	100	720 ÷ 9	80
3 ÷ 0.25	100	300 ÷ 25	12

Worked examples

	Dividend	Divisor
Before	4.8	0.6
× 10	48	6

Work out 4.8 ÷ 0.6. Multiply both numbers by 10: 48 ÷ 6 = 8. Check: 8 × 0.6 = 4.8.

Work out 7.2 ÷ 0.09. The divisor has two decimal places, so multiply both by 100: 720 ÷ 9 = 80. Check: 80 × 0.09 = 7.2.

Mariam pours 3 L of juice into cups of 0.25 L. How many cups? 3 ÷ 0.25 = 300 ÷ 25 = 12 cups.

Class activity

Match the pairs. Write six decimal divisions on cards, for example 2.4 ÷ 0.4, 0.9 ÷ 0.3, 5 ÷ 0.5, 1.6 ÷ 0.08, 0.72 ÷ 0.09 and 4.5 ÷ 1.5, and write the matching whole-number divisions (24 ÷ 4, 9 ÷ 3, 50 ÷ 5, 160 ÷ 8, 72 ÷ 9, 45 ÷ 15) on other cards. Mix the cards, match them in pairs and work out each answer.

Practice

Work out 6.3 ÷ 0.7.

Work out 0.96 ÷ 0.08.

Work out 9 ÷ 1.5 and 2.45 ÷ 0.7.

A 7.5 m rope is cut into pieces of 0.75 m. How many pieces?

Seif says 1.2 ÷ 0.4 = 0.3. What did he do wrong? Give the right answer.