☰ خطة العام · الرياضيات (بالإنجليزية)

Negative numbers and rational numbers

الأسبوع 3 · الأعداد السالبة والمعكوسات والمقارنة وعائلات الأعداد · 3 دروس
2

Comparing numbers with the number line and symbols

Discover Mathematics P6: Term 1, Unit 2, Lessons 1–3
GoalCompare two numbers, including negative numbers, with the symbols <, > and =.
New words
greater than ( > ) · further to the right on the number lineless than ( < ) · further to the left on the number lineorder · put numbers in a line from least to greatest
Explanation

On a number line the numbers get bigger as you go to the right. So of two numbers, the one further to the right is greater and the one further to the left is less. Every positive number is greater than 0, and 0 is greater than every negative number. When both numbers are negative, the one closer to 0 is greater: −2 is greater than −7, so −7 < −2. Be careful: 7 is greater than 2, but −7 is less than −2. In real life, −7 °C is colder than −2 °C, and owing 70 LE is worse than owing 20 LE. The symbols < and > open towards the greater number: 3 > −5 and −5 < 3.

★Remember
Further right = greater. Further left = less. For two negatives, the one closer to 0 is greater.
Worked examples
−8−7−6−5−4−3−2−101234−7−2
Compare −7 and −2. On the number line −7 is further left than −2, so −7 < −2. We can also write −2 > −7.
−8−7−6−5−4−3−2−10123456−35−802
Order −3, 5, −8, 0 and 2 from least to greatest. Mark them on the line and read from left to right: −8, −3, 0, 2, 5.
ChildBalance (LE)
Mina−60
Karim−25
Salma40
Money balances. Salma has 40 LE, Karim owes 25 LE and Mina owes 60 LE. From least to greatest: −60, −25, 40. So Mina is in the worst position and Salma in the best.
Class activity

Number line on the floor. Use chalk or a long string with paper cards from −10 to 10. A grown-up calls two numbers, such as −4 and −9. The child stands on the greater one and says the symbol sentence: −9 < −4. Try ten pairs, then make a line of five children holding cards and order them.

Practice
1
Write <, > or = : −6 ___ −1.
2
Write <, > or = : 4 ___ −9.
3
Order from least to greatest: 7, −2, −10, 0, 3.
4
Which is colder, −5 °C or −9 °C?
5
Hana says −8 > −3 because 8 > 3. What is her mistake?