Discover Mathematics P6: Term 1, Unit 2, Lessons 4–6
GoalOrder a mixed list of fractions, decimals and negative numbers from least to greatest.
New words
least to greatest · from the number furthest left to the one furthest rightequivalent form · the same number written another way, like 1/2 = 0.5compare · decide which number is greater or less
Explanation
To order numbers that are written in different ways, first write them all in the same form, usually decimals. For example 3/4 = 0.75 and −1/2 = −0.5. Then use the number line: put the negative numbers on the left, 0 in the middle and positive numbers on the right. Among negative numbers, the one that looks bigger without its minus sign is further left, so it is smaller: −0.75 < −0.5. Read the line from left to right to list the numbers from least to greatest. You can also compare positive fractions by writing them with a common denominator.
★Remember
Same form first (decimals), then place on the line, then read from left to right.
Worked examples
Order −1/2, 0.25, −0.75, 3/4 and −1.5. As decimals: −0.5, 0.25, −0.75, 0.75, −1.5. On the line A = −1.5, B = −0.75, C = −1/2, D = 0.25, E = 3/4. From least to greatest: −1.5, −0.75, −1/2, 0.25, 3/4.
Number
As a decimal
2/5
0.4
0.35
0.35
3/8
0.375
Order 2/5, 0.35 and 3/8. Write each as a decimal: 2/5 = 0.4, 0.35, 3/8 = 0.375. So 0.35 < 3/8 < 2/5.
Who
Position
Decimal
Diver
−7/2
−3.5
Fish
−2.5
−2.5
Boat
0
0
Seagull
9/2
4.5
Positions in metres compared with sea level: a seagull 9/2 m, a fish −2.5 m, a boat 0 m and a diver −7/2 m. As decimals: 4.5, −2.5, 0, −3.5. From lowest to highest: diver, fish, boat, seagull.
Class activity
Card line-up. Write eight numbers on cards: some fractions, some decimals, some negative. Shuffle them and line them up on the floor from least to greatest. A grown-up checks by changing every card to a decimal. Then swap and let the grown-up make a mistake for you to find.
Practice
1
Order from least to greatest: 0.6, −0.6, 1/2, −1/2.
−0.6, −1/2, 1/2, 0.6.
2
Which is less, −3/4 or −0.8?
−3/4 = −0.75, and −0.8 is further left, so −0.8 is less.
3
Which is the greatest: −2, −1.5 or −2.25?
−1.5, because it is closest to 0.
4
Which is colder, −7.5 °C or −7 1/4 °C?
−7 1/4 = −7.25, and −7.5 is further left, so −7.5 °C is colder.
5
Order from least to greatest: 1.25, −1.25, 1.5, −1.5.
