Week 4 Β· Ordering rational numbers and absolute value Β· 3 lessons
1
Ordering fractions, decimals and negative numbers
Discover Mathematics P6: Term 1, Unit 2, Lessons 4β6
GoalOrder a mixed list of fractions, decimals and negative numbers from least to greatest.
New words
least to greatest Β· from the number furthest left to the one furthest rightequivalent form Β· the same number written another way, like 1/2 = 0.5compare Β· 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 β1/2 = β0.5. 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: β0.75 < β0.5. 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.
β Remember
Same form first (decimals), then place on the line, then read from left to right.
Worked examples
Order β1/2, 0.25, β0.75, 3/4 and β1.5. As decimals: β0.5, 0.25, β0.75, 0.75, β1.5. On the line A = β1.5, B = β0.75, C = β1/2, D = 0.25, E = 3/4. From least to greatest: β1.5, β0.75, β1/2, 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
β7/2
β3.5
Fish
β2.5
β2.5
Boat
0
0
Seagull
9/2
4.5
Positions in metres compared with sea level: a seagull 9/2 m, a fish β2.5 m, a boat 0 m and a diver β7/2 m. As decimals: 4.5, β2.5, 0, β3.5. 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, β0.6, 1/2, β1/2.
β0.6, β1/2, 1/2, 0.6.
2
Which is less, β3/4 or β0.8?
β3/4 = β0.75, and β0.8 is further left, so β0.8 is less.
3
Which is the greatest: β2, β1.5 or β2.25?
β1.5, because it is closest to 0.
4
Which is colder, β7.5 Β°C or β7 1/4 Β°C?
β7 1/4 = β7.25, and β7.5 is further left, so β7.5 Β°C is colder.
5
Order from least to greatest: 1.25, β1.25, 1.5, β1.5.
