Grade 6 · Grade 6: Number, Ratio and Percent · Fractions, Decimals and Integers
Fractions, Decimals and Integers
Divide fractions by fractions, compute fluently with decimals, and place positive and negative numbers on the number line and coordinate plane.
Learning objectives
- Interpret and compute quotients of fractions.
- Add, subtract, multiply and divide multi-digit decimals.
- Use factors, multiples and the distributive property.
- Order rational numbers and interpret absolute value.
- Plot and reflect points in all four quadrants.
AERO Mathematics alignment
AERO.M6.NS.10
Understand opposites, and interpret absolute value as distance from zero on a number line.
AERO.M6.NS.11
Order and compare rational numbers, and interpret statements of inequality on a number line.
AERO.M6.NS.12
Plot points in all four quadrants, identify reflections across the axes, and find distances between points with the same first or second coordinate.
AERO.M6.NS.6
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
AERO.M6.NS.7
Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithms.
AERO.M6.NS.8
Find greatest common factors and least common multiples, and use the distributive property to rewrite sums.
AERO.M6.NS.9
Understand that positive and negative numbers describe quantities with opposite directions or values, and use them in real-world contexts.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion B — Investigating patterns
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
A 3/4 metre ribbon is cut into pieces that are each 2/5 of a metre long.
Think about it
How many full pieces can be cut, and what does the leftover fraction mean?
Hint: Division asks how many groups of the divisor fit inside the dividend.
EXPLAIN
Fractions, decimals and signed numbers
Dividing fractions
3/4 ÷ 2/5 asks how many two-fifths fit into three-quarters. Multiplying by the reciprocal gives 3/4 × 5/2 = 15/8 = 1.875, so one full piece and most of a second.
Decimals and place value
Standard algorithms for decimals are the same as for whole numbers, with place value keeping track of the decimal point. When dividing, scale both numbers by a power of ten so the divisor becomes a whole number.
Factors and multiples
| Tool | What it means | Use |
|---|---|---|
| GCF | Greatest common factor | Simplifying fractions, equal grouping |
| LCM | Least common multiple | Common denominators, repeating schedules |
| Distributive property | a(b + c) = ab + ac | Rewriting 18 + 24 as 6(3 + 4) |
Signed numbers
Positive and negative numbers describe opposite directions: 5 metres above sea level and −5 metres below. The absolute value |−5| = 5 is the distance from zero, ignoring direction. On the number line, a number is greater than another when it sits further right, so −3 > −12.
The coordinate plane
Two perpendicular number lines locate points as (x, y). Reflecting across the y-axis negates x; reflecting across the x-axis negates y. When two points share a coordinate, the distance between them is the difference of the other coordinate.
Common misconception
A larger digit does not mean a larger negative number. −12 is less than −3 because it lies further left, even though 12 > 3.
INVESTIGATION
Try it yourself
Record the daily minimum temperature for five cities, including at least two below zero. Order them, plot them on a number line, and calculate the difference between the warmest and coldest using absolute value.
Watch
Dividing Fractions
Math Antics · 8:00
Explains why we multiply by the reciprocal instead of just memorising it.
Before you watch: How many quarters fit into 3?
- Compute 3/4 ÷ 2/5.
- Explain in words what 5 ÷ 1/2 is asking.
Interactive simulation · PhET
Number Line: Integers
Model temperature and elevation changes, then compare each number with its opposite.
While you explore
- Which two numbers are 7 units from zero?
- Why is −12 less than −3 even though 12 is greater than 3?
Key vocabulary
- Least common multiple
- The smallest number both values divide into.
- Reciprocal
- The fraction turned upside down.
- Absolute value
- How far a number is from zero, ignoring the sign.
Practice questions
0/1 correct
Level 1 · Criterion A
Which statement is true?
MYP criterion tasks
Level 2 · Criterion C
Compute 5/6 ÷ 2/3 and explain what the answer means in words.
Reflect & track
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