SME
Grade 4 Math · Problem type
Compare fractions
Use this for “Which fraction is greater, 3/8 or 3/5?” Explain how you know.
Diagram
6/8 > 5/8, so 3/4 > 5/8
This is an example. Type your own values to start a new problem.
First numerator
First denominator
Second numerator
Second denominator
Common denominator
worked out (not typed)
First new numerator
worked out (not typed)
Second new numerator
worked out (not typed)
Formulas
common denominator of 4 and 8 = 8
A common denominator of the two denominators = common denominator
3 × (8 ÷ 4) = 6
First numerator × (common denominator ÷ first denominator) = first new numerator
5 × (8 ÷ 8) = 5
Second numerator × (common denominator ÷ second denominator) = second new numerator
sign > between 6 and 5
The sign between the two fractions
Assumptions
•
Give both fractions the same denominator, then compare the numerators.
•
If one denominator is a multiple of the other, use it (3/4 and 5/8: eighths).
•
Otherwise count by the bigger denominator until the other one divides it (4 and 6: twelfths).
•
Fractions up to 1, with denominators 2, 3, 4, 5, 6, 8, 10 and 12.
Step-by-step
WE KNOW
First numerator: 3
First denominator: 4
Second numerator: 5
Second denominator: 8
FIND
common denominator, first new numerator, second new numerator, sign
Step 1 · Find common denominator
common denominator of 4 and 8 = ?
A common denominator of the two denominators = common denominator
Count by the bigger denominator until the other one divides it.
8 = 4 × 2: use 8
Common denominator = 8
Step 2 · Find first new numerator
3 × (8 ÷ 4) = ?
First numerator × (common denominator ÷ first denominator) = first new numerator
The denominator became the common denominator. Multiply the numerator by the same number.
8 ÷ 4 = 2
3 × 2 = 6
First new numerator = 6
Step 3 · Find second new numerator
5 × (8 ÷ 8) = ?
Second numerator × (common denominator ÷ second denominator) = second new numerator
The denominator became the common denominator. Multiply the numerator by the same number.
8 ÷ 8 = 1
5 × 1 = 5
Second new numerator = 5
Step 4 · Find sign
sign ? between 6 and 5
The sign between the two fractions
Same-size parts now: the fraction with more parts is greater.
6
8
>
5
8
,
so
3
4
>
5
8
g: >
Check
Put the numbers back in. Both sides should match.
common denominator of 4 and 8 = 8 ✓
3 × (8 ÷ 4) = 6 ✓
6
8
>
5
8
,
so
3
4
>
5
8
✓
6
8
>
5
8
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.