Positive Rational Number Operations — Drills
Positive Rational Number Operations has 8 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 4 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Factor — A number that divides evenly into another.
- Least common denominator — The smallest expression every denominator divides into.
- Mixed number — A whole number with a fraction, like 212.
- Improper fraction — One whose top is bigger than its bottom, like 52.
Addfrac
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 14 + 45.
Worked answer
21/20
14 = 1040 and 45 = 3240
10 + 3240 = 2120
Problem 2
Compute 12 + 34.
Worked answer
5/4
12 = 24 and 34 = 34
2 + 34 = 54
Multfrac
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 23 × 75.
Worked answer
14/15
4 × 76 × 5 = 2830
= 1415
Problem 2
Compute 65 × 43.
Worked answer
8/5
6 × 45 × 3 = 2415
= 85
Divfrac
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 76 ÷ 29.
Worked answer
21/4
76 × 92
= 6312 = 214
Problem 2
Compute 15 ÷ 34.
Worked answer
4/15
15 × 43
= 830 = 415
Mixed
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 434 - 123.
Worked answer
37/12
434 = 194 = 5712
123 = 53 = 2012
57 - 2012 = 3712
Problem 2
Compute 512 - 423.
Worked answer
5/6
512 = 112 = 6612
423 = 143 = 5612
66 - 5612 = 56
Ordering
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Compute 34 + 2 × 12.
Worked answer
7/4
2 × 12 = 1
34 + 1 = 74
Problem 2
Compute 43 + 12 × 1.
Worked answer
11/6
12 × 1 = 12
43 + 12 = 116
Converting units
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write 35 as a decimal.
Worked answer
0.6
3 ÷ 5 = 0.6
Problem 2
Write 12 as a decimal.
Worked answer
0.5
1 ÷ 2 = 0.5
Comparing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which is larger, 87 or 311?
- 87
- They are equal
- 311
Worked answer
87
8 × 11 = 88 and 3 × 7 = 21
The bigger cross-product sits over the bigger fraction
88 > 21, so 87 is larger.
Problem 2
Which is larger, 16 or 89?
- 16
- 89
- They are equal
Worked answer
89
1 × 9 = 9 and 8 × 6 = 48
The bigger cross-product sits over the bigger fraction
48 > 9, so 89 is larger.
Wordfrac
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Theo spent 14 of her money on a book, then 14 of what was left on lunch. What fraction of her original money remains?
Worked answer
9/16
After the book: 1 - 14 = 34 remains
Lunch leaves 34 of that
34 × 34 = 916
Problem 2
Ana spent 15 of her money on a book, then 13 of what was left on lunch. What fraction of her original money remains?
Worked answer
8/15
After the book: 1 - 15 = 45 remains
Lunch leaves 23 of that
45 × 23 = 815