Positive Rational Number Operations — Practice
Fractions, decimals and percents are three costumes for the same number. Choose whichever makes the arithmetic easiest.
What these questions 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.
Problem 1
Compute 14 + 38.
Worked answer
5/8
14 = 28
28 + 38 = 58
Problem 2
Compute 25 × 34.
Worked answer
3/10
2 × 35 × 4 = 620
= 310
Problem 3
Compute 34 ÷ 12.
Worked answer
3/2
34 × 21 = 64
= 32
Problem 4
Write 58 as a decimal.
Worked answer
0.625
5 ÷ 8 = 0.625
Problem 5
Compute 23 + 16.
Worked answer
5/6
23 = 46
46 + 16 = 56
Problem 6
Compute 34 + 25.
Worked answer
23/20
34 = 1520 and 25 = 820
15 + 820 = 2320
= 1320
Problem 7
Compute 413 - 156.
Worked answer
5/2
413 = 133 = 266
156 = 116
26 - 116 = 156 = 52 = 212
Problem 8
How many 23-cup servings are in 6 cups?
Worked answer
9
6 ÷ 23 = 6 × 32
= 182 = 9
Problem 9
Compute 212 × 45.
Worked answer
2
212 = 52
52 × 45 = 2010 = 2
Cancelling first is faster: the 5s cancel and 4 ÷ 2 = 2.
Problem 10
Compute 12 + 13 × 34.
Worked answer
3/4
13 × 34 = 312 = 14
12 + 14 = 24 + 14 = 34
Problem 11
Which is larger, 58 or 711?
- 58
- 711
- They are equal
Worked answer
711
5 × 11 = 55 and 7 × 8 = 56
The bigger cross-product sits over the bigger fraction
56 > 55, so 711 > 58
Problem 12
Write 0.45 as a fraction in lowest terms.
Worked answer
9/20
0.45 = 45100
Divide top and bottom by 5: 920
Problem 13
A board is 814 feet long. How many 112-foot pieces can be cut from it?
Worked answer
5
814 ÷ 112 = 334 ÷ 32
= 334 × 23 = 6612 = 112 = 5.5
You can cut 5 whole pieces, with half a piece of wood left over.
Problem 14
Compute 23 + 1656.
Worked answer
1
Top: 23 + 16 = 46 + 16 = 56
Now 56 ÷ 56 = 1
Problem 15
Maya spent 13 of her money on a book and 25 of what was left on lunch. What fraction of her original money remains?
Worked answer
2/5
After the book: 1 - 13 = 23 remains
Lunch takes 25 × 23 = 415 of the original
Remaining: 23 - 415 = 1015 - 415 = 615 = 25
Shortcut: 23 × 35 = 25.
Problem 16
Which of these fractions gives a decimal that terminates (stops)?
- 712
- 56
- 940
- 415
Worked answer
940
40 = 23 × 5 — only 2s and 5s, so it terminates (940 = 0.225)
12, 6 and 15 each contain a factor of 3, so those repeat.