Math: Fractions
Ontario Mathematics Proficiency Test — study tool.
Scroll down past the quiz for the complete study guide on this topic.
Scroll down past the quiz for the complete study guide on this topic.
1
Which list of fractions is in order from least to greatest? (5/3, 5/8, 5/10, 5/15)
2
Which fraction is equivalent to 8%?
3
What is the value of 5/3 - 1 + 2/3?
4
Which representation shows that exactly 2/5 of the squares are shaded?
5
A cake is cut into thirds. Each third is then cut into 3 equal slices. What fraction of the whole cake is one slice?
6
Order from least to greatest: 2/3, 1/4, 3/8, 4/5, 7/16
7
What is the value of 3/4 + 6 - 1/4?
8
Order from greatest to least: 1, 39/13, 0.13, 13/39, 0.015
9
On which number line are 7/4 and 5/2 placed correctly?
10
Which best describes the sum of 11/5 + 1/7?
11
Which decimal is equivalent to 2/5?
12
A grid has some squares shaded. Which fraction best represents the shaded portion if it equals 1/4?
13
Which fraction is equivalent to the decimal 1.875?
0
out of 13
Quiz Complete!
Study Guide: Fractions
FRACTION BASICS
A fraction is a/b where:
a = numerator (top) = how many parts you have b = denominator (bottom) = how many equal parts the whole is divided into 3/4 means: 3 out of 4 equal parts
ADDING AND SUBTRACTING FRACTIONS
SAME denominator: just add/subtract the numerators.
5/3 - 3/3 + 2/3 = (5-3+2)/3 = 4/3
DIFFERENT denominators: find a common denominator first.
1/4 + 1/3 = 3/12 + 4/12 = 7/12
WITH WHOLE NUMBERS: convert the whole number to a fraction.
3/4 + 6 - 1/4 = 3/4 - 1/4 + 6 = 2/4 + 24/4 = 26/4
MULTIPLYING FRACTIONS
Multiply numerators together, multiply denominators together.
1/3 × 1/3 = 1/9 Example: A cake cut into thirds, each third cut into 3 slices. One slice = 1/3 × 1/3 = 1/9 of the whole cake.
CONVERTING FRACTIONS TO DECIMALS
Divide the numerator by the denominator.
2/5 = 2 ÷ 5 = 0.40 7/4 = 7 ÷ 4 = 1.75 5/2 = 5 ÷ 2 = 2.5
Common fractions to know by heart:
1/2 = 0.5 1/3 ≈ 0.333 1/4 = 0.25 1/5 = 0.2 2/5 = 0.4 3/4 = 0.75 1/8 = 0.125 3/8 = 0.375
CONVERTING DECIMALS TO FRACTIONS
Put the decimal over the appropriate power of 10, then simplify.
0.4 = 4/10 = 2/5 0.125 = 125/1000 = 1/8
For mixed numbers:
1.875 = 1 + 0.875 = 1 + 875/1000 = 1 + 7/8 = 15/8
Or try dividing: does 15/8 = 1.875? Yes (15 ÷ 8 = 1.875).
CONVERTING PERCENTAGES TO FRACTIONS
Put the percentage over 100, then simplify.
8% = 8/100 = 2/25 (divide both by 4) 40% = 40/100 = 2/5 80% = 80/100 = 4/5
ORDERING FRACTIONS
THE METHOD: Convert every fraction to a decimal, then compare.
Example: Order from least to greatest: 5/15, 5/10, 5/8, 5/3
5/15 = 0.333
5/10 = 0.500
5/8 = 0.625
5/3 = 1.667
Answer: 5/15, 5/10, 5/8, 5/3
SHORTCUT: When fractions have the SAME NUMERATOR, a larger
denominator means a SMALLER fraction.
5/15 < 5/10 < 5/8 < 5/3 (denominators decrease = values increase)
FRACTIONS ON A NUMBER LINE
Convert to decimals to place accurately.
7/4 = 1.75 → between 1 and 2 (closer to 2) 5/2 = 2.5 → between 2 and 3 (exactly halfway)
ESTIMATING FRACTION SUMS
Convert to decimals mentally, then estimate.
11/5 + 1/7 11/5 = 2.2 (a bit more than 2) 1/7 ≈ 0.14 (a small amount) Sum ≈ 2.34 → between 2 and 3
VISUAL FRACTION REPRESENTATION
When given a grid/visual, count:
- Total squares = denominator - Shaded squares = numerator
Then simplify: 8 shaded out of 20 total = 8/20 = 2/5
ORDERING MIXED NUMBERS AND DECIMALS
Convert everything to the same form (decimals are easiest).
Example: Order greatest to least: 1, 39/13, 0.13, 13/39, 0.015
1 = 1
39/13 = 3
0.13 = 0.13
13/39 ≈ 0.333
0.015 = 0.015
Greatest to least: 3, 1, 0.333, 0.13, 0.015
KEY THINGS TO REMEMBER
- Same denominator: just add/subtract numerators - Different denominators: find common denominator first - Multiplying: numerator × numerator, denominator × denominator - To compare fractions: convert to decimals - Same numerator, bigger denominator = smaller fraction - Percentage to fraction: put over 100 and simplify - Decimal to fraction: put over power of 10 and simplify - When in doubt, use your calculator to divide numerator by denominator
