Where this sits. This is one of the five number families — the arithmetic that a little under half the test is made of, and that every algebra family is built out of. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
DrillsTwenty drills for this family, one skill each, ten problems at a timeGo to the drills ↓Parts of a whole: what a fraction is, comparing them, adding, multiplying, dividing. On the test, fractions are the usual clothing of division and of “what part of.”
They also turn up inside algebra, where a slope is a fraction and a rate is a fraction, so the work you do here is never only about fractions. If fractions are shaky, three later families will feel harder than they are.
What the test asks in this family
- What the top and bottom numbers each doQuiz 8
- Equivalent fractions — one amount, many namesQuiz 8 · Fractions Practice
- SimplifyingQuiz 8 · Fractions Practice
- Improper fractions and mixed numbersQuiz 8 · Quiz 10 · Fractions Practice
- Comparing and ordering fractionsQuiz 9 · Fractions Practice
- Common denominatorsQuiz 10 · Fractions Practice
- Adding and subtracting fractionsQuiz 10 · Fractions Practice
- Multiplying fractions, and “of” meaning timesQuiz 11 · Fractions Practice
- Dividing fractions, and reciprocalsQuiz 12 · Fractions Practice
All 9 have something on this site.
Six questions across this family. Type an answer and press Check. You get the reasoning for every one, right or wrong.
- Which is bigger, 3⁄5 or 5⁄8? 5⁄8. You cannot compare them as they stand, because the pieces are different sizes. Give them the same bottom: 40 works for both. 3⁄5 = 24⁄40 and 5⁄8 = 25⁄40. Now they are the same size of piece and you just count: 25 beats 24.
- Simplify 18⁄24 3⁄4. Both numbers divide by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. Simplifying never changes how much you have — it just renames the same amount with fewer, bigger pieces. Eighteen twenty-fourths of a pizza and three quarters of a pizza are the same lunch.
- 2⁄3 + 1⁄4 = 11⁄12. You can only add pieces of the same size, so re-cut them both into twelfths: 2⁄3 = 8⁄12 and 1⁄4 = 3⁄12. Now add the count and keep the name: 8 twelfths plus 3 twelfths is 11 twelfths. The bottom number never gets added.
- 3⁄4 × 2⁄5 = 3⁄10. Multiplying is the easy one: across the top, 3 × 2 = 6, and across the bottom, 4 × 5 = 20. That gives 6⁄20, which simplifies to 3⁄10. Notice the answer is smaller than either fraction — taking a part of a part always is.
- 1⁄2 ÷ 1⁄6 = 3. Division asks how many of the second fit inside the first: how many sixths fit in a half? Three. The rule — flip the second and multiply — does the same work: 1⁄2 × 6⁄1 = 6⁄2 = 3. Dividing by a fraction smaller than one makes the answer bigger, which surprises people until they ask the question this way.
- A recipe needs 3⁄4 cup of flour. You are making half the recipe. How much flour? 3⁄8 cup. Half of three quarters — and on this test, “of” means multiply. 1⁄2 × 3⁄4 = 3⁄8. That word is worth watching for, because it turns an English sentence into an arithmetic instruction.
Missed one? The five fraction quizzes are in Learn it just below, and each one teaches its topic before it asks anything. Fractions Practice under On paper has 176 problems for the drill.
Want more than these six questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 8What a Fraction IsThe top number, the bottom number, and what each one does.
- Quiz 9Comparing and Ordering FractionsWhich is bigger, without guessing.
- Quiz 10Adding and Subtracting FractionsCommon denominators, and why you need them.
- Quiz 11Multiplying FractionsThe easiest of the four, once you see it.
- Quiz 12Dividing FractionsFlip the second one, and the reason that works.
Twenty short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 3.01What fraction is shaded?
- 3.02Equivalent fractions: find the missing number
- 3.03Simplify a fraction
- 3.04Improper fraction to mixed number
- 3.05Mixed number to improper fraction
- 3.06Fractions on a number line
- 3.07Compare two fractions
- 3.08Put fractions in order
- 3.09Find the least common denominator
- 3.10Add and subtract, same denominator
- 3.11Add and subtract, different denominators
- 3.12Add mixed numbers
- 3.13Subtract mixed numbers, borrowing
- 3.14Multiply fractions
- 3.15Multiply mixed numbers
- 3.16A fraction of a whole number (2/3 of 24)
- 3.17Reciprocals
- 3.18Divide fractions
- 3.19Divide mixed numbers
- 3.20Word problems with fractions · calculator allowed
No app for this family yet. An app for fractions is one of the ones we most want to build.
- Fractions Practice · 176 problems: simplifying, equivalent fractions, mixed numbers, comparing, adding and subtracting with borrowing, multiplying and dividing, and eight word problems. Each section opens with a worked example and starts with its plainest problems. Answer key at the end. Made to print.
- Khan Academy, math · free videos and practice. Search it for fractions, adding fractions, dividing fractions. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up fractions in the contents of either.
On to decimals, which are fractions written in tenths and hundredths. Quiz 16 shows the two writing the same number, so the two families join up there.