Fractions Flashcards
Free fractions flashcards with the rules you need for equivalent fractions, simplifying, adding and subtracting, multiplying and dividing, mixed numbers and converting to decimals and percents. Flip each card, then mark what you know.
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Fraction basics
| Question | Answer |
|---|---|
| What is the numerator? | The top number. It tells how many parts you have. |
| What is the denominator? | The bottom number. It tells how many equal parts make the whole. |
| What is a proper fraction? | A fraction whose numerator is less than its denominator, such as 3/4. |
| What is an improper fraction? | A fraction whose numerator is greater than or equal to its denominator, such as 7/4. |
| What is a mixed number? | A whole number plus a fraction, such as 1 3/4. |
| What is a unit fraction? | A fraction with a numerator of 1, such as 1/5. |
| What is the reciprocal of a/b? | b/a (flip the fraction). The reciprocal of 3/5 is 5/3. |
| What is the reciprocal of a whole number n? | 1/n. The reciprocal of 6 is 1/6. |
Equivalent fractions and simplifying
| Question | Answer |
|---|---|
| How do you make an equivalent fraction? | Multiply or divide the numerator and denominator by the same nonzero number. 1/2 = 2/4 = 3/6. |
| How do you simplify a fraction? | Divide the numerator and denominator by their greatest common factor (GCF). |
| Simplify 12/18. | 2/3 (divide by the GCF, 6) |
| Simplify 15/45. | 1/3 (divide by 15) |
| When is a fraction in simplest form? | When the numerator and denominator share no common factor other than 1. |
| Are 3/4 and 6/8 equivalent? | Yes. Multiply 3/4 by 2/2 to get 6/8. |
| How can you test whether a/b = c/d? | Cross multiply: a/b = c/d when a × d = b × c. |
Adding and subtracting
| Question | Answer |
|---|---|
| How do you add fractions with the same denominator? | Add the numerators and keep the denominator. 2/7 + 3/7 = 5/7. |
| How do you add fractions with different denominators? | Find a common denominator, rewrite each fraction, then add the numerators. |
| What is the least common denominator (LCD)? | The least common multiple of the denominators. |
| 1/2 + 1/3 = ? | 5/6 (LCD is 6: 3/6 + 2/6) |
| 3/4 − 1/6 = ? | 7/12 (LCD is 12: 9/12 − 2/12) |
| How do you subtract fractions with the same denominator? | Subtract the numerators and keep the denominator. 5/8 − 2/8 = 3/8. |
Multiplying and dividing
| Question | Answer |
|---|---|
| How do you multiply fractions? | Multiply the numerators, multiply the denominators, then simplify. 2/3 × 3/5 = 6/15 = 2/5. |
| How do you divide by a fraction? | Multiply by its reciprocal ("keep, change, flip"). |
| 3/4 ÷ 1/2 = ? | 3/2, or 1 1/2 (3/4 × 2/1) |
| 2/5 ÷ 4 = ? | 1/10 (2/5 × 1/4 = 2/20) |
| What is 1/2 of 3/8? | 3/16 ("of" means multiply) |
| Why can you cancel before multiplying? | Dividing a numerator and a denominator by the same factor does not change the product and keeps numbers small. |
Mixed numbers and improper fractions
| Question | Answer |
|---|---|
| Convert 2 3/5 to an improper fraction. | 13/5 (2 × 5 + 3 = 13, over 5) |
| Convert 17/4 to a mixed number. | 4 1/4 (17 ÷ 4 = 4 remainder 1) |
| How do you add mixed numbers? | Add the whole numbers and the fractions separately, then regroup if needed. Or convert to improper fractions. |
| How do you multiply mixed numbers? | Convert each to an improper fraction, multiply, then simplify. |
Fractions, decimals and percents
| Question | Answer |
|---|---|
| How do you convert a fraction to a decimal? | Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. |
| How do you convert a decimal to a fraction? | Write the digits over the matching power of 10, then simplify. 0.35 = 35/100 = 7/20. |
| How do you convert a fraction to a percent? | Convert to a decimal, then multiply by 100. |
| 1/2 as a decimal and percent? | 0.5 and 50% |
| 1/4 as a decimal and percent? | 0.25 and 25% |
| 3/4 as a decimal and percent? | 0.75 and 75% |
| 1/3 as a decimal and percent? | 0.333… (repeating) and about 33.3% |
| 1/5 as a decimal and percent? | 0.2 and 20% |
| 1/8 as a decimal and percent? | 0.125 and 12.5% |
| How do you compare two fractions? | Rewrite with a common denominator, or cross multiply, then compare the numerators. |
Frequently asked questions
What is the easiest way to add fractions?
Rewrite both fractions over a common denominator, add the numerators and keep the denominator. Then simplify the result.
Why do you flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal. Dividing by 1/2 asks how many halves fit, which is the same as multiplying by 2.
Do you need a common denominator to multiply fractions?
No. Multiply straight across and simplify.
Sources
More free math flashcards
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