Fractions: Understanding Parts of a Whole: 27 flashcards
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1. What does the denominator of a fraction tell you?
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It tells how many **equal parts** the whole is divided into.
2. What does the numerator of a fraction tell you?
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It tells how many of those equal parts are being taken.
3. What does $\frac{3}{4}$ mean in words?
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The whole is split into 4 equal parts, and 3 of them are taken.
4. Why must the parts of a whole be equal for a fraction to be meaningful?
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If the parts are unequal, the numerator no longer counts a fixed amount — the fraction stops representing a definite quantity.
5. Which is larger: $\frac{1}{8}$ or $\frac{1}{3}$? Why?
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$\frac{1}{3}$ is larger. A larger denominator means smaller pieces, so eighths are thinner than thirds.
6. How do you form an equivalent fraction?
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Multiply or divide both the numerator and the denominator by the same non-zero number.
7. Give three fractions equivalent to $\frac{1}{2}$.
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$\frac{2}{4}$, $\frac{3}{6}$, $\frac{50}{100}$ — all equal to $\frac{1}{2}$.
8. What is a proper fraction?
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A fraction whose numerator is less than its denominator, so its value is less than 1.
9. What is an improper fraction?
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A fraction whose numerator is greater than or equal to its denominator, so its value is 1 or more.
10. What is a mixed number?
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A whole number combined with a proper fraction, such as $1\frac{2}{5}$.
11. Convert $\frac{7}{5}$ to a mixed number.
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$1\frac{2}{5}$: divide 7 by 5 — quotient 1 is the whole, remainder 2 goes over 5.
12. What must you do before adding or subtracting fractions?
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Rewrite them with a **common denominator** so the pieces are the same size.
13. What is the smallest common denominator for $\frac{1}{2}$ and $\frac{1}{3}$?
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6 — the LCM of 2 and 3.
14. Compute $\frac{1}{2} + \frac{1}{3}$.
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$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.
15. How do you multiply two fractions?
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Multiply numerators together and denominators together — no common denominator needed. $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$.
16. How do you divide by a fraction?
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Multiply by its **reciprocal**: $\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = 2$.
17. When is a fraction in simplest form?
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When the numerator and denominator share no common factor other than 1.
18. Simplify $\frac{18}{24}$.
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$\frac{3}{4}$ — divide both by their HCF, 6.
19. How do you convert a fraction to a decimal?
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Divide the numerator by the denominator. $\frac{1}{4} = 0.25$.
20. How do you convert a decimal to a percentage?
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Multiply by 100. $0.25 = 25\%$.
21. Write $\frac{1}{4}$ as a decimal and a percentage.
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$0.25$ and $25\%$.
22. Where does $\frac{3}{4}$ sit on a number line?
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Three equal jumps of $\frac{1}{4}$ to the right of 0, between 0 and 1.
23. How do you locate an improper fraction like $\frac{7}{4}$ on a number line?
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Convert to $1\frac{3}{4}$ — it lies past the 1 mark, three quarters further right.
24. On a number line, which of two fractions is larger?
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The one further to the right.
25. What is the most common mistake when adding fractions?
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Adding numerators and denominators straight across, e.g. $\frac{1}{2}+\frac{1}{3}=\frac{2}{5}$ — wrong because the pieces were never the same size.
26. Does a bigger denominator always mean a bigger fraction?
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No — a bigger denominator means **smaller** pieces, so $\frac{1}{8} < \frac{1}{3}$.
27. Name three everyday situations where fractions appear.
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Half a tablet, $\frac{3}{4}$ of an hour, $\frac{2}{3}$ of a group voting yes.
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