Are you preparing for a Math Olympiad and looking for challenging questions on fractions? Fractions are a fundamental part of math, and mastering them is essential for success in competitive exams like the Math Olympiad. In this blog, we’ll explore a variety of Olympiad-level questions on fractions to help you sharpen your problem-solving skills and boost your confidence. Whether you’re a student or a teacher looking for practice material, these questions will offer the perfect preparation.
1. True or false?
Ans. 1/99 x 100 = 1/99 – 1/100
Is this true for the following as well?
1/8 x 9 = 1/8 – 1/9
1/91 x 92 = 1/91 – 1/92
Ans. 1/99 x 100 = 100 – 99 / 99 x 100
= 100/99 x 100 – 99/99 x 100
= 1/99 – 1/100
Any unit fraction whose denominator is the product of two consecutive numbers can be expressed as a difference of unit fractions.
2. Can you write the general formula?
1/n x (n + 1)=(n + 1) — n/n x (n + 1)
=(n + 1)/n x (n + 1) – n/n x (n + 1)
=1/n – 1/n+1
Evaluate: 1/1×2 + 1/2×3 + 1/3×4 + …… + 1/99×100
We can express each term as shown below.
1/1×2 = 2 — 1/1 x 2 = 1 – 1/2
1/2x 3 =3 — 2/2 x 3= 1/2 -1/3
1/3x 4 =4 — 3/3 x 4= 1/3 -¼
1/1×2 + 1/2x 3 + 1/3x 4 + ….. + 1/99x 100
=1 -1/2 + 1/2 –1/3 + 1/3 – 1/4 + 1/4 +…..… + 1/99 – 1/100
=1 – 1/100
=100 -1/100
=99/100
1. | Evaluate: 18+124+148+180+1120+1168 | |
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Solution: 18+124+148+180+1120+1168 =14[12+16+112+120+130+142] =14[2 – 11 2+3 – 22 3+4 – 33 4+5 – 44 5+6 – 55 6+7 – 66 7] =14[1-12+12–13+13–14+14–15+15–16+16–17] =14[1-17] =14[7 – 17] =1467 =314 | ||
2. | Evaluate: 14+512+1124+1940+2960 | |
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Solution: 14+512+1124+1940+2960 =12[12+56+1112+1920+2930] =12[1-12+1-16+1-112+1-120+1-130] =12[5-(12+16+112+120+130)] =12[5-(2 – 11 2+3 – 22 3+4 – 33 4+5 – 44 5+6 – 55 6)] =12[5-(1-12+12–13+13–14+14–15+15–16)] =12[5-(1-16)] =12[5-1+16] =12[4+16] =12[24 + 16] =12256 =2512 |
Fractions may seem simple, but they can be tricky when presented in Math Olympiad questions. With the right practice and understanding, you can master fractions and excel in your Math Olympiad. We hope these questions have given you a good starting point for your preparation. Keep practicing, stay consistent, and you’ll be well on your way to achieving success in the competition!
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