{"id":34062,"date":"2024-10-02T07:06:10","date_gmt":"2024-10-02T07:06:10","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=34062"},"modified":"2024-10-02T07:11:26","modified_gmt":"2024-10-02T07:11:26","slug":"question-on-fraction","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/question-on-fraction\/","title":{"rendered":"Math Olympiad Questions on Fraction"},"content":{"rendered":"\t\t
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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\u2019ll 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.<\/span><\/p>

1. True or false?<\/b><\/h3>

Ans.<\/strong> 1\/99 x 100 = 1\/99 – 1\/100<\/span><\/p>

Is this true for the following as well?<\/b><\/p>

1\/8 x 9 =\u00a0 1\/8 – 1\/9<\/span><\/p>

1\/91 x 92 = 1\/91 – 1\/92<\/span><\/p>

Ans. <\/span>\u00a01\/99 x 100 =\u00a0 100 –\u00a0 99 \/ 99 x 100<\/span><\/p>

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 100\/99 x 100 – 99\/99 x 100<\/span><\/p>

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 1\/99 – 1\/100<\/span><\/p>

Any unit fraction whose denominator is the product of two consecutive numbers can be expressed as a difference of unit fractions.<\/span><\/p>

2. Can you write the general formula?<\/b><\/p>

1\/n x (n + 1)=(n + 1) \u2014 n\/n x (n + 1)<\/span><\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=(n + 1)\/n x (n + 1) – n\/n x (n + 1)<\/span><\/p>

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=1\/n – 1\/n+1<\/span><\/p>

\u00a0Evaluate: 1\/1×2 + 1\/2×3 + 1\/3×4 + \u2026\u2026 + 1\/99×100<\/strong><\/h4>

We can express each term as shown below.\u00a0<\/span><\/p>

1\/1×2 = 2 \u2014 1\/1 x 2 = 1 – 1\/2<\/span><\/p>

1\/2x 3 =<\/span>3 \u2014 2\/2 x 3<\/span>= 1\/2 -1\/3\u00a0<\/span><\/p>

1\/3x 4 =<\/span>4 \u2014 3\/3 x 4<\/span>= 1\/3 -\u00bc<\/span><\/p>

1\/1×2 + 1\/2x 3 + 1\/3x 4 + \u2026.. + 1\/99x 100<\/span><\/p>

=1 <\/span>-1\/2 + 1\/2<\/span> –<\/span>1\/3 + 1\/3<\/span> – <\/span>1\/4 + 1\/4 <\/span>+…..\u2026 + <\/span>1\/99<\/span> – 1\/100<\/span><\/p>

=1 – 1\/100<\/span><\/p>

=100 -1\/100<\/span><\/p>

=99\/100<\/span><\/p>

1.<\/h4><\/td>

Evaluate: 18+124+148+180+1120+1168<\/strong><\/h4><\/td><\/tr>

\u00a0<\/td>
  1. 1<\/span>4<\/span><\/li>
  2. 1<\/span>7<\/span><\/li>
  3. 1<\/span>14<\/span><\/li>
  4. 3<\/span>14<\/span><\/li><\/ol><\/td><\/tr>
\u00a0<\/td>

Solution: <\/b>1<\/span>8<\/span>+<\/span>1<\/span>24<\/span>+<\/span>1<\/span>48<\/span>+<\/span>1<\/span>80<\/span>+<\/span>1<\/span>120<\/span>+<\/span>1<\/span>168<\/span><\/p>

=<\/span>1<\/span>4<\/span>[<\/span>1<\/span>2<\/span>+<\/span>1<\/span>6<\/span>+<\/span>1<\/span>12<\/span>+<\/span>1<\/span>20<\/span>+<\/span>1<\/span>30<\/span>+<\/span>1<\/span>42<\/span>]<\/span><\/p>

=<\/span>1<\/span>4<\/span>[<\/span>2 – 1<\/span>1 <\/span> 2<\/span>+<\/span>3 – 2<\/span>2 <\/span> 3<\/span>+<\/span>4 – 3<\/span>3 <\/span> 4<\/span>+<\/span>5 – 4<\/span>4 <\/span> 5<\/span>+<\/span>6 – 5<\/span>5 <\/span> 6<\/span>+<\/span>7 – 6<\/span>6 <\/span> 7<\/span>]<\/span><\/p>

=<\/span>1<\/span>4<\/span>[1-<\/span>1<\/span>2<\/span>+<\/span>1<\/span>2<\/span>–<\/span>1<\/span>3<\/span>+<\/span>1<\/span>3<\/span>–<\/span>1<\/span>4<\/span>+<\/span>1<\/span>4<\/span>–<\/span>1<\/span>5<\/span>+<\/span>1<\/span>5<\/span>–<\/span>1<\/span>6<\/span>+<\/span>1<\/span>6<\/span>–<\/span>1<\/span>7<\/span>]<\/span><\/p>

=<\/span>1<\/span>4<\/span>[1-<\/span>1<\/span>7<\/span>]<\/span><\/p>

=<\/span>1<\/span>4<\/span>[<\/span>7 – 1<\/span>7<\/span>]<\/span><\/p>

=<\/span>1<\/span>4<\/span>6<\/span>7<\/span><\/p>

=<\/span>3<\/span>14<\/span><\/p><\/td><\/tr><\/tbody><\/table>

2.<\/strong><\/p><\/td>

Evaluate: 14+512+1124+1940+2960<\/strong><\/p><\/td><\/tr><\/tbody><\/table>
  1. 1<\/span>12<\/span>\u00a0<\/span><\/li>
  2. 31<\/span>6<\/span><\/li>
  3. 25<\/span>12<\/span><\/li>
  4. 5<\/span>6<\/span><\/li><\/ol><\/td><\/tr>

Solution:<\/b>\u00a0\u00a0\u00a0<\/span>1<\/span>4<\/span>+<\/span>5<\/span>12<\/span>+<\/span>11<\/span>24<\/span>+<\/span>19<\/span>40<\/span>+<\/span>29<\/span>60<\/span><\/p>

=<\/span>1<\/span>2<\/span>[<\/span>1<\/span>2<\/span>+<\/span>5<\/span>6<\/span>+<\/span>11<\/span>12<\/span>+<\/span>19<\/span>20<\/span>+<\/span>29<\/span>30<\/span>]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[1-<\/span>1<\/span>2<\/span>+1-<\/span>1<\/span>6<\/span>+1-<\/span>1<\/span>12<\/span>+1-<\/span>1<\/span>20<\/span>+1-<\/span>1<\/span>30<\/span>]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[5-(<\/span>1<\/span>2<\/span>+<\/span>1<\/span>6<\/span>+<\/span>1<\/span>12<\/span>+<\/span>1<\/span>20<\/span>+<\/span>1<\/span>30<\/span>)]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[5-(<\/span>2 – 1<\/span>1 <\/span> 2<\/span>+<\/span>3 – 2<\/span>2 <\/span> 3<\/span>+<\/span>4 – 3<\/span>3 <\/span> 4<\/span>+<\/span>5 – 4<\/span>4 <\/span> 5<\/span>+<\/span>6 – 5<\/span>5 <\/span> 6<\/span>)]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[5-(1-<\/span>1<\/span>2<\/span>+<\/span>1<\/span>2<\/span>–<\/span>1<\/span>3<\/span>+<\/span>1<\/span>3<\/span>–<\/span>1<\/span>4<\/span>+<\/span>1<\/span>4<\/span>–<\/span>1<\/span>5<\/span>+<\/span>1<\/span>5<\/span>–<\/span>1<\/span>6<\/span>)]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[5-(1-<\/span>1<\/span>6<\/span>)]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[5-1+<\/span>1<\/span>6<\/span>]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[4+<\/span>1<\/span>6<\/span>]<\/span><\/p>

=<\/span>1<\/span>2<\/span>[<\/span>24 + 1<\/span>6<\/span>]<\/span><\/p>

=<\/span>1<\/span>2<\/span>25<\/span>6<\/span><\/p>

=<\/span>25<\/span>12<\/span><\/p><\/td><\/tr><\/tbody><\/table>

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!<\/span><\/p>

Want to excite your child about math and sharpen their math skills? Moonpreneur’s online math curriculum is unique as it helps children understand math skills through hands-on lessons, assists them in building real-life applications, and excites them to learn math.\u00a0<\/span><\/p>

You can opt for our <\/span>Advanced Math<\/span><\/a> or Vedic Math+Mental Math courses. Our <\/span>Math Quiz<\/span><\/a> for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

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\u2019ll explore a variety of Olympiad-level questions on fractions to help you sharpen your problem-solving skills and […]<\/p>\n","protected":false},"author":116,"featured_media":34064,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[969],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/34062"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=34062"}],"version-history":[{"count":5,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/34062\/revisions"}],"predecessor-version":[{"id":34092,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/34062\/revisions\/34092"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/34064"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=34062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=34062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=34062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}