{"id":244799,"date":"2024-06-24T16:00:03","date_gmt":"2024-06-24T08:00:03","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=244799"},"modified":"2025-06-16T13:21:55","modified_gmt":"2025-06-16T05:21:55","slug":"algebra-how-to-simplify-algebraic-fractions","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/algebra-how-to-simplify-algebraic-fractions\/","title":{"rendered":"Algebra: How To Simplify Algebraic Fractions"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.16″ global_colors_info=”{}”][et_pb_row _builder_version=”4.21.0″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” hover_enabled=”0″ z_index_tablet=”500″ custom_css_main_element=”sub,||sup {||font-size: 75%;||line-height: 0;||position: relative;||vertical-align: baseline;||}||sup {||top: -0.5em;||}||sub {||bottom: -0.25em;||}” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

Introduction<\/strong><\/p>\n

If you clicked on this blog post, you are probably looking for helpful tips in simplifying algebraic fractions.<\/p>\n

We\u2019ve got you covered!<\/p>\n

We previously talked about expanding and factorising algebraic expressions. Click on the link<\/a> if you missed out on that!<\/p>\n

But in this blog post, we will share a detailed guide to simplifying algebraic fractions, along with a recap on adding fractions with the same and different denominators.<\/p>\n

<\/p>\n

<\/p>\n\n

Let’s Take A Look At This Algebra Question<\/span><\/h2>\n

<\/p>\n

<\/p>\n

\"The<\/p>\n

\n

Read Also:<\/h3>\n
    \n
  1. [Secondary 2 Math Explainer Video] Direct Proportion: Finding The Relationship Between A & H<\/b><\/a><\/li>\n
  2. Beginner\u2019s Guide To Cross Multiplication<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    Here, you will see four parts of addition and subtraction of fractions (one involves a combination of both).<\/p>\n

    Before we proceed, read the instructions. You are asked to simplify the algebraic fractions.<\/p>\n

    \n

    \ud83e\udd14\u00a0What Does Simplifying Algebraic Fractions Mean? \ud83e\udd14<\/strong><\/p>\n

    When you are asked to add or subtract algebraic fractions, simplifying means that your answer must be in the form of a single fraction<\/strong>.<\/p>\n<\/blockquote>\n

    How can you do this?<\/p>\n

    Let us recap the things you learned in primary school. How do you add algebraic fractions with the same denominators like the ones below?<\/p>\n

    \"The<\/p>\n

    <\/h3>\n

    Do you take 2+1\/5+5 and then get 3\/10?<\/p>\n

    This is the wrong way to do this! What is the correct way of doing this then?<\/p>\n

    \n

    \ud83d\udca1\u00a0How To Add Algebraic Fractions With The Same Denominators?<\/strong> \ud83d\udca1<\/p>\n

    First, check for the common denominator. In our example, both are 5 so they are the same. Because they have a common denominator, you just add the numerators and copy the denominators.<\/p>\n<\/blockquote>\n

    2 + 1 = 3<\/p>\n

    Therefore, the answer is 3\/5<\/strong>.<\/p>\n

    You might also be wondering now how to add algebraic fractions with different denominators so let us try solving this:<\/p>\n

    1\/2 + 2\/3<\/p>\n

    Are you going to take 1+2\/2+3 to get 3\/5? No! This is not the correct way of doing this.<\/p>\n

    First, find the Least Common Multiple (LCM) of the denominators.<\/p>\n

    \n

    \ud83e\uddd0\u00a0What Is The Least Common Multiple (LCM)?<\/strong> \ud83e\uddd0<\/p>\n

    It is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder.<\/p>\n<\/blockquote>\n

    What is the LCM of the denominators 2 and 3?<\/p>\n

    Their LCM is 6!<\/p>\n

    The first fraction then becomes 3\/6 and the second becomes 4\/6.<\/p>\n

    3\/6 + 4\/6 = 7\/6 or 1 1\/6<\/p>\n

    If you were not able to follow, don\u2019t worry as we will discuss it in detail below.<\/p>\n

    Now that we\u2019ve refreshed your memory on how to add algebraic fractions, we can proceed with simplifying algebraic fractions!<\/p>\n

    <\/h2>\n

    Let\u2019s Solve Part (A)<\/span><\/h2>\n

    \"The<\/p>\n

    First, check for the common denominator. Since both are 5, we can proceed with adding the numerators.<\/p>\n

    2x<\/em> + x<\/em> = 3x<\/em><\/p>\n

    Therefore, the answer is 3x<\/em>\/5.<\/p>\n

    <\/p>\n

    <\/p>\n

    Suggested Answer For Part (A)<\/span>
    <\/h2>\n

    3x\/5\u00a0<\/p>\n

    <\/p>\n

    Let\u2019s Solve Part (B)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    Again, we have to check for common denominators first. We have 18 and 12. Are they the same? No!<\/p>\n

    So, we have to find their LCM.<\/p>\n

    Their LCM is 36. Now, we will convert your algebraic fractions to upon 36.<\/p>\n

    Remember that your teachers might be very particular with presentation so follow these steps.<\/p>\n

    We multiplied our first denominator by 2 to get our LCM. Let us put brackets and multiply the numerator and denominator by 2.<\/p>\n

    \"How<\/p>\n

    For your second fraction, we multiplied our denominator by 3 to get the LCM. Put brackets and multiply our numerator and denominator by 3. <\/p>\n

    \"How<\/p>\n

    The next step will be to expand your numerators.<\/p>\n

    For the first fraction, we are going to have 14x<\/em>+8. For the second fraction, we\u2019ll have 15.<\/p>\n

    \"How<\/p>\n

    Now we have the same denominators, so we can proceed with adding our numerators.<\/p>\n

    \"The<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/h2>\n

    Suggested Answer For Part (B)<\/span>
    <\/h2>\n

    \"How<\/p>\n

    <\/p>\n

    Let\u2019s Solve Part (C)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    First, check if the denominators are the same.<\/p>\n

    They are not! So we have to find their LCM.<\/p>\n

    The LCM of 6 and 9 is 18. Now, we can convert our algebraic fractions to upon 18.<\/p>\n

    We multiplied our denominator by 3 to get our LCM. So let us put brackets and multiply our numerator and denominator by 3.<\/p>\n

    \"How<\/p>\n

    For our second fraction, we multiplied the denominator by 2 to get our LCM. Let us put brackets and multiply the numerator and denominator by 2. <\/p>\n

    \"How<\/p>\n

    Now, we can expand our fractions. For the first numerator, we\u2019ll have 9x <\/span>– 3. For the second numerator, we\u2019ll have 4x<\/span> – 2.<\/p>\n

    \"How<\/p>\n

    The denominators are now the same so we can proceed with subtracting our numerators.<\/p>\n

    When you are subtracting more than one term, remember to put brackets like below.<\/p>\n

    \"The<\/p>\n

    Next, copy the numerators and don\u2019t forget to include the brackets.<\/p>\n

    \"How<\/p>\n

    Now, let us expand our numerator. Collect your x <\/span>(highlighted in blue). Then, collect your numbers (highlighted in yellow).<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Suggested Answer For Part (C)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    <\/p>\n

    Let\u2019s Solve Part (D)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    The first step you have to do is to convert 2 into a fraction. 2 is actually upon 1.<\/p>\n

    \"How<\/p>\n

    Now, you have to find the LCM of 1, 2 and 3.<\/p>\n

    The LCM of 1, 2 and 3 is 6!<\/strong><\/p>\n

    The next step is to convert all the fractions to upon 6.<\/p>\n

    We multiplied our first denominator by 6 to get the LCM. Let us put brackets and multiply the numerator and denominator by 6.<\/p>\n

    \"How<\/p>\n

    Next, we multiplied our second denominator by 3 to get the LCM. Let us put brackets and multiply our numerator and denominator by 3.<\/p>\n

    \"How<\/p>\n

    Lastly, we multiplied our last denominator by 2 to get the LCM. Let us put brackets and multiply our numerator and denominator by 2.<\/p>\n

    \"How<\/p>\n

    Because our fractions have the same denominator now, we can start solving them. There\u2019s a minus sign so remember to put brackets. Let us now expand.<\/p>\n

    \"How<\/p>\n

    Next, collect all your numbers (highlighted in yellow) and your x<\/span> terms (highlighted in pink) and you will get the final answer.<\/p>\n

    \"How<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

    Suggested Answer For Part (D)<\/span>
    <\/h2>\n

    \"The<\/p>\n

    <\/p>\n

    Conclusion<\/span><\/h2>\n

    I hope that after reading this blog post, you have recapped how to solve algebraic equations involving fractions with the same and different denominators.<\/p>\n

    Always remember to show a detailed presentation of your solution to avoid losing marks.<\/p>\n

    Keep on checking for more blog posts that help you tackle challenging Algebra<\/a> questions.<\/p>\n

    <\/p>\n

    <\/p>\n

    <\/p>\n

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    In this article, we\u2019ll be discussing how to solve this Secondary 1 Math question on Simplifying Algebraic Fractions.<\/p>\n","protected":false},"author":41,"featured_media":244803,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","om_disable_all_campaigns":false,"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[59,60],"tags":[],"post_folder":[],"modified_by":"Jaimie Aberia","_links":{"self":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244799"}],"collection":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/comments?post=244799"}],"version-history":[{"count":21,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244799\/revisions"}],"predecessor-version":[{"id":246592,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/244799\/revisions\/246592"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/244803"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=244799"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=244799"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=244799"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=244799"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}