{"id":243930,"date":"2024-03-20T16:00:48","date_gmt":"2024-03-20T08:00:48","guid":{"rendered":"https:\/\/thepiquelab.com\/blog\/?p=243930"},"modified":"2024-06-10T12:25:30","modified_gmt":"2024-06-10T04:25:30","slug":"beginners-guide-to-cross-multiplication","status":"publish","type":"post","link":"https:\/\/thepiquelab.com\/blog\/beginners-guide-to-cross-multiplication\/","title":{"rendered":"Beginner\u2019s Guide To Cross Multiplication"},"content":{"rendered":"

[et_pb_section fb_built=”1″ _builder_version=”4.16″ global_colors_info=”{}”][et_pb_row _builder_version=”4.16″ 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″ z_index_tablet=”500″ global_colors_info=”{}”]<\/p>\n

Have you ever found yourself scratching your head when faced with Algebraic fractions in Math problem sums?<\/p>\n

Don’t worry, you’re not alone! Fractions can be tricky to manipulate, especially when you’re trying to compare or solve equations involving them.<\/p>\n

In the blog post, we discuss a handy technique that can solve your fraction-solving woes: cross multiplication<\/strong>.<\/p>\n

Let me start with a little story time.<\/p>\n

Once, I asked a student, \u201cDo you know when you can use cross multiplication?<\/strong>\u201d He replied, \u201cWhen you see fractions! Like this\u2026\u201d He wrote the following on the board:<\/p>\n

\"The<\/p>\n

Another student overheard and said, \u201cNo, that\u2019s not right!\u201d He then wrote the following on the board:<\/p>\n

\"The<\/p>\n

Who do you think is correct?<\/p>\n

In a way, both of them are right. We use cross multiplication when we see fractions. However, we can only use cross multiplication when we see \u201cfraction = fraction\u201d<\/strong>.<\/p>\n

\"The<\/p>\n\n

\n

\ud83d\udca1 What Is Cross Multiplication?<\/strong> \ud83d\udca1<\/p>\n

Cross multiplication is a technique to solve equations involving algebraic fractions.<\/p>\n<\/blockquote>\n

\n

Read Also:<\/h3>\n
    \n
  1. P5 Math Problem-solving Technique: Unit X Value Method<\/strong><\/a><\/strong><\/li>\n
  2. Solving P5 Math Word Problem Sums With The Assumption Method<\/strong><\/a><\/li>\n<\/ol>\n<\/div>\n

    How Is Cross Multiplication Used?<\/strong><\/span><\/h2>\n

    Can you recall how cross multiplication works? If not, let me show you an easy way to remember!<\/p>\n

    \"How<\/p>\n

    That\u2019s right! Use a butterfly \ud83e\udd8b<\/p>\n

    This is how it works. First, draw two loops as shown.<\/p>\n

    \"How<\/p>\n

    Next, we multiply the numbers in each loop.<\/p>\n

    \"How<\/p>\n

    Now, we solve \"5x\u00a0to get\u00a0\"x=2.4\".<\/p>\n

    It\u2019s always a good habit to check if our answer is correct. Do you know how to do that?<\/p>\n

    That\u2019s right, substitute\u00a0\"x=2.4\"\u00a0into the original equation and check if the values on the left and right sides are the same.<\/p>\n

    Check:<\/strong><\/p>\n

    LHS =\u00a0\"\\frac{4}{x}\"\u00a0=\u00a0\"\\frac{4}{2.4}\"\u00a0=\u00a0\"\\frac{5}{3}\"\u00a0= RHS<\/p>\n

    Since the values on both sides are the same, our answer\u00a0\"x\u00a0is correct!<\/p>\n

    Why Does Cross Multiplication Work?<\/strong><\/span><\/h2>\n

    Let\u2019s try to solve\u00a0\"\\frac{4}{x}\u00a0in a different way.<\/p>\n

    Let\u2019s make both sides of the equation have the same denominator.<\/p>\n

    \"The<\/p>\n

    Now that the denominators are the same, compare the numerators. What do you observe?<\/p>\n

    That\u2019s right!\u00a0\"5x\u00a0which is the same result we had when we did cross multiplication.<\/p>\n

    This is not sorcery!<\/p>\n

    What did we do to the left numerator?<\/strong>\u00a0We multiplied by 3, which is also the right denominator.<\/p>\n

    What did we do to the right numerator?<\/strong>\u00a0We multiplied by\u00a0\"x\"<\/em>, which is also the left denominator.<\/p>\n

    So instead of doing this:<\/p>\n

    \"The<\/p>\n

    We do this:<\/p>\n

    \"The<\/p>\n

    Cross-multiplication speeds things up, don\u2019t you think so?<\/p>\n

    Applying Cross Multiplication To The Algebraic Ratio\u00a0<\/strong>Question<\/span><\/h2>\n

    A student once asked me the following question:<\/p>\n

    Given that\u00a0\"\\frac{2x-y}{x+3y}\u00a0and\u00a0\"\\frac{z}{x}\u00a0.<\/strong><\/p>\n

    (a) Find the value of\u00a0\u00a0\"\\frac{y}{x}\"\u00a0.<\/strong><\/p>\n

    (b) Hence, find the value of\u00a0\u00a0\"\\frac{y}{z}\"\u00a0.<\/strong><\/p>\n

    I can feel some of you cringing!<\/p>\n

    I feel you, so before I reveal the answer to you, let\u2019s see how we can approach this problem using a similar and simpler problem.<\/p>\n

    \n

    Given\u00a0\"\\frac{3x-2y}{4x}\u00a0, find the value of\u00a0\u00a0\"\\frac{x}{y}\" .<\/strong><\/p>\n<\/blockquote>\n

    The Guess and Check Approach<\/strong><\/h3>\n

    Let\u2019s try to guess the values of\u00a0\"x\"\u00a0and\u00a0\"y\". We will use a table to help us to organise our guesses.<\/p>\n

    \"The<\/p>\n

    Now, we have to answer the question. Since\u00a0\"x=10\"\u00a0and\u00a0\"y=3\", the value of is\u00a0\"\\frac{x}{y}\"\u00a0is\u00a0\"\\frac{10}{3}\".<\/p>\n

    This is too time consuming.<\/p>\n

    Is there an easier way? Of course, there is!<\/p>\n

    The Cross Multiplication Approach<\/strong><\/h3>\n

    Let\u2019s use the butterfly to help us. First, draw two loops as shown.<\/p>\n

    \"How<\/p>\n

    Next, we multiply the expressions in each loop. Use the\u00a0distributive law<\/strong>\u00a0to help you.<\/p>\n

    \"\"<\/p>\n

    Then shift all the terms with\u00a0\"x\"\u00a0onto the LHS and the terms with\u00a0\"y\"\u00a0on the RHS.<\/p>\n

    \"How<\/p>\n

    Since we want the fraction\u00a0\"\\frac{x}{y}\", first, we make\u00a0\"x\"\u00a0alone on the LHS.<\/p>\n

    \"How<\/p>\n

    Then we divide by\u00a0y<\/em>\u00a0throughout to get the desired\u00a0\"\\frac{x}{y}\"\u00a0on the LHS.<\/p>\n

    \"How<\/p>\n

    Voila! The answer is\u00a0\"\\frac{10}{3}\"<\/strong>.<\/p>\n

    What if the question instead asks for the ratio\u00a0\"x:y\"\u00a0?<\/p>\n

    That\u2019s right, we can write as\u00a0\"\\frac{x}{y}=\\frac{10}{3}\"\u00a0as\u00a0\"x\u00a0.<\/p>\n

    Let\u2019s apply the cross-multiplication approach to the original question.<\/p>\n

    Question:<\/strong><\/p>\n

    Given that\u00a0\"\\frac{2x-y}{x+3y}\u00a0and\u00a0\"\\frac{z}{x}\u00a0.<\/strong><\/p>\n

    (a) Find the value of\u00a0\u00a0\"\\frac{y}{x}\"\u00a0.<\/strong><\/p>\n

    (b) Hence, find the value of\u00a0\u00a0\"\\frac{y}{z}\" .<\/strong><\/p>\n

    Solving The Question Using The Cross Multiplication Method<\/span><\/h2>\n

    Part (a):<\/h3>\n

    Let\u2019s use the butterfly to help us. First, draw two loops as shown.<\/p>\n

    \"How<\/p>\n

    Next, we multiply the numbers in each loop. Use the\u00a0distributive law<\/strong>\u00a0to help you.<\/p>\n

    \"How<\/p>\n

    Then shift all the terms\u00a0\"x\"\u00a0with onto the LHS and the terms with\u00a0\"y\"\u00a0on the RHS.<\/p>\n

    \"How<\/p>\n

    Since we want the fraction\u00a0\"\\frac{y}{x}\", first, we make\u00a0\"y\"\u00a0alone on the LHS.<\/p>\n

    \"How<\/p>\n

    Then we divide by\u00a0\"x\"\u00a0throughout to get the desired\u00a0\"\\frac{y}{x}\"\u00a0on the LHS.<\/p>\n

    \"How<\/p>\n

    Part (b):<\/h3>\n

    We now have to find the value of\u00a0\u00a0\"\\frac{y}{z}\". We already found the value of\u00a0\"\\frac{y}{x}\"\u00a0in (a). Notice that we have not used\u00a0\"\\frac{z}{x}=-\\frac{9}{11}\".<\/p>\n

    The first question we must ask ourselves is\u2026<\/p>\n

    How are\u00a0\"\\frac{y}{z}\",\u00a0\"\\frac{z}{x}\"\u00a0and\u00a0\"\\frac{y}{x}\"\u00a0related?<\/strong><\/p>\n

    Let me give you a hint. The product of two will give the other.<\/p>\n

    \"How<\/p>\n

    This is the missing link!<\/p>\n

    Now that we know how the 3 fractions are related, we can easily find\u00a0\"\\frac{y}{z}\"<\/strong>!<\/p>\n

    \"How<\/p>\n

    Conclusion<\/h2>\n

    After reading this blog post, I hope that you have gained a stronger understanding of when to use cross multiplication<\/strong> and how to apply the Butterfly Method when solving algebraic fractions<\/strong>.<\/p>\n

    Stay tuned for more articles that help you tackle challenging Math questions!<\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row disabled_on=”off|off|off” admin_label=”Math GAP” _builder_version=”4.21.0″ custom_margin=”0px||” custom_padding=”0px||” global_module=”244058″ saved_tabs=”all” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.16″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_divider color=”#898989″ admin_label=”Divider” _builder_version=”4.16″ locked=”off” global_colors_info=”{}”][\/et_pb_divider][et_pb_image src=”https:\/\/thepiquelab.com\/blog\/wp-content\/uploads\/2024\/03\/The-Pique-Lab-Grade-Accelerator-Programme.-CTA.png” align=”center” _builder_version=”4.21.0″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.21.0″ text_font=”||||||||” text_text_color=”#333333″ text_font_size=”18px” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

    If you like our methodology, we’ve some ongoing weekly Math classes:<\/p>\n

    [\/et_pb_text][et_pb_text _builder_version=”4.21.0″ text_font=”geomanist-medium||||||||” text_text_color=”#f44a4a” text_font_size=”18px” text_line_height=”2em” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

    P5 Mathematics Grade Accelerator Programme<\/b><\/a>
    S1 Mathematics Grade Accelerator Programme<\/a><\/strong>
    S2 Mathematics Grade Accelerator Programme<\/a><\/strong>
    S3 Mathematics Grade Accelerator Programme<\/strong><\/a><\/p>\n

     <\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”4.21.0″ _module_preset=”default” global_colors_info=”{}”][et_pb_row _builder_version=”4.21.0″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.21.0″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

    In this article, we’ll be discussing how to use Cross Multiplication to solve this Secondary 1 Math Algebra question.<\/p>\n","protected":false},"author":41,"featured_media":243999,"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\/243930"}],"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=243930"}],"version-history":[{"count":33,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/243930\/revisions"}],"predecessor-version":[{"id":244984,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/posts\/243930\/revisions\/244984"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media\/243999"}],"wp:attachment":[{"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/media?parent=243930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/categories?post=243930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/tags?post=243930"},{"taxonomy":"post_folder","embeddable":true,"href":"https:\/\/thepiquelab.com\/blog\/wp-json\/wp\/v2\/post_folder?post=243930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}