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Grade 12

<h2 class="wp-block-heading">Key Concepts</h2>



<ul class="wp-block-list">
<li>Solve constant speed problems</li>



<li>Solving unit-price problems</li>



<li>Using an equation to represent unit rate problems</li>
</ul>



<h2 class="wp-block-heading">Multiply fractions and whole numbers&nbsp;&nbsp;</h2>



Model: Standard multiplication of whole numbers and fractions&nbsp;



<ol class="wp-block-list">
<li>Hal spent ¾ hour each day for 7 days. How much total time did he spend reading?&nbsp;</li>
</ol>



<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="422" height="60" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7281.png" alt="" class="wp-image-26956" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7281.png 422w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7281-300x43.png 300w" sizes="auto, (max-width: 422px) 100vw, 422px" /></figure>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7282-1024x381.png" alt="Multiply fractions and whole numbers" class="wp-image-26957" style="width:655px;height:243px" width="655" height="243" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7282-1024x381.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7282-300x112.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7282-768x286.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7282.png 1476w" sizes="auto, (max-width: 655px) 100vw, 655px" /></figure></div>


<a href="https://www.turito.com/learn/math/multiply-by-multiples-grade-4" data-type="link" data-id="https://www.turito.com/learn/math/multiply-by-multiples-grade-4">Multiply</a> to find the number of fourths 



7 x 3/4 = 7 x 3 x 1/4


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/1-49.png" alt="2 1/4" class="wp-image-26959" style="width:730px;height:72px" width="730" height="72" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/1-49.png 943w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/1-49-300x30.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/1-49-768x77.png 768w" sizes="auto, (max-width: 730px) 100vw, 730px" /></figure></div>


= 21 x 1/4 = 21/4



Rewrite as a <a href="https://www.turito.com/learn/math/multiply-mixed-fractions-grade-6" data-type="link" data-id="https://www.turito.com/learn/math/multiply-mixed-fractions-grade-6">mixed fraction</a> number <div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes" data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



21/4 = 5 1/4&nbsp;



Hal spent 5 1/4 hours of reading.&nbsp;


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7283-1024x696.png" alt="hal " class="wp-image-26958" style="width:527px;height:357px" width="527" height="357" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7283-1024x696.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7283-300x204.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7283-768x522.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7283-1536x1044.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7283.png 1600w" sizes="auto, (max-width: 527px) 100vw, 527px" /></figure></div>


<ol class="wp-block-list" start="2">
<li>Explain how 3/4 x 7, 7 x 3/4&nbsp; and 3 x 7/4&nbsp; are all related?&nbsp;</li>
</ol>



Given that, prove



3/4 x 7 = 7 x 3/4&nbsp; = 3 x 7/4



Case 1:&nbsp;<div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes" data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>



3/4 x 7 = 1/4 x 3 x 7&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;



= 1/4 x 21&nbsp;



= 21/4



Case 2:&nbsp;



7 x 3/4



= 7 x 3 x 1/4



= 21 x 1/4



= 21/4



Case 3:&nbsp;



3 x 7/4



= 3 x 7 x 1/4



= 21 x 1/4



= 21/4



So,



3/4 x 7 = 7 x 3/4&nbsp; 



= 3 x 7/4&nbsp; 



= 21/4



<h3 class="wp-block-heading">Practice</h3>



1. 4/5 x 500&nbsp;



Solution:&nbsp;



4/5 x 500 = 2000/5



4/5 x 500=400&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;



2. 5 x 2/3&nbsp;&nbsp;



Solution:&nbsp;



5 x 2/3



= 5&nbsp;X&nbsp;2/3



= 10/3 x 2/3



= 3 1/3



3. 9/10 x 25&nbsp;



Solution:&nbsp;



9/10 x 25 = 9&nbsp;X&nbsp;25/10



= 225/10



= 9/10 x 25&nbsp; = 22.5 or 22



5/10 or 12