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Welcome to Brainfuse.
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At a local pizza shop, customers can have their pizzas cut in three different ways.
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So I'll copy this appetizing Pizza on screen, two, three.
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Alright, so here are the 3 different ways.
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that you can have it cut.
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You can have it cut into 4 slices
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You can have it cut into 8 slices
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Right now they cut into 12 slices
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Here's a problem based on that menu
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Three politicians each order a mini pizza. The mayor eats 3 out of 4 slices;
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the senator eat 6 out of 8 slices; the governor eats 9 out of 12 slices.
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The mayor eats 3 out of 4 slices;.
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The senator eats 6 out of 8 slices.
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And the governor eats 9 out of 12 slices.
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Which customer has eaten the most Pizza?
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To picture this, let's shade in the slices that each politician ate. The mayor ate 3 out of 4.
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Okay, the blue scribble means it's eaten. Now the senator, we'll shade in green: the senator ate 6 out of 8.
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I apologize, these pizzas now look really gross. Okay, and the governor
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eats 9 out of 12 slices
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Not quite even, but imagine they are.
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Okay, yum.
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Even though these pizzas have a different number of slices, notice that each politician ate
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The same amount
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The mayor ate 3/4 of his pizza, the senator ate 6/8 of his pizza, and the governor
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9/12 of his pizza.
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So, in the numerators, notice that
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6
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And 9 are both multiples of 3.
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3 times 2 is equal to 6. And 3 times 3 equals 9
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And in the denominators
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Notice that 8
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And 12
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Are both multiples of 4
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4 times 2 equals 8. And 4 times 3 equals 12
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In other words, when we multiply 3/4 by 2/2
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The product will be
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6/8.
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And 2/2 is equal to 1.
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1 times any number, is equal to that number
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Here we have 3 in the numerator; here we have 6 in the numerator. So even though these fractions are made up of
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different numbers, they must have the same value. In the same
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way
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3/4 times 3/3 equals
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9/12. 3/3
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is equal to 1, and 1 times any number equals that number
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And 1 times any number equals a number with the same value, so 3/4 must be
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Equal to 9/12. Let's erase the disgusting pizzas and look at this
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Another way. Okay.
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Fractions are also forms of division problems, so let's find the quotient of each fraction in this problem
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We need to divide the numerators
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by their denominators.
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So 4 goes into 3, 0 times.
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3 minus 0 equals 3
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Bring down a 0. 4 goes into 30:
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7 times 4 is 28.
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So there is a remainder of 2, you bring down the next zero.
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4 goes into 20, 5 times. So the quotient is 0.75. Okay, let's compare that to 6 divided by 8.
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8 goes into 6, 0 times
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Okay, there's a remainder of 6. We'll bring down the next zero
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8 goes into 60, 7 times. 8 times 7 is 56.
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So there's a remainder of 4.
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Bring down the next 0 and 8 goes into 40, 5 times.
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So 6/8 has the same quotient, has the same value. Let's test
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9/12 to see if this works out. 12 goes into 9, 0 times.
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Mark that decimal point
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Okay, we have a remainder of 9, we bring down the zero and 12 goes into 90, 7 times because
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7 times 12 is 84
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Borrow one from the tens column, 10 minus 4 is 6. And 12 goes into 60, 5 times.
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These fractions all have a value of 75 hundredths or 0.75
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These fractions all have a value of 75 hundredths or 0.75
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You may also need to use these skills to solve proportions.
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Here we have 40 over 72 equals 5 over x, and we need to solve for x.
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So the equal sign tells us that these need to be equivalent fractions and
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We know that 5 is a factor of 40, 40 divided by 8 equals 5.
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And what we do to the numerator, we need to do to the denominator, if we want these values to be equal. So 72 divided 8 equals x, so x must equal 9.
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Telling us that 40 over 72 is equal to
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5/9.
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When working with fractions, no matter how you divide a place, space, shape, or an object, its
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value does not change. Thank you for watching this lesson.