Mixed Numbers and Improper fractions

This chapter explores mixed numbers and improper fractions. It covers converting improper fractions to mixed numbers, multiplying fractions by whole numbers and adding fractions to make whole numbers.

Improper fractions

Michael ate thirds of a pizza. The image below shows one full pizza.
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We want to find four thirds of the pizza. That is we’re trying to find this;
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Here is 1/3 of a pizza;
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And here is 4/3 of a pizza;
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If we combine the pieces of pizzas shown above;
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Michael eats 1 1/3 pizzas that he eats that is, he eats one full pizza and an extra piece of pizza that is 1/3 of a full pizza.
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It is improper because the top number/numerator is bigger than the bottom.
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It is a mixed number because it contains whole numbers and fractions.

Converting between mixed and improper fractions

Suppose we wanted to convert nine fifths into a mixed number. The following is nine fifth;
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First we divide 9 with 5. 9 divide by 5 is 1 and a reminder of 4. Here we just write the whole number of one as shown below;
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The 5 in the mixed number above is the denominator of the original improper fraction. Then we write the reminder of 9/5 on top of 5 as shown below; The remainder is a 4.
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Converting mixed numbers to improper fractions

Suppose we wanted to convert a mixed number back into an improper fraction. Here is a mixed number we could use.
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We’re trying to find;
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To find the numerator we multiply the denominator of the fraction within the mixed number and add the numerator of the of the fraction.
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…and..
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So now we have found the numerator which forms part of our improper fraction.
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The denominator of the improper fraction we’re trying to find is simply the denominator of the fraction within the mixed number.
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Multiplying a fraction with a whole number

We can multiply a fraction with a whole number. Suppose we wanted to work out;
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We know that the above means;
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We can illustrate this with a pizza as shown below;
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We can break the pizzas in thirds which gives us 8 thirds or;
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That gives us;
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We can write 8/3 as a mixed number, the broken pieces of pizza can help us. Let us put the thirds of pizza together to form pizzas. 3 thirds gives us a pizza so we need 3 pizzas to form a pizza.
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That gives us;
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Simple steps

We could have also used the much simple steps, we just write 4 as;
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This give us;
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Now we just multiply directly;
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…and…
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…giving us the answer of;
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We can convert 8/3 into a mixed number easily.
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That gives us;
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