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Convert the following improper fractions to mixed numerals (also known as mixed numbers):

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Note: Write the whole number part in the first box and the fraction part in the second 

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$\\displaystyle\\frac{\\var{a1*c1+b1}}{\\var{c1}}=$[[0]][[1]]

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$\\displaystyle\\frac{\\var{a2*c2+b2}}{\\var{c2}}=$[[2]][[3]]

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Do the division and write your remainder over the original denominator. Simplify the fraction if possible. 

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For example, converting $\\frac{21}{9}$ into a mixed numeral, you ask yourself \"how many times does 9 go into 21?\", it goes in twice (since $2\\times 9=18$ but $3\\times 9=27$), with a remainder of 3 (since $21-18=3$). So we can write our answer as $2\\frac{3}{9}$ (which actually means $2+\\frac{3}{9}$). But notice we can simplify the fraction, so we should rewrite our answer as $2\\frac{1}{3}$.

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Note: we could have cancelled common factors at the beginning. 

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Convert the following mixed numerals to improper fractions:

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$\\var{a3}\\frac{\\var{b3}}{\\var{c3}}=$[[0]]

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$\\var{a4}\\frac{\\var{b4}}{\\var{c4}}=$[[1]]

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Multiply the whole number and the denominator, add the numerator, and put it all over the denominator.

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For example $2\\frac{3}{4}$ can be written as $\\frac{2\\times 4+3}{4}$ that is, $\\frac{11}{4}$.

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To understand why, realise that $2\\frac{3}{4}$ is shorthand for $2+\\frac{3}{4}$ and if we want to add these numbers we need to have a common denominator (recall the denominator of a whole number is 1). Our working could look like this:

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\\[2\\tfrac{3}{4}=2+\\frac{3}{4}=\\frac{2\\times 4}{4}+\\frac{3}{4}=\\frac{2\\times 4+3}{4}=\\frac{11}{4}\\]

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but in practice we normally don't write anything more than \\[2\\tfrac{3}{4}=\\frac{2\\times 4+3}{4}=\\frac{11}{4}\\]

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