Calculate twenty-three twenty-fourths divided by five-sixths minus four-fifths. Give your answer in its simplest form.
Our first step is to work out the calculation inside the parentheses or bracket. This is twenty-three twenty-fourths divided by five-sixths. Dividing a fraction by a fraction is the same as multiplying the first fraction by the reciprocal of the second fraction. In this case, we have twenty-three twenty-fourths multiplied by six-fifths. One way that can be used to remember this is using the letters K, C, and F. We keep the first fraction the same. We change the sign from a divide to a times. And we flip the third fraction. Five-sixths becomes six-fifths.
When multiplying two fractions, we multiply the two numerators and then separately the two denominators. Before doing this, it is always worth checking to see if we can cross-cancel or cross-simplify. In this case, six and 24 are both divisible by six. Six divided by six is equal to one. 24 divided by six is equal to four. So the calculation simplifies to twenty-three fourths multiplied by one-fifth. Multiplying the numerators gives us 23 as 23 multiplied by one is 23. Four multiplied by five is equal to 20. So our denominator is 20. Twenty-three twenty-fourths divided by five-sixths is twenty-three twentieths.
We have worked out the first part of the calculation. We now need to subtract four-fifths from this fraction. Our second calculation is twenty-three twentieths minus four-fifths. When adding or subtracting fractions, we need to make sure we have a common denominator. The denominator of both fractions needs to be the same. Five multiplied by four is equal to 20. So we need to multiply the second fraction by four. If we multiply the denominator by four, we must multiply the numerator by four. Whatever you do to the top, you must do to the bottom.
The fraction four-fifths is equivalent to sixteen twentieths. The calculation therefore becomes twenty-three twentieths minus sixteen twentieths. At this stage, we need to subtract the numerators, 23 minus 16. This gives us an answer of seven. The denominator stays the same. So twenty-three twentieths minus sixteen twentieths is equal to seven twentieths. As the numerator and denominator have no common factor apart from one, the fraction is in its simplest form.
Twenty-three twenty-fourths divided by five-sixths minus four-fifths is equal to seven twentieths.