Mixed numbers and improper fractions

Express 5 and 2 ninths as an improper fraction. Try it first. Pause if you like. How many ninths are in the 5 wholes? Count those before adding the extra parts. Each whole has 9 equal parts. Separate the parts slightly to see the ninths. Their sizes do not change. 5 times 9 equals 45. The 5 wholes have 45 ninths. 45 plus 2 equals 47. Add the 2 ninths in the last strip. 5 and 2 ninths equals 45 ninths plus 2 ninths. That equals 47 ninths. The denominator stays 9 because every part is still one ninth. Bring the same parts back together. 5 and 2 ninths and 47 ninths show exactly the same amount.

Express 26 eighths as a mixed number in its simplest form. Try it first. Pause if you like. How many full groups of 8 eighths can you take out? What is left? Separate the eighths slightly. Each complete strip still has 8 equal parts. Start with the first full strip. These 8 eighths make one whole. The next full strip has another 8 eighths. We have two full groups of 8. The third full strip has another 8 eighths. That is three full groups of 8. 8 plus 8 plus 8 equals 24. These three full strips use 24 of the 26 eighths. The last strip has 2 eighths left. So the 26 parts split into 24 parts and 2 parts. 26 eighths equals 24 eighths plus 2 eighths. 24 eighths make 3 wholes. So this equals 3 plus 2 eighths. Write that as the mixed number 3 and 2 eighths. Now pair the eighths. Each pair covers one quarter of the same whole. The shaded pair is 2 eighths, or one quarter. 3 and 2 eighths equals 3 and one quarter. Divide both the numerator and the denominator of the fraction part by 2. The simplest form is 3 and one quarter. First take out the wholes. Then simplify the fraction part.