Simplifying and Ordering Fractions

Work out what the numerator has been multiplied by, then do the same to the denominator.

Count the shaded squares and count all the squares.

Find the highest common factor of 18 and 24 and divide both numbers by it.

Write each fraction with a denominator of 8.

Work out how many whole lots of 5 fit into 17, and how many are left over.

All four fractions have the same number on top. Think about the size of each part.

1. Each fraction is 3 equal parts of a whole.
2. The smaller the number on the bottom, the bigger each part is.
3. 4 is the smallest number on the bottom, so \frac{3}{4} is the largest.

Work out how many thirds there are in 4 whole ones, then add the 2 thirds.

1. There are 3 thirds in each whole one, so 4 whole ones make 4\times3=12 thirds.
2. 12+2=14 thirds, so 4\frac{2}{3}=\frac{14}{3}.
3. Answer: 14.

Start with \frac{45}{60} and keep dividing the top and bottom by the same number until you can't any more.

Part (a)

1. The fraction is \frac{45}{60}.
2. Divide both by 5: \frac{9}{12}.
3. Divide both by 3: \frac{3}{4}. Nothing else divides into 3 and 4, so the top is 3.

Part (b)

1. \frac{45}{60}=\frac{9}{12}=\frac{3}{4}, so the bottom is 4.

Simplify each fraction, or check whether the top and bottom are 2 and 3 multiplied by the same number.

1. \frac{4}{6}=\frac{2}{3} (top and bottom divided by 2).
2. \frac{10}{15}=\frac{2}{3} (divided by 5) and \frac{14}{21}=\frac{2}{3} (divided by 7).
3. \frac{9}{12}=\frac{3}{4}, so \frac{9}{12} is not equivalent to \frac{2}{3}.

Count the shaded squares and all the squares, then simplify.

1. There are 4\times5=20 squares and 8 of them are shaded, so \frac{8}{20} is shaded.
2. Divide the top and bottom by 4: \frac{8}{20}=\frac{2}{5}.
3. \frac{8}{20} is the right amount but is not in its simplest form. Answer: \frac{2}{5}.

Write every fraction with a denominator of 20.

1. \frac{4}{5}=\frac{16}{20}, \frac{7}{10}=\frac{14}{20} and \frac{3}{4}=\frac{15}{20}.
2. In twentieths the fractions are 16, 14, 15 and 13.
3. Smallest first: \frac{13}{20},\ \frac{7}{10},\ \frac{3}{4},\ \frac{4}{5}.

Write \frac{19}{7} as a mixed number, then compare the fraction parts.

1. 19\div7=2 remainder 5, so \frac{19}{7}=2\frac{5}{7}.
2. Both numbers are 2 and a bit, so compare \frac{3}{4} and \frac{5}{7}.
3. \frac{3}{4}=\frac{21}{28} and \frac{5}{7}=\frac{20}{28}, so \frac{3}{4} is bigger.
4. So 2\frac{3}{4} is bigger than \frac{19}{7}.

Each part is \frac{1}{10}. Write \frac{3}{5} in tenths.

1. Each part of the number line is \frac{1}{10}.
2. \frac{3}{5}=\frac{6}{10}, so it is at the sixth mark after 0.
3. C is at the sixth mark.

Write every number as a decimal with three decimal places.

1. \frac{3}{8}=3\div8=0.375.
2. 35\%=0.35.
3. As decimals: 0.400, 0.375, 0.350 and 0.380.
4. Smallest first: 35\%,\ \frac{3}{8},\ 0.38,\ 0.4.

Simplifying a fraction must not change its value. Does taking 8 away from the top and bottom keep the value the same?

1. Taking the same number away from the top and bottom changes the size of the fraction.
2. To simplify, divide the top and bottom by a common factor. The HCF of 12 and 16 is 4.
3. 12\div4=3 and 16\div4=4, so \frac{12}{16}=\frac{3}{4}.
4. \frac{6}{8} is equal to \frac{3}{4} but is not fully simplified.

One fraction is less than 1 and the other is more than 1. Work out how far each one is from 1.

Part (a)

1. 1=\frac{9}{9}.
2. \frac{9}{9}-\frac{7}{9}=\frac{2}{9}.

Part (b)

1. 1=\frac{5}{5}.
2. \frac{6}{5}-\frac{5}{5}=\frac{1}{5}.

Part (c)

1. \frac{2}{9}=\frac{10}{45} and \frac{1}{5}=\frac{9}{45}.
2. \frac{9}{45} is smaller than \frac{10}{45}, so \frac{6}{5} is closer to 1.

Write \frac{2}{3} and \frac{3}{4} as fractions with a denominator of 24.

1. \frac{2}{3}=\frac{16}{24}, because 2\times8=16 and 3\times8=24.
2. \frac{3}{4}=\frac{18}{24}, because 3\times6=18 and 4\times6=24.
3. The only whole number between 16 and 18 is 17.
4. Answer: 17.

Two shaded halves of small squares make one whole small square.

1. 4 small squares are fully shaded.
2. 4 more small squares are half shaded, and 4 halves make 2 whole small squares.
3. Shaded: 4+2=6 small squares out of 16, which is \frac{6}{16}.
4. Divide the top and bottom by 2: \frac{6}{16}=\frac{3}{8}.

a and b are 3 and 5 multiplied by the same number.

Part (a)

1. a and b are 3 and 5 multiplied by the same number.
2. 3+5=8 and 40\div8=5, so the number is 5.
3. a=3\times5=15.

Part (b)

1. b=40-15=25.
2. Check: \frac{15}{25}=\frac{3}{5} (divide the top and bottom by 5).

Write every number as a decimal.

1. 1\frac{2}{3}=1.666\ldots and 1\frac{5}{8}=1.625.
2. \frac{7}{4}=1\frac{3}{4}=1.75 and \frac{17}{10}=1.7.
3. In order: 1.625, 1.666\ldots, 1.7, 1.75.
4. Smallest first: 1\frac{5}{8},\ 1\frac{2}{3},\ \frac{17}{10},\ \frac{7}{4}.