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Comparing and equivalent fractions

الأسبوع 18 · مقارنة الكسور والكسور المتكافئة · 3 دروس
1

Comparing fractions with like parts

Discover Mathematics P4: Term 2, Unit 9, Lessons 8–12
GoalCompare fractions that have the same denominator or the same numerator.
New words
compare · to decide which of two amounts is greater, smaller or equalgreater than > · the symbol that points its small end to the smaller numberless than < · the symbol that points its small end to the smaller number
Explanation

To compare two fractions, think about how many parts we have and how big each part is. If the denominators are the same, the parts have the same size, so the fraction with more parts is greater: 5/8 > 3/8. If the numerators are the same, we have the same number of parts, but the parts are different. A whole cut into fewer parts has bigger parts, so 3/4 > 3/8, because fourths are bigger than eighths. Never decide by looking at the denominator alone as a normal number: a bigger denominator means smaller pieces. Use the symbols >, < and =. The points of the symbols always point to the smaller fraction. A picture of two equal bars is a good check.

3/41/41/41/41/43/81/81/81/81/81/81/81/81/8
Worked examples
5/81/81/81/81/81/81/81/81/83/81/81/81/81/81/81/81/81/8
Compare 5/8 and 3/8. Both are eighths, so we compare the numerators: 5 > 3. Therefore 5/8 > 3/8.
3/41/41/41/41/43/81/81/81/81/81/81/81/81/8
Compare 3/4 and 3/8. Both have 3 parts, but a fourth is bigger than an eighth. In the bars, 3/4 covers 6 of the 8 small steps and 3/8 only covers 3. Therefore 3/4 > 3/8.
Compare 2/3 and 2/5. The numerators are both 2. A third is bigger than a fifth, so 2/3 > 2/5. Tip: with the same numerator, the smaller denominator gives the greater fraction.
Class activity

Strip race. Cut two strips of the same length. Fold one into 4 parts and the other into 8 parts. Cut off 3 parts from each and put the pieces side by side. Which is longer, 3/4 or 3/8? Write the comparison with the symbol.

Practice
1
Write >, < or =: 7/10 __ 9/10.
2
Write >, < or =: 4/6 __ 4/8.
3
Write >, < or =: 5/12 __ 5/6.
4
Order from the smallest to the greatest: 7/8, 3/8, 5/8.
5
Omar says 1/6 > 1/3 because 6 > 3. What is wrong?