الأسبوع 16 · كسور الوحدة والأعداد الكسرية · 3 دروس
1
Building fractions from unit fractions
Discover Mathematics P4: Term 2, Unit 9, Lessons 1–4
GoalBuild a fraction from unit fractions and read the numerator and the denominator.
New words
unit fraction · a fraction with numerator 1, such as 1/4, one equal part of the wholenumerator · the top number: how many parts we countdenominator · the bottom number: how many equal parts make the whole
Explanation
A fraction names equal parts of a whole. The denominator tells into how many equal parts the whole is cut. The numerator tells how many of those parts we take. When the numerator is 1 we have a unit fraction, such as 1/8, which is one part out of eight equal parts. Every other fraction is built by joining unit fractions: 5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8, five parts that are each 1/8. We can also say 5/8 = 5 × 1/8. On a number line from 0 to 1 cut into eight equal steps, 5/8 is the point after five steps of 1/8. The parts must be equal. When the whole is cut into more parts, each part is smaller, so 1/8 is smaller than 1/4.
Worked examples
A tray of basbousa is cut into 8 equal pieces. Salma eats 3 pieces. She ate 3/8 of the tray, which is 1/8 + 1/8 + 1/8. The 5 pieces left are 5/8 of the tray, and 3/8 + 5/8 = 8/8 = 1 whole tray.
Show 5/8 on a number line from 0 to 1 cut into eighths. Start at 0 and make five jumps of 1/8: 1/8, 2/8, 3/8, 4/8, 5/8. The point 5/8 is a bit more than halfway, because 4/8 is the middle.
A ribbon is cut into 10 equal pieces and 7 are red. The red part is 7/10, which is seven 1/10 pieces. In 7/10 the numerator 7 counts the red pieces and the denominator 10 tells that the whole ribbon has 10 equal pieces.
Class activity
Fold a paper strip. Fold a paper strip into 4 equal parts, colour 3 and write the fraction. Fold another strip of the same size into 8 parts, colour 3 and compare. Which coloured part is longer: 3/4 or 3/8?
Practice
1
A pizza is cut into 6 equal slices and Omar eats 4. What fraction did he eat? Write it as a sum of unit fractions.
4/6 = 1/6 + 1/6 + 1/6 + 1/6.
2
Write 3/5 as a sum of unit fractions.
3/5 = 1/5 + 1/5 + 1/5.
3
How many pieces of 1/8 make 7/8?
7 pieces: 7/8 = 7 × 1/8.
4
A ribbon is cut into 10 equal pieces and 3 are blue. What fraction is blue and what fraction is not blue?
Blue: 3/10. Not blue: 7/10, because 10 − 3 = 7.
5
Mina says 1/3 is bigger than 1/2 because 3 is bigger than 2. What is wrong?
When a whole is cut into more equal parts, each part is smaller. A third is smaller than a half, so 1/3 < 1/2.
