Discover Mathematics P6: Term 2, Unit 8, Lessons 1–2
GoalDivide a fraction by a whole number using fraction strips and say why the answer is smaller.
New words
divide · to share into equal partsequal parts · pieces that are all the same sizequotient · the answer to a divisionequivalent fractions · fractions with different names but the same value
Explanation
To share a fraction equally among some people, cut that fraction into that many equal parts. Take 1/2 and cut it into 3 equal pieces. Six of these pieces would fill the whole, so each piece is 1/6. We write 1/2 ÷ 3 = 1/6. When the top number divides exactly we can share it directly: 3/4 is 3 quarters, and sharing 3 quarters between 3 people gives 1 quarter each, so 3/4 ÷ 3 = 1/4. When it does not divide exactly, first rename the fraction: 2/3 = 4/6, and 4 sixths shared between 4 gives 1/6 each. The quotient is smaller than the fraction we started with. We can always check by multiplying: 1/6 × 4 = 4/6 = 2/3.
★Remember
Fraction ÷ whole number: share the fraction into equal parts. Rename the fraction if the top will not divide. Check by multiplying.
Worked examples
1/2 ÷ 3 = 1/6. The first strip is one whole made of two halves. The second strip shows the half cut into three equal pieces; each piece is 1/6 of the whole.
Division
Rename
Share
Answer
3/4 ÷ 3
3/4
3 quarters ÷ 3
1/4
2/3 ÷ 4
4/6
4 sixths ÷ 4
1/6
Two more quotients. 3/4 ÷ 3: 3 quarters shared by 3 gives 1 quarter, so the answer is 1/4. 2/3 ÷ 4: rename 2/3 as 4/6, then 4 sixths shared by 4 gives 1/6.
A ribbon is 3/4 m long and is cut into 6 equal pieces. 3/4 = 6/8, and 6 eighths shared by 6 gives 1/8. So each piece is 1/8 m long. Check: 1/8 × 6 = 6/8 = 3/4.
Class activity
Paper strips. Cut a strip of paper into 4 equal parts and colour 3 of them. Now fold those 3 parts into 3 equal pieces and say what fraction of the whole strip one piece is. Write the division sentence and check it by multiplying.
Practice
1
Find 1/3 ÷ 2.
Cut a third into 2 equal pieces; 6 of them fill the whole, so 1/3 ÷ 2 = 1/6.
2
Find 4/5 ÷ 2.
4 fifths shared by 2 is 2 fifths, so 4/5 ÷ 2 = 2/5.
3
Find 3/4 ÷ 2 by renaming 3/4.
3/4 = 6/8. 6 eighths shared by 2 is 3 eighths, so 3/4 ÷ 2 = 3/8.
4
2/3 L of juice is poured equally into 4 glasses. How much is in each glass?
2/3 ÷ 4 = 4/6 ÷ 4 = 1/6 L.
5
Hazem says 1/5 ÷ 2 = 2/5. Explain why that cannot be right and give the correct answer.
Dividing 1/5 into 2 parts gives something smaller than 1/5, but 2/5 is bigger. The correct answer is 1/10, because 10 pieces of 1/10 make a whole.
