Fractions, Proportions and Ratios  
Stage 7 Overview 
I can solve stage 7 problems.  
Learning Outcome: I can...  | Problem to solve   | Thinking and Answer  | 
Use a range of  multiplication and  division strategies  to solve problems  with fractions,   proportions   and ratios.  | 1. Convert the following improper fractions to mixed number  fractions:  a.214 = 5¼  b. 152 = 7½  c.2710 = 2 7/10  | 
2. Convert the following mixed numbers into improper fractions: a. 4 23 14/3 b. 3 12 7/2 c. 3 35 18/5  | 
3. Write these fractions in their simplest form:  a.515 ⅓  b. 1025 2½ c.416 ¼   | 
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Fractions, Proportions and Ratios  
  | 4. Find the missing number in these to make these fractions  equivalent:  a.25 = 1320 b. 58 = 2040  c.56 = 2530  | 
5. In a bag of marbles, we find blue  marbles, red marbles, and yellow  marbles in a ratio of 6 : 1 : 2.  If the bag of marbles contains 22  yellow marbles, how many marbles  are there in total?  | Thinking:  6+2+1=9 + 22=31 Answer:31?  | 
Convert and   rename common  fractions, decimals  and percentages.  | 6. Fill in the blanks so the fractions, decimals and percentages are all  equivalent:  Fraction Percentage Decimal  2.05-1=1.05 75%-10%=65%  0.50-0.25=0.25 
 
  | 
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Fractions, Proportions and Ratios  
Can find fractions  of whole numbers  using multiplication  and division facts.  | 7. There are twenty one bottles of  honey for sale and three sevenths  have sold? How many jars have  been sold?  
  | Thinking:  21 divided by 7 is 3 and 3x3=9 also 3x7=21 Answer:9  | 
8. There are forty trees in the orchard  and four fifths of them are apple  trees. The rest are pear trees.   How many apple trees are there?   | Thinking:  40 divided by 5=8  8x4=32 Answer:32  | 
Can add and   subtract fractions  with the same   and different   denominators.  | 9. Rachel ate one eighth of the cake.  Leo ate five eighths of the cake.  How much cake is left?  
  | Thinking:  ⅛ + ⅝ = 6/8  Answer:6/8  | 
10. In the surfing shop, 25 of the  surfboards are shortboards and 310 are longboards. What fraction are  either shortboards or longboards?  Show your working out.  | Thinking: ⅖x2=4/10 shortboards  3/10 longboards Answer:7/10  | 
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Fractions, Proportions and Ratios  
Compare fractions  using < > =  | 11. Use the < > = signs to compare these fractions:  a.36<26  b. 710>910  c.36=12  d. 58>34  | 
Order mixed   fractions.  | 12. Put these fractions in order from smallest to largest. 4/8, 21/4,  3, 4, 4, 17  |