1. What is the value of 4⁄9 × 3⁄2? 

 

📖 REMINDER: When multiplying fractions, multiply the numerators together and the denominators together. Simplify before multiplying if possible.

 

WA1,NY,2024,Fractions
1.
2.
3.
4.
2. The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. The length of the cuboid is 10 cm.
Find the volume of the cuboid. 

 

📖 REMINDER: When given a ratio, find the value of one part first using the given measurement, then calculate other dimensions before finding volume.

 

WA1,NY,2024,Measurement
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2.
3.
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3. Sarah had 18 m of ribbon. She used it to make as many bows as possible.
She used 3⁄4 m of ribbon to make each bow. How many metres of the ribbon were left? 

 

📖 REMINDER: When finding how many items can be made, divide total length by length per item. The remainder is what’s left over.

 

WA1,NY,2024,Fractions
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2.
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4. The table below shows the number of books collected by a school library in 2021 and 2022.
Part of the table is covered by a stain. The number of fiction books collected and the total
number of books collected were both three-digit numbers. 

 
Type of Book20212022
Science Books11590
History Books7584
Fiction Books28■
Total number of books■384
 

Which of the following statement(s) can be true?

A. In 2022, 25% of the total number of books collected were damaged.
B. In 2021, 30% of the total number of books collected were history books.
C. In 2021, 40% of the total number of books collected were fiction books.

WA1,NY,2024,Percentage

📖 REMINDER: The fiction books for 2022 and the total for 2021 are both three-digit numbers (100-999). Check each statement mathematically.

1.
2.
3.
4.
5. The table below shows the number of marbles in different coloured boxes.
David has some red boxes and some yellow boxes.The ratio of the total number of marbles in
David’s red boxes to the total number of marbles in his yellow boxes is 4⁄3.
Express the number of his yellow boxes as a fraction of the total number of his boxes. 

 
Colour of boxNumber of marbles in each box
Red20
Yellow40
Green50
 

 

📖 REMINDER: Find the ratio of boxes first by using the given marbles per box and the total marbles ratio.

WA1,NY,2024,Ratio
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2.
3.
4.

6. 2⁄3 of a cake was shared equally among 4 people. What fraction of the cake did each person receive?

 

Answer:

 

📖 REMINDER: When sharing a fraction equally among people, divide the fraction by the number of people.

 

 

WA1,NY,2024,Fractions

7. The breadth of a rectangle is 3⁄4 m and its area is 3 m². Find the length of the rectangle.
Express your answer as a mixed number in its simplest form.

 

Answer: m

 

📖 REMINDER: Area of rectangle = length × breadth. To find length, divide area by breadth.

 

 

WA1,NY,2024,Measurement

8. Sarah is 3⁄4 as tall as David. What is the ratio of David’s height to Sarah’s height?

 

Answer:

 

 

📖 REMINDER: When A is a⁄b as tall as B, then A:B = a:b. The ratio of B:A is the reciprocal.

 

 

WA1,NY,2024,Ratio

9. The ratio of the number of stamps Alex had to the number of stamps Ben had was 3 : 5 at first.
After Alex bought 12 more stamps, the ratio of the number of stamps Alex had to the number of
stamps Ben had became 2 : 3. How many stamps did Ben have?

 

Answer:   stamps

 

 

📖 REMINDER: Use the concept of unchanged quantity (Ben’s stamps didn’t change) and make the units for Ben the same in both ratios.

 

 

WA1,NY,2024,Ratio

10. Alex, Ben, and Chris collected some cards. The ratio of the number of cards Alex collected to the
number of cards Ben collected was 3 : 8.The ratio of the number of cards Chris collected to the
number of cards Ben collected was 5 : 2. Alex collected 18 cards. How many cards did Chris collect?

 

Answer: cards

 

 

📖 REMINDER: Connect the two ratios using a common person. Find the value of one part for that person first.

 

 

WA1,NY,2024,ratio

11. Ben had some money at first. He spent 20% of it on a book and $100 on a game.
He then gave 50% of the remaining money to his sister.
In the end, he had $150 left. How much money did Ben spend on the book?

 

Answer:  $

 

📖 REMINDER: It is often easier to work backwards in problems involving percentages of a remainder. Start from the final amount and reverse each step.

 

 

WA1,NY,2024,Percentage

12. Priya had some flour at first. She used 36 g of flour to bake some bread and 3⁄4 of the
remaining flour to bake some cakes.In the end, she had 1⁄5 of the original flour left.
How much flour did she have at first?

 

Answer: g

 

📖 REMINDER: The fraction left at the end is a fraction of the *original* amount. Work with the remainder after the first step carefully.

 

 

WA1,NY,2024,Fractions

13. Daniel and Eva had 90 stickers altogether at first. Daniel gave away 2⁄3 of his stickers.
Eva gave away 4⁄5 of her stickers. In the end, Eva had 2 more stickers than Daniel.
How many stickers did Daniel have in the end?

 

Answer: stickers

 

 

📖 REMINDER: The relationship “in the end” involves the fractions they kept, not the fractions they gave away. Express what they kept as simple fractions of their original amounts.

 

 

WA1,NY,2024,Fractions


 

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