Question 1
Adam thinks of a number. He multiplies it by 9 and subtracts 41. The answer is 49. What number did Adam think of?
Solution:
Given: Adam multiplies a number by 9 and subtracts 41 to get 49.
Let’s represent the number Adam thought of as (x).
So, the equation is: (9x -41 = 49).
Adding 41 to both sides: (9x = 49 + 41), (9x = 90).
Now, to find (x), we divide both sides by 9: (x = 10).
Hence, Adam thought of the number 10.
Question 2
Simplify the following fraction.
38/323
Solution:
To simplify the fraction 38/323, we need to find the greatest common factor (GCF) of the numerator and the denominator.
The factors of 38 are 1, 2, 19, and 38.
The factors of 323 are 1, 17, 19, and 323.
The greatest common factor of 38 and 323 is 19.
To simplify the fraction, we divide both the numerator and the denominator by the greatest common factor (19).
38 ÷ 19 = 2
323 ÷ 19 = 17
Therefore, the simplified fraction is 2/17.
38/323 = 2/17
Question 3
A shop sells cupcakes for £5.25 each. If you buy more than 8 cupcakes, the shop reduces the price to £5 for the additional cupcakes. What will be the cost of 10 cupcakes?
Solution:
The cost of the first 8 cupcakes is £5.25 each.
Cost of 8 cupcakes = 8 × £5.25 = £42
The cost of the additional 2 cupcakes is £5 each.
Cost of 2 cupcakes = 2 × £5 = £10
Total cost of 10 cupcakes = Cost of 8 cupcakes + Cost of 2 cupcakes
Total cost of 10 cupcakes = £42 + £10 = £52
Therefore, the cost of 10 cupcakes is £52.
Cost of 10 cupcakes = £52
Question 4
Calculate the fraction of the following shape that are shaded.
Solution:
To calculate the fraction of the shape that is shaded, we need to count the number of shaded parts and the total number of parts in the shape.
The shape has 36 parts in total, and 14 of them are shaded.
The fraction of the shape that is shaded is 14/36.
To simplify the fraction, we find the greatest common factor (GCF) of 14 and 36, which is 2.
Dividing both the numerator and the denominator by 2, we get:
14 ÷ 2 = 7
36 ÷ 2 = 18
Therefore, Fraction of the shape that is shaded = 7/18
Question 5
I am facing North East. I then turn 135° anticlockwise. What direction am I facing now?
Solution:
When you are facing North East, you are facing 45° clockwise from the North direction.
Turning 135° anticlockwise from the North East direction means you are turning 135° from the 45° direction.
45° + 135° = 180°
Therefore, you are now facing West.
You are now facing West.
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