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primary 6 | Maths
| Fractions
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Date Posted: 3 years ago
Views: 538
From the information we can figure out that :
Ratio of A to B = 1 : 2
Ratio of B to C = 4 : 7
Ratio of shaded to B = 3 : 8
Since the area of B is unchanged we should make their units the same for all ratios.
So we need to change them. We can change them all to 8 since the units for B are all factors of 8. So 8 is a common multiple.
Ratio of A : B = 1 : 2 = 4 : 8 (multiply by 4)
Ratio of B to C = 4 : 7 = 8 : 14 (multiply by 2)
Ratio of shaded to B = 3 : 8 (leave it as it is)
We can now combine them all.
A : B : C : shaded = 4 : 8 : 14 : 3
Since area of A is 144cm², 4 units = 144cm²
1 unit = 144cm² ÷ 4 = 36cm²
Unshaded area of figure
= Unshaded of A + unshaded of C
= A - shaded + C - shaded
= 4 units - 3 units + 14 units - 3 units
= 12 units
= 12 x 36cm²
= 432cm²
Ratio of A to B = 1 : 2
Ratio of B to C = 4 : 7
Ratio of shaded to B = 3 : 8
Since the area of B is unchanged we should make their units the same for all ratios.
So we need to change them. We can change them all to 8 since the units for B are all factors of 8. So 8 is a common multiple.
Ratio of A : B = 1 : 2 = 4 : 8 (multiply by 4)
Ratio of B to C = 4 : 7 = 8 : 14 (multiply by 2)
Ratio of shaded to B = 3 : 8 (leave it as it is)
We can now combine them all.
A : B : C : shaded = 4 : 8 : 14 : 3
Since area of A is 144cm², 4 units = 144cm²
1 unit = 144cm² ÷ 4 = 36cm²
Unshaded area of figure
= Unshaded of A + unshaded of C
= A - shaded + C - shaded
= 4 units - 3 units + 14 units - 3 units
= 12 units
= 12 x 36cm²
= 432cm²
See 1 Answer
done
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clear
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If it’s not clear enough :
Step (1) work backwards:
Since it is given that A= 144cm^2,
And B is twice of A ,
B= 2 x 144 = 288 cm^2
Since B is 4/7 of C,
C = 7/4 x 288
= 504cm^2
By observation, one part of the unshaded area is in C, in which it is equivalent to the area of C- the shaded area. Moreover, the other part is in A, in which it is equivalent to the area of A - the shaded area. A good tip is to regard the A and C as two separate entities.
It is given that the shaded area is 3/8 of B so just calculate accordingly to find the total unshaded area.
Step (1) work backwards:
Since it is given that A= 144cm^2,
And B is twice of A ,
B= 2 x 144 = 288 cm^2
Since B is 4/7 of C,
C = 7/4 x 288
= 504cm^2
By observation, one part of the unshaded area is in C, in which it is equivalent to the area of C- the shaded area. Moreover, the other part is in A, in which it is equivalent to the area of A - the shaded area. A good tip is to regard the A and C as two separate entities.
It is given that the shaded area is 3/8 of B so just calculate accordingly to find the total unshaded area.
Date Posted:
3 years ago
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