A rectangular flag is divided into two equal halves by a vertical line. The left half is divided into 6 equal vertical strips and 4 of these strips are shaded. The right half is divided into 8 equal vertical strips and 2 of these strips are shaded. What is the ratio of the unshaded area to the shaded area of the whole flag? Give your answer in the form a : b, where a and b are whole numbers in simplest form.
Need a hint?
Work out the shaded fraction of the whole flag for each half first, using that each half is 1/2 of the flag, then add them.
Worked answer
- Each half is 1/2 of the flag.
- Shaded part of the left half is 4/6 of that half, so 1/2 × 4/6 = 4/12 = 1/3 of the flag.
- Shaded part of the right half is 2/8 of that half, so 1/2 × 2/8 = 2/16 = 1/8 of the flag.
- Total shaded = 1/3 + 1/8 = 8/24 + 3/24 = 11/24 of the flag.
- Unshaded = 24/24 − 11/24 = 13/24 of the flag.
- Unshaded : shaded = 13 : 11.
The mistake this question tests
Stopped at one part in ratio
Adding 4/6 and 2/8 directly gives 11/12, but each fraction only applies to its own half, so each must be halved before adding.
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