Here are the solutions to the problems on your worksheet. I have used the "easy percentage method" for each one, which means using simple mental math tricks like doubling or dividing by 10.
1. 50% of what number is 71?
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Logic: 50% is exactly half. To find the whole number, you just need to double the part you have.
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Calculation: $71 \times 2 = 142$
2. 20% of what number is 21?
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Logic: 20% is one-fifth ($1/5$). To get back to 100%, you multiply by 5. An easy way to do this is to first multiply by 10 (to get to 200%) and then divide by 2.
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Calculation: $21 \times 10 = 210$. Then, $210 / 2 = 105$.
3. 10% of what number is 67?
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Logic: To find 10% of a number, you move the decimal point one spot to the left. To go backward (from 10% to 100%), you move the decimal point one spot to the right (which is the same as multiplying by 10).
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Calculation: $67 \times 10 = 670$
4. 25% of what number is 32?
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Logic: 25% is one-quarter ($1/4$). To find the whole, you multiply by 4. An easy trick is to just double the number twice.
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Calculation: Double 32 is 64. Double 64 is 128.
5. 1% of what number is 57?
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Logic: 1% is one out of 100. To get back to 100%, you simply multiply by 100. This adds two zeros to the end of the number.
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Calculation: $57 \times 100 = 5,700$
6. 5% of what number is 8?
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Logic: 5% is half of 10%. First, find what 10% would be by multiplying by 10. Since 5% is half of that, you take that result and double it to get to 100%.
* *Alternative Logic:* 5% is $1/20$. Multiply by 20.
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Calculation: $8 \times 10 = 80$ (this is 10%). $80 \times 10 = 800$? No, wait.
Let's stick to the simplest path: 5% is $1/20$. So, $8 \times 20$.
$8 \times 2 = 16$, add a zero $\rightarrow 160$.
7. 10% of what number is 7?
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Logic: Just like problem #3, multiply by 10 to go from 10% to 100%.
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Calculation: $7 \times 10 = 70$
8. 20% of what number is 6?
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Logic: 20% is $1/5$. Multiply by 5 to get the whole.
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Calculation: $6 \times 5 = 30$
9. 25% of what number is 3?
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Logic: 25% is $1/4$. Multiply by 4 to get the whole.
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Calculation: $3 \times 4 = 12$
10. 50% of what number is 15?
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Logic: 50% is half. Double the number to get the whole.
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Calculation: $15 \times 2 = 30$
Final Answer:
1. 142
2. 105
3. 670
4. 128
5. 5,700
6. 160
7. 70
8. 30
9. 12
10. 30
Parent Tip: Review the logic above to help your child master the concept of percentages worksheet year 8.
