Fractions
- Adding: 2/3 + 3/4. Use the common denominator 12: 8/12 + 9/12 = 17/12 = 1 5/12.
- Dividing: 3/5 ÷ 9/10. Multiply by the reciprocal: 3/5 × 10/9 = 30/45 = 2/3.
- Always reduce your answer to the lowest terms and check whether the choices use mixed numbers or improper fractions.
Percentages
- Percent of a number: 15% of 240 = 0.15 × 240 = 36.
- Finding the whole: 20% of a number is 30. The number is 30 ÷ 0.20 = 150.
- Discount: 25% off a ₱800 item means you pay 75% of ₱800 = ₱600.
- Percent change: from 40 to 50 is an increase of 10, and 10 ÷ 40 = 25%. Always divide the change by the original value.
Ratio and proportion
To share a quantity in a ratio, add the parts and divide. Share 120 in the ratio 3 : 5. There are 3 + 5 = 8 parts, and each part is 120 ÷ 8 = 15. The shares are 3 × 15 = 45 and 5 × 15 = 75.
Average
The average is the sum divided by how many numbers there are. The average of 12, 15, 18 and 21 is 66 ÷ 4 = 16.5.
Word problems
- Work: A can finish a job in 6 days and B in 12 days. In one day they finish 1/6 + 1/12 = 3/12 = 1/4 of the job together, so they take 4 days.
- Age: A father is 4 times as old as his son, and their ages add up to 45. Let the son be x. Then x + 4x = 45, so x = 9 and the father is 36.
- Tip: write down what the unknown is, build one equation, solve it and put your answer back into the problem to check.
Next step
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